In vitro assays of BCG products

WORLD HEALTH ORGANIZATION ORGANISATION MONDIALE DE LA SANTE 1

WHO /TB/TECHNICAL GUIDE/77 . 9* ENGLISH ONLY

IN VITRO ASSAYS OF BCG PRODUCTS CONTENTS Introduc tion

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..... 2 2

PART A Physical tests • • . . . • • Semi -dry (moist ) weight Dry weight Re sidual moisture Homogeneity Opacity . . Vacuum Vi ability tests Cu lturable particles Heat stability Oxygen uptake • . Ge rmination rate

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2 2 3 3 3

3 3 4 5

5 5 5 6 7 9 10

PART

B

Culturab le particles: laboratory pr oc edur es Mater ials . . Design Randomization Sequence and recording of labora tor y pr ocedures Punching • • • . . M athematical aspects of error Sampling error . • . . • The Poisson distribution Experimental error and the norma l distribution Statistical tests . . . . . • . . Sta tistical analysis of colony counts Analysis by ca l culating machine • Ana l ysis of variance for each dilution l evel Es t imation of average number of colonies Adding counts for different dilu tion l evel s . Difference s between dil ution leve l s . . . . . Estima t ion of number of culturable par ticles Di fference s between dilution series Anal ysis and pr i ntout by computer APPENDI X I . APPENDIX II. APPEND I X III .

11 11 11 11

12 12 12 13 15 15

16 16 18 18

Recording sheets • . . Punch codes . . • • • Notat i ons f o r dilution levels

20

32 38

APPENDIX APPENDI X APPENDIX APPENDIX

IV. V. VI. VII.

Examination r eport . . . . . . Examination r eports prepared by compu t er Derivation of computational pr ocedures The distribution of log difference

39 40 42 45

1 This supersedes WHO/TB/ Technical Gui de/67.6. Prepared by the Tuberculosis and the Health St atis tical Methodology units of the World Health Organiz a tion, Gen eva; and the WHO Collabor ating Cen tre for Wor ld- wide r e ference for BCG seed lots and for co-o rdination of control of BCG products, Copenhagen, a ft er consulting c entres i n Moscow, Prague, Budapest, Bucharest and Madras participating in the WHO assis t ed qua lity control of BCG products . The issue of this document does not constitute Ce document ne constitue pas une publication. formal publication. It s hould not be reviewed, II ne dolt faire !'objet d'aucun compte rendu ou abstracted or quoted without the agreement of resume ni d'aucune citation sans l'autorisation de the World Health Organization. Authors alone !'Organisation Mondlale de Ia Sante. Les opinions are responsible for views expressed in signed exprimees dans les articles signes n'engagent articles. que leurs auteurs.

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WHO/TB/TECHNICAL GUIDE/77.9 page 2 INTRODUCTION Laboratory Ln vitro methods routinely used for testing of BCG suspensions in the c ou~ SP of pr oduction, as well as tests used in the quality control of the final product, are presented in the following. For tests of the seed-lot. reference is made to "Req u irem~ nts for Dried BCG Vaccine"; 1 tests for virulence and inununogenicit:y in animal experiment s c1re described in the literature;2-6 tests of BCG induced tuberculin sensitivity and skin l csionr in man are described in a separate document. 7 Routine safety tests in guinea pigs, as well as tests for absence of contaminating micro-organisms, are also specified in "RequiLemen ts for Dried BCG Vaccine". 8 For a general discussion of the efficacy of BCG vaccination in man, see ten Dam et al. 9 The methods described below are currently being used in the ~·JHO-spons o re: d international quality control of BCG vaccine.lO Part A below describes shortly the various in vitro methods currently used, with references to the literature. Part B describes in much greater detail the determination of estimates of culturable particles, with special emphasis on hitherto unpublished statist<cal designs and procedures. PART A Physical tests Semi-dry (moist) weight This measurement is traditionally made for each harvest after removal of excess liquid by filtration and gentle pressure, or by centrifugation. Traditionally, the concentration of the vaccine is calibrated by diluting the suspension to a volume proportional to the semidry weight. Dry weight At the production stage, the dry weight may be measured by desiccating a sample of the semi-dry harvest or bulk until constant weight is reached. For the final product, the dry weight may be estimated by filtration of the liquid or reconstituted vaccine through a bacteria-tight filter and desiccation until constant wei~ht The method is imprecise, requires a large sample in terms of number of ampoules, and is rarely used in routine control. Residual moisture Whereas residual moisture is of great importance for the keeping qualities of the freezedried vaccine, its determination is not very accurate. The determination of heat stabilitv is a more reliable and direct measure of the quality of the freeze-drying. 1 2

.

WHO Technical Report Series, 329:

25-51 (1966).

74.:

Dubos, R. J. & Pierce, C. H. 699 (1956). 3 4 5

American review of tuberculosis and pulmonary diseases , 137 (1960)

Willis, H. S. et al. Jespersen, A.

American journal of the medical sciences, 240:

The potency of BCG determined on animals, Copenhagen ( 1971 ) 435 (1976)

Ladefoged, A. et al. Bulletin of the World Health Organization, 53: Fok, J. S. et al. The journal of infectious diseases, 133:

6

137-143 (1976).

7

WHO/TB/Techn.Guide/2 Rev.4.65 (A revised version is under preparation). See also WHO Technical Report Series, 530, 40-57 (1973) ten Dam, H. et al. Bulletin of the World Health Organization. 54: 255 (1976)

8 9

lO WHO/TB/Techn. Guide/77.8.

WHO/TB/TECHNICAL GUIDE/77. 9 page 3 Homogeneity In examining a smear of vaccine under the microscope ( e.g. a smear stained for the purpose of identifying the ac1.d-fastness of the material) clumping may be recorded on the following scale of ranking: 0: 1: 2: 3: ~:

single bacilli only predominantly single bacilli; predominantly single bacilli; single bacilli and small clumps

some small clumps some small and medium sized clumps

single bacilli and small and medium sized clumps single bacilli, and small and medium sized and big clumps medium sized and big clumps e.g. cord

5: 6:

Non-quantitative attributes will still have to be described with words . shaped, net-like, non- acid-fast, eight , ball-shaped, long bacilli. Opacity

Measurement of opacity may be used as a routine check on the final product when the calibration of the vaccine con centration has been based on the semi-dry or dry weight of the bulk material. Measurements of opacity, rather than determination of the semi-dry weight, may be used in the production process for calibrating the vaccine concentration. However , the traditional expression of potency in terms of milligrammes of semi-dry weight per millilitre is then of dubious meaning . In the comparison of several products, the determination of both dry weight and opacity may permit a critical evaluation to be made of the validity of so-called "estLmates of semi-dry ~.;eight '' based on opacity alone. The opacity depends not only on the number and size of the bacilli but presumably also on the degree of clumping . Nevertheless, the method is relatively simple and precise and is of value also in the control laboratory as a test of consistency from batch to batch of a particular product. The opacity is measur ed in an instrument that for a given light source, voltage, etc. is ca librated in terms of International Units of Opacity. Vacuum The vacuum of the i ndividua l container is tested routinely. Containers without proper vacuum may contain severely damaged vaccine, as in such containers the keeping qualities of the vaccine are very poor . Viability tests Culturable particles Determination of the numbe r of culturable particles by means of colony counts on solid medium is generally considered the backbone of quality control of BCG. The principle of the test has been applied for a long time: counting the number of colonies on a suitable solid medium inoculated with an appropriate vaccine dilution, and from the count calculating the number of culturable particles in the undiluted vaccine . However, the efficiency of the various methods used was often ill-defined or known to be low: in many laboratories the experimental error of the investigations was not even determined.

WRO/TB/TECHNICAL GUIDE/77.9 page 4 To arrive at an efficient method, a technique had to be developed that is amenable tO statistical analysis and in this way can be shown, each time, to have given a meaningful result. Such a method was introduced some 10 years ago 1 after several collaborative studies (World Health Organization, unpubli.shed data 1958; World Health Organization, 19642) and eve~ since efforts have been made Lo increase its efficiency and facilitate its application, Thus, tedious operations such as the preparation of codes for the containers to be randomized, the decodjng, the statistical analysis, and even the actual printing of the reports, were computerized, the results from the original data sheets being transferred directly to punch cards. The method may be quoted as one in which electronic data processing has proved to 6ive important improvements in accuracy and tremendous savings in processing time and costs. More recently, after several collaborative experiments (WHO Collaborating Laboratories· unpublished data , 1973) had indicated that the experimental error in diluting the vaccine before inoculation was often much greater than previously suspected, examination of dilution series in duplicate from each pool of vaccine was introduced for at least a significant fraction of all examinations. Most recently, standardized recording sheets have been introduced, designed for maximum convenience in the laboratory . At the same time, the punch codes have been changed so as to facilitate punching directly from these sheets. Currently used designs for these procedures are given in detail in Part B of this document. Heat stability Determining the stability of a freeze-dried vaccine at 37°C (a temperature readily available in any laboratory) serves two purposes . It is a direct test of the stability of the product at what may often be the ambient temperature in tropical countries, and may thus serve as a guide for formulating instructions on field storage . It may also be taken as a "degradation test" in chat relative stabilities at this temperature are assumed to reflect the stabilities at lower temperatures for longer periods; whether this is actually so for dried BCG is insufficiently documented but is not contradicted by what little evidence is available. Usually a length of exposure is selected that according to previous experience is likely to give a reduction of 50% in viability (corresponding to a significant yet not major reduction in BCG- induced allergy in man). An exposure for one month is often suitable, in particu l ar if results for several products are to be compared. An attempt may also be made at obtaining t he degradation curve for a product, by exposing ampoules to37°C for varying periods (e . g. one week, two weeks, etc . , up to, e . g. seven weeks ). The ampoules are moved from the refrigerator to an incubator at different times, but finally are all examined at one time. Statistical analysis may be carried out by computing the regression of the logarithm of culturable particles on duration of exposure to 37°C. 1f the regression curve does not deviate significantly from a straight line (i.e. if the curvature LS insignificant) the degradation may be expressed in terms of ''half- life", i.e. the time taken for a 50% reduction in viability . Some manufacturers have the definite impression that the reduction is more rapid initially, in which case a significant curvature would be expected, and computation of a 50% point not justified.

The derivation of an accurate regression function presumes a considerable number of data. A single experiment with eight points (0-7 weeks), for instance, 1-1ould yield only five degrees of freedom for error after accounting for mean, slope, and curvature. With a duplicate experiment there might be more hope of a meaningful analysis of variance, as the corresponding l WHO/TB/Techn.Guide/67.6. 2 World Health Organization, Bulletin of the World Health Organization, 31:

183 (1964).

WRO/TB/TECHNICAL GUIDE/77. 9 page 5 number of degrees of freedom would now be 12 . would of course be essential. Randomization of all aspects ( see page 7)

For routine q uality control, however, batch-to-batch variation in stability is followed by examination in parallel, for every batch, of a non-exposed (4°C) sample and a sample exposed to 37°C for a pe r iod of some 2- 8 weeks, but fixed for each product, Oxygen uptake Measurement of the oxygen uptake by a sample of BCG is a test of metabolism, and t hus the results are likely to be in proportion to the amount of live organisms, but independent o f dead organisms. The test is usua l ly carried out wit h a sample of 30-120 mg (semi-dry weight) over one hour or more, in a Warburg apparatus . The test is fast and simple, but in the routine control of freeze - dr ied vaccine for i n tradermal use the large amount (many ampoules) of BCG required is a problem. In the production phase ({~here large samples are readily available) the test has an important place because of its ease and speed . Thus the basic suspension obtained after homogenization may be immediately tested before further processing. Another use is the calibration of the bactericidal effect of homogenization, independently of clumping, by testing samples before and after (and at various stages of) homogenization. 1 In basic comparisons of different products the test serves as an indirect check on the ratio of live and dead organisms, in conjunction with estimates of bacterial mass . Germination rate 2 This method, described by p rskov & Engbaek, is difficult and would norma l ly not be left to a techn ician. It i s on ly half-quantitative (though it may be analysed by methods of nonparametric statistics). The optimum reading time appears to be 24 hours for a liquid vaccine, and 48 hours for a dried vaccine. Apart from relative speed, the main advantage of the method is that it is the only one that gives a direct estimate of the proportion of living and dead organisms .

PART B

Culturable particles :

laboratory procedures

Emphasis is given here to statistical aspects, while other technical details are mostly le f t to the choice of the individual laboratory. The statistical routines suggested are based upon experience gained in laboratory studies coordinated by WHO . The use of the statistical routines and standard forms suggested has been found to encourage the routine undertaking of analysis of variance and to fac i litate the comparison of data from different laboratories . Materials No standard diluent, container, or solid medium is specified here. Tools or recipes that have come to work well in one laboratory (after much trial and error) do not necessarily work i f copied elsewhere; it would scarcely be possible, for example, to prescribe a particular medium for viability counts as the standard to be used in all laboratories. Control methods on vaccine lots with reference to the meaning Bunch- Christensen, K. of different viability tests. In : International Symposium on BCG Vaccine, Frankfurt (Main) 1970. Basel, Ka r ger, 1971, vol. 17, 199-204. 2

1

prskov, J. & Engbaek, H. C.

Acta pathologica et microbiologica scandinavica, 30:

395

(1952) .

I·THOjTB/TECHNICAL GUIDE/77 . 9 page 6 The basic suspension should normally be vaccine ready for use in the standard strength recommended by the manufacturer. Freeze-dried products should be reconstituted as recommended by the manufacturer. The sample to be tested may be an ampoule of liquid or reconstituted vaccine or a pool of two or more ampoules (to even out possible ampoule-toampoule differences), or it may be a sample of t he stock suspension not yet in ampoules (either in original concentration or diluted down to normal vaccine strength) . Further dilution is in terms of volume, i.e. in terms of millilitre of vaccine and not in terms of milligrame semi-dry weight (though a note is made of the nominal strength, as specified by the manufacturer, in terms of mg per ml for the liquid or reconstituted vaccine). Commonly used media for diluting the reconstituted vaccine are : liquid Sauton me d1um ( as used for BCG cultures ) diluted 1:4 (i.e., 1 + 3); isotonic saline with or without buffer. A wetting agent (e.g . Tween 80) or bovine albumin is sometimes added to the diluent. 1 Reference is made to descriptions in the literature of the L~wenstein-Jensen medium, the 3 Ogawa medium2 and the Oleic-acid-albumin-agar medium with blood, which are the most commonly used solid media. A variety of containers are used for the solid medium, such as cotton stoppered glass tubes sealed with paraffin, Legroux flasks, Petri dishes, screw-capped tubes, or flat screw-capped bottles. Major considerations in selecting such a container are the control of ventilation, the avoidance of contamination, and the size of t he surface area . Only solid or semi-solid media should be used, as these allow t he number of colonies to be counted . Liquid media, which yield only "growth" or "no growth" for each tube, require the use of a large n umber of tubes for reasonably accur ate estimates4 and are therefore not recommended for routine use. Design If the viabil i ty i s roughly known in advance, a dilution level can be chosen that is likely to yield a number of colonies optimal for counting . 5 In anticipation of variations in viability, three dilution levels are seeded at the same time, in dilution steps of 1:2:4 . The advantage of twofold dilutions (as compared with fourfold or tenfold) is that the validity of the levels will overlap (with a tenfold series, one level may give confluence and the next one too few colonies). Furthermore, two or even all three dilution levels will contribute signi ficantly to the estimate for as long as they show neither confluent nor zero growth. Examples of possible steps in the dilution process are shown in Appendix I: Sheet 3. In selecting the dilution levels, it is necessary first to define an optimal number of colonies per container , i . e., a number not too small yet small enough to assure discrete, easily counted colonies . One aims at obtaining this number at the intermediate dilution level, so that for moderate variations (within the range 1:4) one of the three l evels will always yield an adequate number of colonies . In the statistical analysis full weight is 1

.

1

Jensen, K. A. Obayashi, Y.

Bulletin of the International Union against Tuberculosis, 24 : Dried BCG Vaccine, World Health Organization , Geneva (1955) .

78- 112

(1954). 2 3

Dubos, R. J . & Middlebrook, G. American review of tuberculosis and pulmonary disease, 56: 334-345 (1947). 4 For statistical handling of such data, see Fisher, R. A. & Yates, F. (1957) Statistical tables for biological, agricultural and medical research, 5th ed . , Edinburgh, Table VIII2. 5 If the viability is not known at all, a preliminary viability test must be carried out. The design might be in tenfo ld steps ( 1 : 10:100) or in more than t hree twofold steps, e.g . , 1: 2:4 :8:16:32:64:1 28 . In the latter case a single container of solid medium per dilution level may suffice, since only a preliminary estimate is aimed at.

WHO/TB/TECHNICAL GUIDE/77.9 page 7 given to colonies for dilution levels that yield , on the average, the optimum number or less, while reduced weight is given to a dilution level that yields up to twice the optimum, and little or no weight to levels yielding more than twice the optimum. Colonies are nevertheleRs counted up to 2.5 times the optimum, beyond which counts are reported as "exceeding limit". As will be seen later, the statistical inte r pretation of the latter class is quite different from that of "missing data", e.g., in case of contaminated containers. For the most concentrated suspension and for the middle suspension the same number of con tainers is inocu la t ed, e . g. five for each. For the most dilute suspension twice the number of containers is inoculated , in this case 10. Or the respective number of containers may be three, three, and six . It may be noted that in this design- the amount of vac~ine inoculated at the most concentrated level is the same as the sum of the amounts inoculated at the more dilute levels (1 = 0.5 + 2 x 0.25). Similarly, the amounts inoculated at the two more dilute levels are equal (0.5: 2 x 0.25) . Thus the number of colonies counted will be at least 10 times (or six times respectively) the optimum count for a single container, on the condition that the count for the most concentrated level is not below the optimum and for the most d i lute leve l not above the optimum. Thus the precision wi ll be fairly uniform over this r ange. From one ampoule , or pool of ampoules, may be prepared either one dilution series, to be inoculated in 5+5+10 containers, or two dilution series each to be inoculated in 3+3+6 contain e r s . The purlose of the latter design is to check the experimental error inherent in t he dilution process . Randomization The sta t i stica l procedures and significance tests specified in the following are based on a fiel d of mathematics developed for t he purpose of describing probabilities of games of " pure chance", i . e . games of dice and certain simple card games , Statistical deductions made on t his basis assume that the elements of the experiment have been randomized as thoroughly as an honest p layer wou ld shuffle the cards before a game. Without such randomization the stat istical deductions a r e not valid . The subject is treated in several textbooks of 2 mathema tical statistics ; for a classical, non-mathematica l discussion, see Fisher (1960). The s pecific justification for randomization of containers of solid medium is as follows In the coagulation phase, in particular, a certain part of the batch may have become degraded; or it is possible that the previous c l eaning of the glassware has not been uniform. It is even possible that an experimen ter may find it necessary to use containers of two batches, possibly of different quality. In all such cases, certain vaccines might well happen to be seeded exclusively on the damaged portion , and would come out as statistically significantly inferior to other vaccines tested at the same occasion. Furthermore, during the incubation period it might happen that the incubator d i d not offer uniform conditions throughout, and a vaccine placed solely in one particular corner might for that reason give different results. finally, randomization offers the opportunity to have blind reading of colonies; while reading of colonies is usually fairly accurate there is very much the possibility that a reader who '' knows " that one con t ainer ought to show twice as many colonies as another will be influenced by this knowledge in cases of doubts . While this might not reduce the precision of the test it could very well distort t he basis for statistical statements about error etc.

A batch o f sol id medium is not necessarily entirely uniform.

The same design cannot immediately be used for checking the ampoule-to-ampoule variation (by pr eparing one dilution series from each of two different ampoules) because the estimate of experimen tal error in this case would confound ampoule-to-ampoule variation with dilu t ion error . A proper check on ampoule- to-ampoule variation requires four dilution series as a basic design, two for each ampoule. 2 Fisher, R. A. , The Design of Experiments, 7th ed., Edinburgh, Oliver and Boyd, 19o0, pp. 11-26 .

1

WHO/TB/TECHNICAL GUIDE/77. 9 page 8 Usually several vaccine suspensions are investigated at a single session, and mutual comparison of the results for such suspensions might seem particularly valid because of the uniform circumstances of an investigation made within a single day . It is nevertheless desirable that these suspensions are examined in random order. For instance, if a reference preparation is included in every investigation, and if there is any tendency for a slight systematic variation in t he course of the day, always to examine the reference (for instance) first, might in the course of a series of investigations give a false impression, taken to be significant because it was consistent. Containers of solid medium might be physically shuffled, for instance by placing them on a table and letting several persons make a large number of aimless shoves of one or several conrainers at a time. Such a procedure is likely to be either cumbersome or incomplete or both. In practice, the randomization is done by matching the containers, one by one, with a ~et of random numbers, these having been obtained in turn from a set of subjects more amenable to shuffling. Thus the consecutive numbers originally allocated to the containers may be copied on pieces of cardboard, these pieces then placed in an urn in which they may be mixed up blindly by hand, or in a suitable drum that may be rotated many times . After the mixing, the pieces are dra\m one by one and their numbers noted do\m in the order in which they were drawn. A more indirect method is the use of published tables of random numbers, prepared and tested by mathematicians. Random numbers are now often obtained from a computer; usually such numbers are "pseudo-random", such as the non-recurring digits of 11fT" . Random numbers are of two kinds, ''without replacement '' (in which case a particular number occurs either only once, or a prearranged number of times), and "with replacement" (in which case the chance for any number to occur at a particular place is independent of whether it has occurred before). A permutation is "without replacement" if it is obtained from the urn by not replacing the pieces in the urn as t hey are drawn; another example of a random permutation "without replacement" is a shuffled pack of cards . Random numbers from an urn are "with replacement" if each piece drawn is replaced in the urn, before shuffling and drawing of the next piece; the successive showings of a roulette of 10 positions or the non-recurring digits of 11' are also "with replacement". While more details will be given below, the principles of randomization of containers and suspensions are as follows: l. The containers are placed in any order, for instance as they are taken from the cold storage. 2. With reference to the random permutation to be used (for an example, see the computergenerated permutations in Appendix I, Sheet 4b, second line) the containers are labelled consecutively from the lowest to the highest number of the permutation, e . g. 1, 2, 3, -,-, 119, 120; or 751, 752 ... 965, 966. In the case illustrated in sheet 4a, where the last block is not used, the corresponding labels are discarded before the actual labelling. 3. The suspensions to be investigated are also randomized (see page 10, second paragraph).

4. For the suspension that was selected at random to be the first, the containers with the label numbers shown in the top most block of the permutation (Sheet 4) are searched out, using the top most line of the block for the most concentrated suspension, etc . The containers are thus rearranged in the order of the random permutation, to be ready for inoculation. 5. After inoculation the containers are rearranged in the consecutive order of the labels (1,2,3 etc.) before they are placed in the incubator. 6. The reading of colonies is made in this consecutive order, and recor ded in this order (ref. Appendix I, Sheet 5). One might visualize randomization of several other aspects (for instance, glassware used for the dilution process) and wherever there is a suspicion of uncontrollable variation randomization is always strongly indicated .

WHOjTBjTECHNICAL GUIDE/77.9 page 9 Sequence and recording of laboratory procedures The standard laboratory fonns shown in Appendix I have been designed to cover widely differing needs, from analysis by computer of investigations including more than one product to routine production control of lots of one or more batches. For analysis without computer a separate sheet 'will be needed for decoding. Most of the infonnation may be entered (and is more easily entered) at the stage of planning the investigation rather than after starting the laboratory work. This is true for all of Sheet 1, all of Sheet 2 except the last column and the last two lines, the upper part of Sheet 3, and all of Sheet 4 except for the columns for time of inoculation and the last line. Sheet 5 is filled i n only at the time of reading. The first line of all sheets, in addition to "Investigating labo ratory" and "Date of investigation'' has room for a serial "No . of investigation within day". The concept of an "investigation" is defined by the use of a particular random pennutation as shown in Sheet 4 . Thus, if it is decided to use two such permutations on one day (e.g. if two teams are working simultaneously and independently, or if the number of vaccine suspensions on a single day is very large), the two investigations may be distinguished by using the numbers land 2 respectively for "No. of investigation withi-n day". Note that two such investigations are mutually no more comparable than are investigations from different days. Thus, if a reference vaccine is used as a control, the re ference should be included in both investigations. Sheet 1 lists the products included in an investigation. The second line (Subject) can be used to indicate the nature or purpose of the investigation (e .g. examination of bulk material, re-examination of expired vaccine , etc . ). Any two-digit number \'oli ll be printed out by the computer. If all particulars indicated in the headings of columns are identical for two or more suspensions (e.g . d i fferent filling lots of one ~roduct) only one line is filled in. But if, for instance, the same batch comprises a lot of 20-dose ampoules and a lot of 50-dose ampoules, one line is filled in for each. Similarly, if samples of one and the same product have been received on different dates, each shipment is given a separate line. The lines are numbered (any one-digit numbers) in the left-most column . Sheet 2 gives detailed information about each vaccine suspension. The information i n Sheet 1 is not repeated, but for each suspension the number of the product as given in the first column of Sheet 1 is entered for reference in the first column of Sheet 2. The second column (and also the last column but one) is filled in in conjunction w1th Sheet 4 . Ln the third co lumn, "Lot number and description" any words or numbers may be entered, up to a maximum of 26 characters including spaces (compare the corresponding punch code, Appendix I I, card 4, cols 17-24). "Date prep. bulk" is the day the final bulk (basic suspension) is prepared. If the date is unknown, leave blank. The next three columns ("Text, first date, second date" ) indicate the dates of preparation and freeze-drying. Codes for the column "text" are shown in Sheet 2. The first date is the date of start of freeze-drying or, for liquid vaccine , the date of dispensing the vaccine in ampoules and closing these. The second date is that of expiry, except in the special case of a suspension that is a pool of several lots, when the two dates may be the first and the last date of freeze-drying (there is then no space for expiry). ''Total no. amp.jvials 1' indicates if the suspension is from a single container only or a pool of more than one container (enter l, 2, 3 etc . as the case may be) . For "Exp . 37°C 1' (i . e., exposure to 37°C in days) enter a two-digit number, or 00 for no such exposure; no explicit record is made of other storage, which is taken to be at 2-6°G. The total volume of reconstitution fluid ("Total vol. reconst. fluid") is given, if indicated, with one digit after the decimal place; note that in the case of a pool of, e.g., three ampoules each of 2 . 5 ml (25 doses) the number to be entered is 7.5 ml . The last column is filled in, in hours and minutes, in the course of the laboratory work. So are the three entries at the bottom of the sheet.

WHO/TB/TECHNICAl. GUIDE/77. 9 page 10 Sheet 3 is filled in partly with reference to Sheets 2 and 4 and partly in the cours e of the laboratory work. In Sheet 4, consecutive numbers (usually 3-digit numbers) are entered in the lef t -mos t column, to give serial numbers to the vaccine suspensions. It may be practical not t o us e the same serial numbers in consecutive weeks or even months, but to continue serial numbering up to close to 999, before returning to 001 as the first number for the next investigation. Thus if in the previous investigation the last suspension number was 725, an investigation of nine suspensions may be given the numbers 726-734, allocated consecutively to blocks 1-9 in Sheet 4. Thereafter, the suspensions are randomized, for instance by copying these numbers on (in this case 9) pieces of cardboard, by mixing these in an opaque container, and by drawing them blindly, one after the other. The random order drawn is now entered in Sheet 2, line by line, both in the second column and the last column but one ( the latter f o r the purpose of easy reference at the time of filling in the last column of this sheet). Each of the suspensions is now considered in turn, and a suitable degree of dilution decided upon according to all available knowledge about the product and suspension. For instance, a suspension from ampoules exposed to 37°C may be diluted only half as much as the non-exposed sample examined at the same time, if a SO% reduction in viability is expected. Similarly, liquid vaccine (or bulk) from a particular batch might be diluted twice as much as a freeze-dri.ed lot wou ld be, from the same batch. Each suspension number is now entered in the upper part of Sheet 3, in a line corresponding to the desir ed degree of dilution (one line may contain several suspension numbers). For each suspension, the degrees of dilution are then copied from Sheet 3 on to Sheet 4 (note that the upper part of Sheet 3 is used only for reference during the laboratory work of diluting the suspension and is not punched). The reconstitution, dilution, and inoculation of the suspensions are carried out in the order of Sheet 4, not of Sheet 2, since the latter normally gives the vaccines in some systematic order, while in the former they are in random order. At the time of reconstitution , the last column of Sheet 2 is filled in (hours and minutes); also, the kind of reconstitution fluid and its date of preparation if known are entered, together with the initial of the laboratory worker. Similarly, the lower part of Sheet 3 is filled in at the time of making the dilution series (normally, dilution series 1 and 2 of one s uspension are made directly one after another). If there is only one dilution series, the columns for "series 2 11 are left blank. Similarly for Sheet 4, the two columns for "inoculation time11 and the entries at the bottom are made by the worker making the inoculation. Sheet 5 is filled in at the time of reading. The upper part is largely self-explanatory. Note that the limit for count (rather than the optimum count) is of importance to the read e r. It is also the limit of count that is punched. In designing the investigation, however, it should be kept in mind that the computer will take the optimum count as 40% of the limit. Sheet 5 has space for 200 counts, and it may be necessary to use two sheets for an investigation . The hundred position is entered in front of the appr opriate two digit number (to be found in the left half of the sheet) and the counts entered in serial order from there. Note that after the inoculation the containers were arranged in the order of the labels, and will still be in that order, ready for counting and recording, when removed from the incubator. Punching The punch code (Appendix II) is based on the standard 80 columns punch card and is designed for easy punching directly from the laboratory sheets, with little coding or copying . The uniform punch in col. 1 is meant to distinguish the cards from cards punched for entirely different purposes. Col. 2 indicates the type of card. Cols 3-10 are specific for a particular investigation, and decks of cards comprising several investigations may be separated by sorting on these columns. Cols 14-16 are reserved for the code number of the suspension, and may also be used for sorting .

WHOjTB/TECHNICAL GUIDE/77.9 page 11 Card 1 instructs the computer concerning a particular investigation. Card 1 is punched from Sheet 4. Card 2, the counting card, is punched from Sheet 5, and each card can take 10 containers, so usually some 10-25 continuations will be needed. Card 3 is punched from Sheet l , one card per product (line) . Card 4 is punched from Sheet 2, one card for each suspension (line) . Card 5 is punched from Sheet 3 (lower part) and Card 6 from Sheet 4, one of each for each suspension. Information conunon to all suspensions is gang-punched in the relevant card s, (Compare also card 6, cols 19-21, with Appendix III.) Mathematical aspects of error Sampling error It is well known that estimates based on small samples (e.g., opinion polls) are subject to substantial errors , not on ly avoidable biases (such ·as limiting an opinion poll to telephone owners), but also an unavoidable random element, called "sampling error", inheren t in the drawing of a limited sample. Mathematical studies of this phenomenon were fi rst made in connexion with games of pure chance. It was shown that for instance the distribution of the probabilities of finding one or another number of hearts i n a hand of 13 cards, out of a well-shuffled pack of 52 cards, would follow a mathematical function called the binomial distribution . On the average, of course, the number of hearts per hands is 13/4, or 3.25, but the binomial dis tribution predicts how often, in the long run, there will be two hearts, how often three hearts, etc. This mathematical model la ter found a very important use in connexion with the Mendelian theory of inheritance, where, for instance , the hypothesis may be that the probability of obtaining a recessive homozygote from heterozygote parents is 0.25. Just as for the hand from a shuffled pack of cards, litters of offspring will have a var ying proportion of recessive homozygotes, and the distribution of this proportion is predicted by the same binomial function. Whether an empirical distribution agrees reasonably with the prediction is examined with significance tests that are based on an a priori assumption of perfect shuffling or randomization; and this latter assumption is thus inherent in any statement such as : ''the probability of obtaining such and such a fit, or a worse one, is 0.05". The Poisson distribution The binomial function describes the distribution of the fraction, p, of members with a particular attribute over a large number of samples of a given size. It thus also describes the distribution of the fraction (1 - p), of members without this attribute. If, however, pis very small compared with (l- p), so that (l - p) equals l for practical purposes, a simpler version of the binomial distribution may be used, known as the Poisson distribution. Note that it is the relative frequency, not the absolute number, that permits the use of the Poisson distribution . Thus, if a batch (final bulk) of 10 11 organisms is distributed on 1000 ampoules, each ampoule will contain 108 organisms, which is a small fraction, i.e. 0.1%, of the batch (the l'universe'' ) . Thus the dist ri bution of number of organisms over ampoules may Similarly, if the content of an ampoule is diluted so be assumed to be Poisson distributed. that a fraction of lo-6 of the total content of the ampoule may be inocula te d in a container with solid medium, this is again a small fraction, and the numbers of colonies over a series of containers may be expected to be Poisson distributed, although the number of colonies actually expected per container, namely 100, is not a small number. Experimental error and the normal distribution The normal , or Gaussian, distribution is in principle a continuous function, used for measurements rather than for counts (frequencies). For instance, repeated measurement of the coordinates of a star on the firmament will give varying results, and if the results of a large number of such measurements are plotted they are seen to fit the be l l shaped symmetrical mathematical function called the normal distribution . A normal distribution obtained through observations has two parameters, the mean (arithmetic average) and the variance (arithmetic mean of the squared deviations from the true mean). In any but the most simple statistical manipulations the variance is used, rather than the standard error (the square root of the variance), because variances can be added and standard errors cannot. Thus if two sources of

WHO/TB/TECHNICAL GUIDE/77.9 page 12 error contribute variances of 4 and 9 respectively, the total variance may be expected to be 13; whereas the total standard error is not 2 + 3 = 5, but~= 3.6. The normal distribution occurs very widely in practice. It may be expected, for instance, that the volume delivered by repeated use of a pipette varies in this way, with a mean that may well deviate from the nominal capacity and a variance depending both on the skill of the user and on the limited precision inherent in the construction of the pipette. It may happen that: it is not possible to calculate the arithmetic mean because certain values are too large to be exactly counted or measured (e . g., confluent growth of colonies } In this case the median may be used instead of the arithmetic mean,l the median being the "50% value", or the result that is higher than 50% of the rest of the observations and lower than the other 50%. The median is not quite as precise as the mean but still useful. For simplicity, measurements are often expressed in discontinuous grouping; for instance, tuberculin reactions --~· 0e measured to the nearest whole mill i metre or in 2- or even 5millimetre classes. It turns out that if the number of classes is not too small, the approximation to the normal curve is still good. With 15 or even better 25 classes it is excellent. It turns out that both the binomial and the Poisson distributions are also approximations to the normal distribution. The approximation is good where the average number observed in the Poisson distribution (or in the smaller fraction of the binomia l distribution) is not very small. Where this average is below 5, formulae derived from the normal distribution are conventionally not used. For average counts of 15 or 25 or more the approximation is very good to exce ll ent. In treating the Poisson distribution as a normal distribution particularly simple formulae apply, because, as it turns out, this distribution has an expecte d variance equal to its mean. It is possible to devise a simple formula for calculating the chance that the variance may exceed the mean beyond a given point . If such a calculation (statistical test) shows a low probability, the conclusion is drawn that the vari ance observed is likely to reflect elements of experimental error that are in addition to the predictable sampling error. Statistical tests The most common concepts in the testing of normal distributions are: the normal deviate; ~ the t-value; the variance ratio; the ")(:. (chi-square); and degrees of freedom. These concepts are mutually much more closely related than is sometimes apparent from the average textbook of statistics. 2 The normal deviate, the t-value and the ?Clare all limiting cases (in the mathematical sense) of the variance ratio, though this '1 may be concealed by the traditional use of sums (or means) of squared deviations for ~ and for the variance ratio, but square roots of such means of squares for the normal deviate and the t-value. The latter two may be positive or negative, whereas t he first two are always positive, STATISTICAL ANALYSIS OF COLONY COUNTS Analysis by calculating machine While a computer programme has been created for this analysis, the user will do well in calculating himself sets of data so as to come to understand what the computer is doing. There l A tee h n~que . . ex1sts for computing the mean in this case, but it is cumbersome and is not used here (see Hald, A. Statistical theory with engineering applications, New York, Wiley, 1952, pp. 144-15 1). 2 Statistical Analysis in Biology, For a clear summary of this problem, see Mather, K. 1949 3rd ed. Methuen & Co., London, chapter 4, pp. 46-49.

WHOjTBjTECHNlCAL GUIDE/77.9 page 13 may also be readers that do not have access to computer processing. In the following, therefore, the use of a simple calculating machine is assumed; though the machine should not be so simple as to be without a special memory for accumulating products (e . g., squares). 1 The procedures are described below in terms that would be used when processing with a simple calculating machine . Appendix IV shows a form developed for such computations, with space in the left-most part for description of the vaccine. The colony counts are "decoded'' by comparing Appendix I, sheets 4 and 5. Thus for each dilution level, for each suspension, the count corresponding to each container code in Sheet 4 is found in Sheet 5, and the count entered in the appropriate box (Appendix IV, under "Container/Medium") in the order corresponding to Sheet 4. The degree of dilution (d) for each dilution level is entered, but if it is given in Sheet 4 in terms of concentration (such as, e.g., 2 x l0- 4 ) it should be converted as indicated in Appendix III (in this case to 5000 , or 5 x 103, corresponding to the punch-code notation 05 3). Analysis of variance for each dilution level As mentioned above, the counts vary between one container and another because of the sampling error, as predicted by the Poisson distribution, and may further vary because of experimental errors. The existence of the latter is thus revealed if the observed variation is bigger than the predicted sampling error. In principle, the computations are made as follows: each set of counts corresponding to a particular dilution of a particular vaccine is inspected separately, and the number of "readable" containers (n) is noted in the column "No. of containers" on the form (Appendix IV). Containers with counts exceeding the limit (or confluent) are taken as "readable", while contaminated or broken containers are taken as "unreadable". Thus the following record of 10 containers: 98, ct . , 80, 93, ct., 100+, 100+, 99, 100+, 85, would yield an "n" of eight readable containers (even though three of the readable ones are not "countable" ). If all readable containers for a particular dilution are countable (no r ecord of "exceeding limit" or confluent growth) the sum of colonies (Sx) in all readable containers is computed and entered in the column "Total colony count". If at least one container is readable but not countable no Sx is computed and the analysis of variance is abandoned for that dilution. Next, the counts are squared (each count multiplied by itself), the squares added together, and the result (Sx2 ) entered under "Sum of squares". A check to reveal computational errors is then carried out; for each count, the figure one higher (x + 1) is squared and these squares are added together; the result is entered as S(x + 1) 2 • From the other columns, the sum sx 2 + 2Sx + n is computed and the result mus t equal S(x + 1) 2 ; if it does, a check mark (v) is made against the value computed for S(x + 1) 2 ; if it does not, the computations are erroneous and must be redone from the beginning. A

so-called "X.2 may no\" be computed as follows: 2 X2 = nSx. _ S;< Sx 2

where n, Sx and sx2 have the same meanings as above. The~ is then compared with the figure (n - 1) and if the two are of the same order of magnitude, this is a sign that the inoculation and growth have been uniform from container to container with sampling error as the only significant source of variation. The figure (n - 1) is called "degrees of freedom". The critical values of ~ 2 corresponding to different degrees of freedom and probability levels have been tabulated in standard tables.2 The number of degrees of freedom, here called (n - 1), is sometimes designated in such tables simply as ''n". There also exist today much more sophisticated calculating machines, and even desk-top as well as pocket computers with storable programme . Among many such publications may be mentioned: Fisher, R. A. & Yates, F. (1957) Statistical tables for biological, agricultural and medical research, 5th ed ., London . 2

1

WHO/TB/TECHNICAL GUIDE/77.9 page 14 The following are values of~ for various degrees of freedom corresponding to a five per cent. probability level; i . e., if the)(2 value as calculated exceeds the critical value, the chances are one in 20 or less that the observed variations are due to random causes (sampling error) only. n (n -

2 1) 1

3 2 6.0

4

5

6

7

8

9

10 9

ll

12 11

3

4 9.5

5 11.1

6 12 . 6

7 14.1

8 15.5

10 18.3

'X...2 (P=O.OS)

3.8

7 .8

16.9

19.7

In practice, i£)(2 as calculated exceeds the critical value for five per cent., we would say tbat it is significant at the five per cent . level and reject the hypothesis that the variations arise from sampling error alone; the experiment may then need to be repeated and possible causes of the variation should be investigated. A

numerical example of the computations discussed above is given in the following:

Let us assume that 10 containers have been inoculated from one dilution of one vaccine, resulting in the following counts : 24, 33, 27, 18, 26, 37, ct., 24, 22, 30. Out of the 10 containers, nine are both readable and countable, while one is contaminated. Thus, n = 9 and (n - l) = 8. The total number of colonies, Sx = 241 . The sum of squares, Sx 1s (24 + 33 + 27 + --- + 30 ) which equals 6723, while the sum of squares of (x + 1), or S(x + 1) 2 , is (25 2 + 34 2 + 28 2 + --- + 312 ), which equals 7214; sx2 + 2Sx + n = 6723 + 2 · 241 + 9 = 7214, so the computations seem to be correct . We may now compute =. - -

2 .

2

2

2

2

nsx 2 Sx

Sx = _9_•_6_7..,.2_3 - 241 241

251.07 - 241

10.07.

For eight degrees of freedom, the critical value of)l2 at the five per cent. probability level is 15.5. Hence, as the computed value, 10.07, is clearly less than the critical value, we can conclude that the variation is not significant, i . e., that it could easily arise from sampling error alone. When several vaccines have been examined, or several experiments carried out, it is permissible to add up the)(2 values obtained from the individual experiments. The corresponding degrees of freedom would then also have to be added . An analysis carried out in this way will avoid the vagaries of the individual experiment. If, for instance, the following )(2 values were obtained in the course of a vaccine comparison : )(2 10 .07 12.47 3.14 7.05 0.10 n 9

5 5 lO

(n - l) 8 4 4 9

3

2

it might be concluded that the second value, 12.47, for four degrees of ~reedom was significant at the five per cent. level. However, when all the values are added up, a1(2 value of 32.83 for 27 degrees of freedom is found, which is not significant, since the critical value at the five per cent. level for 27 degrees of freedom is 40.1. The combined~ value affords a more reliable basis for judgement, and in any case in which more than one ;;(2 value is available, it is incorrect to single out the largest value for evidence against the hypothesis that the counts have a variance corresponding to the Poisson 2 in 20 distribution. The very concept of a five per cent . probability implies that one)l will be "wrongly" significant. 2

WHOjTBjTECHNICAL GUIDE/77.9 page 15 Estimation of average number of colonies Where all readable containers are countable , and Sx has already been found, the "average Sx = colony count" may be computed as the mean x , which for convenience may be rounded off to n

the nearest whole number or i f exactly midway between two whole numbers, to the nearest even whole number. If one or more (but no more than half) of the readable containers are uncount-

able the median is found:

the counts are ranked, and the middle number is noted (or

if

the

number of counts is even the mean of the middle two). follows:

Thus for the example on P• 13, the two

contaminated containers are excluded and the counts for those remaining are arranged as 80 85

93

98

99

100+

100+

100+

and the median is seen to be 98.5 (average of 98 and 99); rounded off to the nearest even integer, in this case 98.

for simplicity, the figure may be I f exactly half of the readable

containers are countable, the number formally adopted as the limit is taken as the median. Thus four containers with the counts: 85 , 98, 100+, 100+ would be accepted as having a median of 100. The mean or median is entered in the column 11

Average colony count". + 11 •

If more than

half the readable containers are uncountable (count exceeding limit, or confluent growth) no computations are made but the average is recorded as tations described below are abandoned. Adding counts for different dilution levels 1 2 and d , the latter being the most extreme; thus i f d is 20 000 , d will be 40 000 and d 1 2 3 3 80 000 . Similarly, average counts for the respective degrees of dilution are called~' i , 2 and x3. After the average counts~' x 2 , and i have been computed, the expressions (2i ), 3 3 2~), and (~ + x2 + 2X3) are derived and entered as "cumulative values", as follows: Average count Cumulative value In the following, the degrees of dilution for a vaccine will be referred to as d , d , 11

If more than half the containers

are unreadable (e.g. contaminated) an average may still be computed, but the further compu-

(i2

+

~ + x2 + 2x3 x2

+ 2~ 2x 3

or, a numerical example: Average count Cumulative value 140 71

69 31 20

40

On the form (Appendix IV) the values for ~ and ~ + 2~ on the third line.

for each vaccine' the values for i2 and x2 + 2~ on the second line;

x2 +

2~ are entered in the first line

and those for ~ and

The doubling of ~ corresponds to the feature that there are in

principle twice as many containers for the third dilution as for either the first or the second.

WHO/TB/TECHNICAL GUID E/77.9 page 16 Differences between dilution levels One would expect to be approximately twice but not precisely, because of sampling error.. A statistical significance test may be made in each case , comparing (i - 2i ) with 2 3 i ts expected standard deviation. The standard error as derived f rom Poi sson' s distribution is:

x2

i3'

This term may be used only i f x2 and i are means, not medians, and only if the variations 3 from container to container f or the single dilution are no greater than would be expected owing to pure chance. Thus , i f (and only if) the ?<,2 values already computed for each of the two dilutions are not significant (or if the ~2 values for the study as a whole are distributed as expected) , one may use the term:

\/ n;+n; approximately 19 out of 20 cases ) .

~

as a signti'icance test ( the resul. t should be within the interval minus two to plus two, in Another possible comparison is that between the mean ~' for the least diluted suspension , and either 2i or (i + 2i ) . The latter comparison, i . e., (~ - (x + 2i )) , is more 2 2 2 3 3 sensitive . The difference may be tested as follows :

and also this term should be within minus two to plus two, in about 19 out of 20 cases. In the form Appendix IV there is room for the results of these computations, in the fourth line for each suspension , under the corresponding formulae. Estimation of number of culturable particles In the followin8, the symbol c.l is used for the optimum count, which, as mentioned before,

is taken by the computer to be 40'% of the "limit for count" recorded on sheet 5 ( Appendix I) and punched in card 2, cols 11- 13 (Appendix II). In the case where one or another of the cumulative values ( either 2i or i 2 + 2i3 or 3 ~ + i + 2i ) is exactly equal to twice the optimum count (2c.l) the counts for the more con2 3 centrated suspensions (if any ) are disregarded, and the estimate of culturable particles is based entirely on the 2c.l colonies.

WHO/TB/TECHNICAL GUIDE/77.9 page 17 equals w (that is, ~ = 2w) it means that the fraction v of a millilitre of a 3 suspension diluted d times, inoculated per container, has on the average yielded w colonies. 3 Thus the undiluted vaccine would have yielded wd colonies, and had it been inoculated with 3 one millilitre of the undiluted vaccine, rather than v, it would have yielded wd /v which then 3 is the estimate of culturable particles in 1 ml of vaccine. If x If

times plus 2v of a suspension diluted d times, equal to 2v diluted d times since d = ~ • 2 2 2 3 3 So one millili tre of undiluted vaccine would have yielded 2wd~2v or wd~v colonies. It may d similarly be shown that if ~ + i + ~ = 2w then the estimate of cu1 turable particles is 2 wd /v. 1

i2+

~ equals 2w this corresponds to an inoculated volume v of a suspension diluted

In the case where 2w is lower than a particular cumulative value, and higher than the next (which will be the usual ' case) it would not seem reasonable to disregard completely the counts slightly higher than the optimum. Instead, a reduced weight is given to such counts, the weight depending not upon the count itself but on the lower counts. Thus if the cumulative value of the lower counts almost, but not quite, reaches 2w, very little weight is given, whereas if the cumulative value of the lower counts is only slightly higher than w, almost full weight is given to the next higher count. For the formulae given below, the rationale and derivation are given in Appendix VI. But it is important to understand that they are just formulae of interpolation between the simple, limiting values of wd/v. The first step in the calculation is the identification of the lowest "cumulative" value exceeding twice the optimum (2w). There are four possibilities (not counting the limiting cases already discussed), and the computation of the number of culturable particles proceeds in

a different way in each case, as follows:

for:

the number of culturable particles per ml is

d2 v d3 v

(A)

.~

2w + ~- (i2 + 2~) (A)

• x2

2w + x2- 2i3

2i3

~ 2w

d3 • v ~

-

WHO/TB/TECHNICAL GUIDE/77.9 page 18 The follow:ing is a numerical example of the computations: mum" count is defined as 40 colonies, i.e., 2w = 80.

let us assume that the "opti-

The following averages are found for a

particular dilution series of a particular vaccine :

~ = 69 x2 = 31 x3 = 20 Since 140 > 80

~+ x2

-

+ 2x3

= 140 71 40

x2 +

~ = ~=

> 71, we must use the formula ~

w.

-----=----~----=-~

2w + ~ - (i + 2i ) 2 3

-

40 ! 69 80 + 69 - 71

v

If, for instance, d vaccine is 2

g.~oo

· 35.4

2

= 20 =

000 and v = 0.1 ml, the number of culturable particles per ml of 7 080 000. +~'either these2 (The reader may try to verify that the result then always

In the limiting cases there is no discontinuity;

thus, i f 2w = i

cond or third fo:::mula may be used. reduces to wd/v). Differences between dilution series

Two dilution series from the same suspension may be expected to differ both because of sampling error (limited number of colonies) and because of dilution error and other experimental errors. With the design described above , of two dilution series each with three plus three plus six containers, the number of colonies on which each of the two estimates is based will be the equivalent of 6w, as is seen particularly easily in the limiting case of

x 3

=

w.

Where the formulae of interpolation (previous section) are used the number of Only

colonies may be slightly higher but this can be disregarded for the following argument. where (~ + i

+ 2X ) is smaller than 2w the argument below would be invalid. 2 3 The errors in estimates derived from wd/v (or f rom any of the formulae of interpolation )

depend on experimental errors in preparing the dilution d , in addition to the sampling error 1 2 proper and the errors expressed in the ":.Xv and t-values described above. The -?r} and t-values may be significant because of errors in, e.g., the volume v or the uniformity of the solid medium. If these tests are not significant, only the errors in preparing d will be added 1 to the predictable sampling error of, e.g., 6w colonies. If then the difference between two that d1 has been prepared in a sufficiently precise way.

dilution series is significantly larger than predicted from the sampling error, there is doubt

WHO/TB/TECHNICAL GUIDE/77.9 page 19

Since the number of colonies counted in the estimate is fairly constant (equal to or slightly larger than 6w) whereas d and v may take any values , the sampling error of the estimate i s best s tandardized by taking either its coefficient of variation (the standard error as a per cent . of the estimate) or- as done in the following - by considering the logari thm of t he estimate. The difference between the logarithms of two estimates (dilution series in duplicate) has an expected mean of zero and a dispersion that can be calculated from 6w, on the null hypothesis that 6w colonies have been counted and that there are no experimental errors in addition to the sampling error . (See Appendix VII). The standard error of this log difference, and its confidence limits, can be tabulated for . various values of w, as follows: Standard error 0. 080 0.056 0.040 0. 028 0 . 020 Probabilit y : 5~~

2(1- P) 0. 5% . 224 . 158 .111 . 079 . 056

t•l

~ . 186 .131 . 092 . 065 . 046

1% .206 .145 . 102 . 072 . 051

0.2% . 247 . 174 . 123 .087 . 061

0 .. 1% . 263 .185 . 131 . 092 . 065 Thus, the 95 per

10

20 40 80 160

.157 .110 .078 . 055 . 039

here it should be noted that the limits are doubl e s i ded (two-tailed). w cent. confidence interval for w ::: 40 is from + 0 . 078 to - 0.078. Ana1ysis and printout by computer

Wherever possi ble, r esults are pr oces sed and printed out by comput er , using punched cards as shown in Appendix II as input . Two examples of such printouts are shown in Appendix V .

Appendix Va shows an examination of a bulk suspension, that is, a liquid suspension before freeze-drying . Many of the statements are self- explanatory, and t he printout of the counts and estimates largel y follow Appendix IV. Note, however, that the column with heading "T" gives the significance tests for differences between dilution levels , as described on p.l6;the vertical order is logical, i . e. the lower value describes x2 - 2x3, and the upper The column "average count'' refers to values of ~,x , and i • The ast~ 2 3 . risk in the same column indicates , by the line in which it is given, the computational for-~

- (x2 +

2i3 ) .

mula used out of the four formulae given on p. 17. In this case the asterisk in the second line refers to the second formula (containing d /v). In Appendix Yb an example is shown of 2 an examination of a freeze- dried lot elsewhere than in the production laboratory. In this case two dilution series have been examined and the log difference bet ween estimates (log 3 374 000 - log 2 988 000) is shown in the last line .

::.>

., ll>

'1::1 '1::1 ['l

H H

z t:J X

~~ 0""'--... Nt:xl

~

t-3

@ (")

WHO QUALITY CONTROL OF BOG PRODUCTS 13' Ul

H

sa ~ c::: G">

Investigation laboratory: Subject: _ _ --:.1..:;.0_ _ __ _

No. of investigation within day :

I

Date of investigation:

--=~-'-....4.::::.,_ Is-- 1- ?6

rt

ro ro

n

H ll>

H

~ -.J ..... \.0

t:J

Product no.

Production laboratory

Strain

Dried or liquid

AmAoule vial

BCG

/bulk f3 u.lk fimJ:)ou.le

(mg) Volume per amp/ (ml) per vial/ml amp/vial 30 OmQ I~- mq q

Sent from

Sent on date -

Received a t

Received on date

I

SS 1 Cootnhoqen Dani.sA /33/ LiCJtA.id ~

2 3 'i

•

2 rnL

-

-

-

SSI Cooenhatwt banish /33/

D,...ied.

-

-

SSI CotJenh~IL Danish /33/ Dri~oL SSI Cooenhaqtn 'f:rench /1?3P.Z Drieo/

fimooule

3 ?j-m, S:Omt~ <I

!lmpou.le

"

S'rnL 5mL

-

-

-

WHO QUALITY CONTROL OF BCG PRODUCTS Investigation laboratory: _ _ _ ___.lf _ _ _ _ _ _ No. of investigation within dey: _.L_ Date of invest.: Jj' -1- ?6

Prod. no.

Code no. susp.

Lot number and description

Date prep. bulk /Y-1 · 76 IY-1- ?' 3-l.t-7~-

k Q)

E-1

1st date

2nd date

Total no. amp./ ¥i:IW.&

Ex:poa. 37' 0 0

(d:ays)

Total vol. reconst. fluid

Code Time for no . reconstitution susp. lf> 3 h~

I I

63 (, 6

3 07 s~ ries I 307sert"eg '30S"- Ill

-

..2

.z .2 .2

i-l.t- 'l~·

9-12· 'lj"

'i lj

0 0 () ()

~mt

930- 93b

z .2 3

67

~7

6¥

30.$'30~--

2~

3-/2 ·'Jj• 3-12-?J'

9-/2-'h- /()·/2· 'h. /o-1../· z,j- 11-I.J -7~· /J-14- ?~· 1.2. 1,2. 7J'

lrnL

t.'l 09 ~i

9/i- tj..13

69 62 71 ~ 5-

38

2 2

0 ()•

/OrnL /OmL /j-m/ Jj-rn I j-m{

9 Yt _ 9Yi. q 3~ - q 1;'/ 9P - _tj~S> q.t3- 930

3 3

306'-'18 301 • Ir:; - 2 l3 - 3 R 30 2 -Ill- J.B • 319 Work i n4 1

3-1.2· zj· ,z 11-II-7J' .2,

17-11-7.1' .20- II· 7.J'

3 3 I

0 3c• 0

71 ~5-

3

It· II-.?.>. 2 /1{-

17-11- ?~- 2tJ ·II- ?.J'

lf

70

Reference

3·73 .2

19-3- ?3 .20- 3· 73

70

q ¥6 _ 9.s-o

Reconst. fluid: Date of prep.:

5a.uttM ( />" 3) 6 -/- 76

Text (code) : dr ied (date) dried (date) to (date) expiry (date) dried (date) expiry (date) liquid (date) liquid (date) expiry (date)

:1

Reconstitut. by: -~B~::::;._-

:2

:3 :4 :5 :6

.

\0

WHO/TB/TECHNICAL GUIDE/77.9 page 22 Appendix I, sheet 3a

WHO QUALITY CONTROL OF BCG PRODUCTS

Invest. lab.:_..;..'{_ _ No. of invest. within day: _ 1_ Date of invest. : Code nos. of suspensions: --li:~ 3 r~6:.__

/S"-1-U

_ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __

4 4--:lb~'S~JE:-l~Q~ Vaccine ~ 10- 2 ~ 10-4 __, :rl,"''2MxHl~O- 4 ~-:tl:t/"44-:xlf-:lli*OI--...:. -;...._'* 1"' ~i ~xr-,r,la,._O -4 1 14 3o,.,~ltnl J•')~

1+'19--..,'1¥xto- s· 1+'39

1/te

xto ·~-

'hzx/o->' ;. ..

1 /~vx

].+(,

ty

/o·~;. .. 30

Code nos . of suspensions: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Code nos. of suspensions: Vaccine ~ 10- 2 ~ 10-4 4 o,•um,hnl , .. ,, u•H

~~ . ~ ~~~ , r=· . ~~.~;...._

f

'I r. ? 'i! ' ,

?o 71

_____________________

1/2 x 10-4 1.{~'1

1/4 x 10- 4 1.~'

Code nos. of suspensions: - - - - - - - - - - - - - - -- - -- - - - --

Code nos. of suspensions: Vaccine ~ 2 X

-~----------------------------X

'j'

o,,,-,.);,.,,

10- 2 ~ 4

10- 4 --7 2

J+H1

.to~'la

X 10'f+'l

4

10- 4 .2+'-

Code no. susp. (;3

Time for dilution Series 1 Series 2

Code no. susp.

Time for dilution Series 1 Series 2

'If (,!) ~6

9 23_ 930 9 3r> - 9 3l. 93 " - 9 '1! 9Y3 _ 9Y' 9'~"- 9 ~-~9 ~-~-- lo()2

C.9 ?o

;o()z- Jo"' !o"' - /tJ ~~/0 1s·_

71

to.z'

&7 4-i

Diluted by:

1<13

Diluent: ___ s _ a_"~t~ o~ ~~ ( ~/ ~ +~ 3 ~) ~----

Date of prep. : -----a: t ...:. -.:.. 1_ - "?x e ______

1

WHO/TB/TECHNICAL GUIDE/77.9 page 23 Aeeendix ! 1

sheet 4a

WHO QUALITY CONTROL OF BCG PRODUCTS INVEST. LAB.: 4CG CODE: 1401

NO. OF INVEST. WITHIN DAY: CODE NUMBERS: 751

DATE OF INVEST.: - ~~-·-~ TO 950

-------------------------------------------------------------------------------CODES OF CODES OF CONTAINERS BLOCK DILUTION INOCULATION -------------------------------------------------------------------------------~lb )(

SET:

1

SUSPENSIONS

NO.

TIME

10-~ . 812 10~~

I.S

1

~

~

I(

• ,.-t

835 r98 753

859 769 940 918 932 759 882 752 811 770 844 875 792 902 942 779 809 893 894 842 884 855 832 838 905 919 799 920 930 848 764 826 947 901 790 784

822 926 802 " 922 857 870 755 841 865 788 895 888 771 803 823 781 860 761 765 879 853 856 852 929 938 837 830 805 941 861 866 774 903 910 885 937

820 819 785 899 789 786 829 869 881 836 757 840 868 763 886 897 839 806 817 911 787 846 814 845 914 772 751 797 906 948 933 816 900 795 944 908

939 833 912 890 858 934 782 863 896 878 775 913 873 931 892 923 915 808 849 767 907 756 864 924 862 921 851 946 760 776 793 762 891 824 945 821

~~~

-

') 2(1

ro-lf< 883 ~'+

2

>.i:

ll

10-'+

.>.+.• ~.-:

807 to•,. t887 831 lo~'+ 758 10-~ IO

'"'

- ~~' IOofo

3

4 .1

• )l

827

~~-

~Ct ~50 843

bb

~

lC

4

~a. Yw,.

-"

IO_, 935 ,•• ~ 818 10

" lt

-<en 783

;o

oe

-

lo"'·

bf

5

..%:

~ b~

.k

,.,-'t 916 II

949 10~'+ {791 9Qq lo-'+

IO

1:1.

10

llf'

6

• If-

Y.

l(

-

828 904 10 - '+ t773 834 IO_ ., 10....

IO

rr

14 -

to~

IO_...

b~

7

-"i ~

"t

IO_ ...

766 943

Io •

lo 'll

11

••• ~78 25 ,. ... 871 10 -9 850 {928 ro-lt 796 1o·" 794

8

"" " -t. l(

),

IO

"11

..

Jo i.'l-

1-1

9

~ _.!,.,-

)(

to•.. 876 10 _..1768

10 l~- 10 .....

14-

1.

780

10

VOLUME INOCULATED PER CONTAINER: 0. I MEDIUM: L..ow~-t'"6-iN INOCULA TED BY: BATCH NO.:

ML

eONTA INER: Tu8£ DATE OF PREP.: 'g-1· ~

~.,..,:

k.&..

WHO/TB/TECHNICAL GUIDE/77.9 page 24 Appendix 1 1 sheet 5a WHO QUALITY CONTROL OF BCG PRODUCTS Invest. lab.: Limit for count: CoWlted by: br

Lf / 00

No . of m vest . within day: _L Date of invest.: Optimum count:

/5--1- ?6

'TO

Interval between inoculation and reading:

'3'f dr

days

Date of reading:

/f - ,? - ?6

RP

= broken 31 32 33 34 35 36 37 38 39 40 41 42 43

ct

= contaminated 791 13 92 If'! 93 94

= dry b> 21

+ = exceeding limit

01 02 03 04 05 06 07 08 09 10 ll

?61 27 62 / 0 63 64

13 }/

~51

/0

281 82

?~t

22 '10 23 24 2b 25 26 rt 27 3/ 28 Lift. 29 .20 ?30 .20 ~

52 12 53 'il 54 55 ,3.s56 Zlj 57 58 ~60

9 '12 t,

;e ~

9 3~

83 84 5''1 85 86 II 87 /'I 88 .20 89

65 !If 66 H 67 17 68 / j ' 69 2?> 7 70 .2 'i 7 7l 'I&

95 19 96 /0 97 21 98 /3 99 12 &' 00 ~01

!)? ~rz

59 37 60

-

.? 90 /j~

-

12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

72 ct 73 9 74 /0 75 hi 76 I?

02 II 03 I'} 04 05 12 06 23 07 Jj08 2!>09 If? ~10

31 /'I 32 2&, 33 20 34 Jtl 35 .2 y 36 39 37 37 38 9 39 'fj-

?61 J') 62 '19 63 19 64 lb 65 '-19 66 II 67 68 lfj69 /'I ~70

91 .5'? 92 .20 93 2? 94 ? 95 96 /6

44 45 46 47 48 49 50 751 II 52 II 53

s-.z

77 78 1/ 79 /~ ?80 0781 /3

97 1'3 98 99 13

j-(;,

~40

23

zo 33

qoo

"''

&'ll

82 / 0 83 II 84 13 85 86 33 ')

2

12 '19 13 14 ~~-

f41 I? 42 g 43 /3 44 19 45 16 46 br 47 48 17 49 13 ~50 2~r

~ 71

72 73 S7' 74 75 /5 76 I? 77 78 .29 79 / j ' ~80

54 55 ~ 56 30 57 15' 58 60 59 19 760 '30

87 !/0 88 H 89 5-1{

15 16 9 17 I 'I 18 2$' 19 2.2 ?20 '19

790 /'I

-

~oTHO/TB/TECHNICAL GUlDE/77. 9 page 25 Appendix 1, sheet Sa cont.

WHO QUALITY CONTROL OF BCG PRODUCTS Invest. lab.: Limit for count: Counted by : br

lf JOo

No. of invest. within day: _j_ Date of invest. : Optimum count:

lj--1-?G

'10

Interval between inoculation and reading: --"-3-'-lf__ deys

Date of reading: limit

lf-.t-?k

RP

= broken q 31 I~

ct

= contaminated 61 62 63 64 65 66 67 68 69 70 71 72

dr

= dry 21 22 23 24 25 26 27 28 29 30 31

+

= exceeding 51 52 53 54 55 56 57 58 ?9 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76

901 2.0 02 .20 03 5·o 04 05 06 07 08 2~-

6"7 /.II{

32 Lf7 33 ~ 34 .t 'I 35 j'{, 36 37 II 38 ~.~~ 39 j'3 9 40 ?

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11

81 82 83 84 85 86 87 88

1.1/

12

09 /6 ~10 1'1 911

89 90 91 92 93 94 95 96 97 98 99 00

17 I~ ~

9 41 :30 42 '? 43 2'( 44 I? 45 ;e 46 lb 47 1.12, 48 2/ 49 I? 9 50 /{, 51 52 53 54 55 56 57 58 59 60

12 l3

32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

14 itO 15 j'() 16 If? 17 Ill 18 7 19 .;~-

73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88

9 20 I'!

'J 21 29 22 ~ 23 I !J24 I 'I 25 /0 26 I'J 27 28 b 29 /{, '130 .z~

12 13 14 15 16 17 18 19 20

77 78 79 80

89 90

::r (1) (1) ~

(J>

VrHO

QUALITY CONTROL OF BCG PRODUCTS No. of investigation within day: _ Date of investigation: __8::.--..:...'-~...~.z .... p.__

.... cT

0

H t:j

c::

~ -..J -..J _.J.._

Investigation laboratory:

----..>r...-----

'C

Subject: _____.~-------

Product Production laboratory no.

Strain

Dried or H: ~!:d

Ampoule I~

~

BCG (mg) Volume per amp/ (ml) per amp/vial vial/ml

Sent from

Sent on date J/-1.2?~-

Received at

Received on date 1.2-1.:7~-

I

Pasi~:ur D ... ~<o,. Ih·~ nch II IJ 3 P.Z Dri.~oL

lllrnooule. II

2

Po.s lt:w r (),.~,. .- F.-Pnc-h //73P2 8CG Lob.l•k«•

1/

Sma

2 j-,L

(ocenhaae n { OJ:Jcnhaa trt If

_ 8uc.hqr_ etJt f3wcho..r~'i.t

IO.omL lOOm/ lOOm{ !/Om! <I

"

II- 1.<·7j" 1~-

/)_ -;.z- 7~· 19-1.<-?j19-12 -7:>12 · /.2·7:>

3 l.f

l1aoanere 17.2 1"1

1/

/1

Con~nhaael'l. q

/,(_ -75'

f31-4 chtJ res 1-

G-lo.xo LondM Glo..xo SI CootnhtJa.rn f1

II

/I

-

(onenAoacn ~

;g

-;~- 7:>-

f3uchaYest

s

lf,.~ncJ.

11?3 P.<-

II

If

!>rna

Conen haaen

11-1.2- ?::.-

f3 k chtv-es f

"

"

WHO QUALITY CONTROL OF ECG PRODUCTS Investigation laboratory: _ _ _ _....;5:.,_______ No. of investigation within day: _ / _ Date of invest.: _ _.801-.o<-I:...-_Zu6.:...-

Prod. no.

Code no. susp. ).OJ

Lot number and description

Date prep. bulk

.p

H 8

Q)

1st date

2nd date

Total Expos. no. 37°C amp./ Y:i:a.le (days)

Total vol. reconst. fluid

Code Time for no. reconstitution susp.

I

75-'?f.D

I

),Oif

'lS-LfOR

-

I g-

·-

·9-zJ-

-

2

0

!>-m L j - J?)!

201 20'1 20f 20.)202

923- 9.29

2

0 0 60

93? 95"6 -

9 trz /001

2 2

.zog 2os.Z0--2

1/LfS¥ /1¥5'1 //lf07

z 2

20mL .ZOrn! .ZOmi :ZOrn!

I I I

g- '3- 'Jj' /)--II- 7j/j'-11- Jj'

3 3

207

//'167

-

1-1!-76 J-IJ - 76

9 Y3- 9 Y'l 92L

2 2

0 60 0 30

c;u. 9s-~·

207 .Z09 .20 3 .20~

95"1

-

'1

.209 203 206

7Lf.29 7 LJ29 Refe r-ence. Work ina q

3 3

'I j-

-

··-

z 2 J

20m!

;oo' - /oos-

20mt. 5rnl

qn- CJ3? 9 lf? - 9 ~-I

/1{-3-73 2

/1-.3-?3 lzo-3-73

0

Reconst. fluid: SaktOJl (/;.3) Date of prep.: 2¥ - 7- Jj-

Text (code): dried (date) dried (date) to (date) expiry (date) dried (date) expiry {date) liquid (date) liquid (date) expiry (date)

:1

:2

Reconsti tut. by: -,.JJ~-o~P...;·-::r ('0 ('0

Cl>

H

:3 :4 :5 :6

n

N

0'

~ ~ H

C"l

~ ~ ~

1:::1

\C

WHO/TBjTECHNICAL GUIDE/77 . 9

page 28 Appendix I, sheet 3b

WHO QUALITY CONTROL OF BCG PRODUCTS

Invest. lab.::

_..:::s__ No.

of invest. within day: _L Date of invest .: ~02

9 - 1-76

Code nos. of suspensions:

----~,--~~---------------------------------:l!!

.zee

2 Vaccine ~ 10- ~ 10- 4 ~ 1/2 J·•99 J·-'19

10- 4

l/4 x 10- 4 .Z+b

l/8 x 10- 4 .Zt/'1

l/16 x 10- 4

.z •30

Code nos. of suspensions:

_.:Z;=..;;.O~ S:r:-2-. o ._, z ...: .""'o ? ;..9 ,__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __

Code nos. of suspensions: Vaccine

~~-----------------------------------Ll+'f .2.+6

2 CJ3

~ 10-2 ~ 10- 4 ~ l/2 x 10- 4 1/4 x 10- 4 l·d9 1~99

Code nos. of suspensions: ~2~~~~~.~ ~~ 0~t~ ~~ O ~k~------------------------------Vaccine ~ 10- 2 -7 2 x 10-4 --) 10-4 1+99 2~9J>

l/2 x 10- 4 .Z+~

'fr'(

Code nos. of suspensions:

----------------------------------------

Code no. susp.

Time for dilution Series 1 9~-:t_

Series 2

Code no. susp.

Time for dilution Series 1 ;;o1 - j;P7

Series 2

20/ 11).2

9"-7

9 n _ ;~oY /0 /() - /0 IJ" lo~" -

.2C>7

II n -II 1;. 11/7_ ;;.U 11

/0°"'- /0 1c

tot_ 2tJ9

II l.t- /117 Jj.ZL jj.H

2a3

/CI ~~- ~ Jo :.;

;o:."

u _11 33

loY ,2/)j-

lo 2"- 10 33 /O Ill- /O IIi /{) ~-J.- /() ~-?

/O 3~ _ /()Yo /() t;r;- /() ~ -.z

2 tJ&,

10 s·7_ jjOI

Diluted by:

LB

Diluent :

5,'4v.to-,_ (/ -+ 3)

Date of prep.: _ __./:;..S:;._ -..:. /..;;:-Z_-_2:;..:>::.-------

WHO/TB/TECHNICAL GUIDE/77. page 29

WHO QUALITY cn.rHRu L nF BCG PJ.\ODUCTS

Appendix I, sheet 4b I NVtST. : ~-1-76

I NVEST . CG CODe :

LAB.:

s-

Nu.

OF INVe ST. wITH I 1~ DAY : 751

I TLJ

Dl\ TE uF

1'10 1

CUD E NUMB Ei{ ~: OlllJTI DN

CGDES lJF S USPE NS IUNS 8 LOCK

-----------------------------------------DI LUTl U ll UT W N SI: R IES 1 2 (~ ~ t Rl fS

966

::- ;:. r :

l

COOtS OF CGN TA TNf.,~S

I NUC lJLAT I ON

cor>t: s

IJ F

11\uCULI\TI U N

NO.

TIME

CLNTATNEkS 764 82':1 dSO ~6:i 771t [952 769 ti 34 954 9')2 qy7 810 doO 15':)

TIME

-------- -- --- -~ ---------------------- - ----------------------

2~1

1

2x ;o·'i Cl52 8'-j6 84 a lo-'t 823 do 7 846 '!~ x. 10-Y 5 8~9 <;5b b12 9.!1 SOo

t2

/00"- 100&

/Oor.._ j(J14

20~

'Ax /o-'1 2

1Pxlo·Y ~6 X /o·Y 1

f962

7':J 9 908 854 no 831:l 88 0 < 853 ?75 86L 9l1 dt.) 765 Sd2 93_7 8~5

/O 12 _

IO I f

75 7 CJSJ 770 ':11ti 7f, (j

[ J24

s no

10

tt _

J(J-tY

l7j 'J4 6

.~

13 /0 30 - /0'3!1:

•

Jo-Y

.203

'h x lo ·Y 948 771 886 '/y x /0 -Y f933 780 934 8411 842 2JC!t>-Y

/O 2Y _ /O

3o

riJo 8 /O 3s·_ IO Yl

'-107 Yl? n2j 900 66 '3 cl32 1~2 (J

7do 785 d31.J 794 to'~~-

.ZoY

Cl5S' 7 99 S?5 7~1

4

/0 -Y

aa

oZCI

'ltxlo-'1 ~X /0-'f

ra61 879 957 898 66 7 7S2 850 3 772 79 3 895

874 ti 16 '144 8 78 912 843 964

844 H1'::1 195 797 <;51 ~ dd [CI3 7 17'J 7 76 820 78d 754 ,!'13 117::, 9 4 2 '-l49

10 1f7

2o ~-

5

1 /y it

/0 - Y

1? x 1o -r .2 X ~0, /P-'1

to o

/0 '17- lo s·3

f~03

8J4 d~o 75 3 c3 33

/O

5'~_

/loo

ens 76o 904 ~:!5o

'317

6

/D-r

92.2 812 dU2

1.z JC lo-Y ~07

[.d 35

915 !:U6 $i.J3 9:>C s4u c; L <; 1327 .;J2

//oo_//ot,

s )5

767 //

1'3-1 ;141 [94:J qz r '-IZ fl t13l 8 Ju ciJ1

0

,.-11 12

•

7

lf.z X/o- y 792 901 77f1 1r x '"-Y 939 966 d~2 777 >l o 4 1,x 10 -Y 814 132 7 5b

7b0

[913

II 1:2

- ;;IP

nd ~8-f.l ~4J

7'-Jt..J .)21: tiJ '7 >Hl dOd \'j 61 947 :! :> d 88~

I I I? - II .z ~-

2oR

1v x ;o-Y 1/~x;~·Y

lj;, X ;o·Y ~

[811 873

751 (HJ9 876 869 914 l o3 847

II:;.:,·- II 31

Y59 ~29

•) (; c flYl

80?

11"'- II

'3?

921 7d L 935

8<j4 '116

[845 763 13o4 B8l 7'1fJ 787

209

9

758 924 818 936 1/~ x lo-Y c23 784 811 840 If+' )( /o -Y

x jo·'f

II 37_ IJY3

96j 92u d 51

790 <;1.)9

r:no 8o6 '300

870 801 1:.!57 821 7o2 7~1

I j'13

-

II

!tO

VOLUME INOCULATED PER CONTAINER : 0 ./ ~EOIUM:J..ow~nsfein ~ATCH "JU.:

~L

C 1J IH AI NE R :

7 U f3 ~

Lf 35"'

DATt: UF PRfP . : 6-1- ?e:,

INOCUL ATED BY:

R. 8

WHO/TB/TECHNICAL GUIDE/77. 9

page 30 Appendix I, sheet Sb WHO QUALITY CONTROL OF BCG PRODUCTS Invest. lab.: Limit for count:

5100

No. of invest. within day : _L_ Date of invest . : Optimum count : 7'0

g-;- 76 {)-- .l- '?'-

Interval between inoculation and reading : Counted by:

2i dr

days

Date of reading :

Rs ct

br = broken

= contaminated 7 91 92 LfZ

= dry ~

+

= exceeding

limit

01 02 03 04 05 06 07 08 09 10 ll

31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

761 17 62 I'J 63 11, 64 (, !J65 t>O 66 !b 67 S7 68 /'r' 69 /If

21 22 24

/8 1.1{,

~51

?o 6~

~81

If(

s-.z

52

82 ?I 83 17 84 /(:, 85 !1-ro 86 lf3 87 3'1 88 '-10

93 17 94 26 95 ~0 96 6'1 97 '16 98 /'r' 99 75'

23 'II Jl.(

53 20 54 !>'2

25 7? 26 Z2 27 lh 28 If'( 29 ~ 30 {,0

55 lb 56 30 57 3¥ 58 I? 59 +g 60 :3 I

89

~-~~

7 70 57

800 20 ~01

J'f

'i 90 h l.f ~91

'1 71 cl:r 72 /4 73 IS 74 27 75 9 76 23 77

3?

g-31 l'i 32 30 33 IZ 34 l'i 35 /7 36 27 37 .zo 38 31 39 ..22

12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

02 69 03 21( 04 3/ 05 .e:i 06 /b

47 48 49 50 7 51 s~-

11 (,0

78

07 I!J' 08 l'l 09 '-I¥ 210 32 ~11

g 61 12 62 I;;· 63 3'1 64 / ;;65 /If 66 .ZI 67 ~3 68 22 69 ~70

30 92 3&> 93 {,lf 94 /.(, 95 / f/ 96 6g 97 I? 98 :/8

79 ..20 7 80 21

1~

HO ~

21

'10

99 /!;{ 900 '-If(

7 81 82

52 3b 53 /? 54 26 55 27 56 /fo 57 ss58 7; 59 Sl ? 60 6"1

"" /'I I?

/l.

41 /(, 42 21 43 1'1 44 9-?. 45 /3 46 15 47 /3 48 &9 49 17

12

'2

871 33 72 lb

83 2584 22 85 II. 86

13 /2 14 I? 15 !5 16 2G 17 I 'I 18 2(, 19 7;;~ ~ 20 2'-1

73 /;, 7 4 J;j' 75 ~0 76 &3 77 1'3

87 /3 88 2~

78 S2 79 .2/ 880 '3lf

89 21( 7 90 .23

~50

31

WHOjTBjTECHNICAL GUIDE/77.9 page 31 Appendix I, sheet 5b cont .

WHO QUALITY CONTROL OF BCG PRODUCTS Invest. lab. : Limit for count :

S" /oo

No. of invest . within day : _!_Date of invest. : Optimum count:

i-1-76

l.fo ~~

Interval between inoculation and reading: Counted by : ._:R..:..;S ::.___

deys

Dat e of reading :

~--.1· ?'

br

= broken 9 31 32 33 34 It, 12 J&,

ct

= contaminated 61 Jfj 62 13 63 ?0 64 If/ 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11

dr

= dry 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

+

= exceeding 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71

limit

9 Ol 6$ 02 /:[ 03 IS

~

81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00

04 &I 05 'If 06 l i 07 2 j08

/(,

35 3~ 36 29 37 ?fc, 38 3 j ' 39 940 w~ 1).

65 9 66 67 68 69 70 7l

,Zj'

s..s-

'3 17

09 /i 910 1:r ~11

941 23 42 43 44 ~-g

12 Z!? 13 I? 14 3 0 15 27 16 II( 17 t-9 18 29 19 IZ

72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90

19

zo

45 I?; 46 / j ' 47 lb 48 If! 49 32 <} 50 I!?

9 20 921 22

~'3

17 J~3

9 51 52

lf5~

I j'

12 13 14 15 16 17 18 19 20

12 73 74 75 76 77 78 79 80

23 20 24 'tl 25 26 17 'j;

53 so 54 17 55 2o 56 2 '3 57 .2S 58 .Zo 59 t.;g

27 /3 28 /:;~ 29 21f '3 30 27

? 60

'7 2'

49 50

\ffiO/TB/TECHNICAL GUIDE/77. 9

page 32 APPENDIX II, card L

PUNCH CODE FOR NHO QUALITY CONTROL OF BCG PRODUCTS

Card 1: Col. l Col . 2 Col . 3 Col. 4 CoL 5-10 CoL 11-12 Col. 13-16 Col. 17- 20 Col . 21 Col . 22- 80

Investigation- card Punch 1 Punch l Investigating laboratory (code) Number of investigation within Date of investigation Total number of suspensions in investigation (blocks skipped in the C G code are always the last ones) Skip Serial no. of computer-generated code for containers Number of print-outs required (even number) Skip and out d~

WHOjTBjTECHNICAL GUIDE/77.9 page 33

Appendix II, card 2

PUNCH CODE FOR WHO QUALITY CONTROL OF BCG PRODUCTS

Card 2: Col. 1 Col. 2

Coun ti.ng-card Punch 1 Punch 2 Investigating laboratory (code) Number of investigation within da.y Date of investigation Limi t for count

Col. 3 Col . 4Col . 5- 10 Col. 11- 13 Col. 14--16 Col. 17-18 Col. 19- 20 Col. 21-23 Col . 24- 26 Col. 27- 80

Skip

Interval between :inoculation and reading (days) Counted by (initi als) Code number of f i rst container Count* of first container Codes and counts* of another 9 containers; if no further counts , skip to 80 and out

*punch

digits only :

if not given, for unknown reasons, punch 901 i f container broken if If

902 903 904 999

contaminated count exceeds limiv

i f medium dry if

" " "

WHO/TBjTECHNICAL GUTDE/77.9 page 34 Appendix II, card 3

PUNCH CODE FOR WHO QUALITY CONTROL OF BCG PRODUCTS

Card 3: Col. 1 Col. 2 Col. 3 Ool. 4 Col. 5-10 Col. 11- 12 Col. 13 Col. 14-16 Col. 17- 18 Col. 19- 20 Col . 21 Col. 22 Col. 23- 27

Product-card Punch 1 Punch 3 Investigating laboratory (code) Number or investigation within day Date or investigat10n Subject Product number Skip Production laboratory (code) Strain (code) Dried or liquid (dried punch 1, liquid punch 2) Ampoule or vial or bulk (ampoule punch 1 , vial punch 2, bulk punch 3) Content or BCG in units or 0 . 01 mg 1 in col. 2l indicate as mg/amp. (vial) 2 in col. 21 indicate as mg/ml Col . 28-30 Col. 31- 32 Col. 33- 38 Col. 39- 40 Col. 41- 46 t;ol. 47-79 Col . 80 Nominal volume per amp./vial in units of 0.1 ml; i f 3 in col. 22, ski.p Sent from (code) Sent on (date) Received at (code) Received on (date) Skip

Total number of products in 1nvestigation

WHO/TB/TECHNICAL GUIDE/77.9 page 35

Appendix II, card 4

PUNCH CODE FOR WHO QUALITY CONTROL OF BCG PRODUCTS Card 4: Col. 1 Col. 2 Col. 3 Col. 4

Suspension-card Punch l Punch 4 Investigating laboratory (code) Number of investigation within day Date of investigation Skip Product number Code number of suspension (never 000) Lot number and description of ampoules, vials or bulk Date of preparation of final bulk Code for explanatory text for next 12 col. 's First or only date of freeze-drying; or, i f liquid, date of preparation Expiry, or last date of freeze- drying

Col. 5-10 Col. 11- 12

Col. 13 Col. 14-16

Col. 17-42 CoL 43-48 Col. 49

Col . 50-55 Col. 56- 61 CoL 62

Total number of ampoules/vials Exposure 37°C (days) Total volume reconstitution fluid in 0. 1 ml Time for reconstitution Reconstitution fluid (code) 1.

Col. 63-64 Col. 65-67 Col. 68-71

Col. 72

2.

Sauton (1+3) Diluent from producer Saline Destilled water Isotonic glucose solution

3. 4. 5. Col. 73-78 Col . 79-80

Date of preparation of reconstitution fluid Reconstituted by (initials)

WHO/TB/TECHNICAL GU1DE/77.9 page 36 Appendix II, card 5

PUNCH CODE FOR WHO QUALITY CONTROL OF BCG PRODUCTS Card 5: CoL l Col. 2 Col. 3 Col. 4 Col . 5-10 Col . 11-13 Col. 14-16 Col. 17- 20 Col. 21-24 Col. 25-26 Col. 27 Dilution-card Punch 1 Punch 5 Investigating laboratory (code) Number o£ investigation within day Date of investigation Skip Code number of suspension (never 000) Time of first dilution series Time of second dilution series (skip if only one series) Diluted by (initials) Diluent (code) 1. Sauton (1+3) 2.

3. 4. 5. 6. 9. Col. 28-33 Col. 34-59 CoL 60-80

Saline , 0.025% Tween 80 Sauton (1+3), 0 .1% Bovin v Buffered saline Saline De stilled water Special text to be punched in columns 34-59

Date of preparation of diluent Skip or text if special code in col. 27 Skip and out

WHO/TB/TECHNICAL GUIDE/77.9 page 37

Appendix II, card 6

PUNCH CODE FOR WHO QUALITY CONTROL OF BCG PRODUCTS Card 6: Col. 1 Col. 2 Col. 3 Col. 4 Col. 5-10 Col . 11-13 Col . 14-16 Col. 17-18 Col . 19- 21 Col . 22- 25 Col. 26- 29 CoL

Inoculation-card Punch 1 Punch 6 Investigating laboratory (code) Number of investigation Date of investigation Skip Code number of suspension (never 000) Block number Most concentrated dilution (two digits and power: see Appendix III) Time of inoculation first series Time of inoculation second series (skip i f only one series ) Volume inoculated per container in 0 . 01 m1 Container (code) Medium (code) Medium batch number Date of preparation of medium Inoculated by (initials) Skip or text i f special code in col. 32 Skip or text if special code in col. 33 Codes for col. 33 1. LOwenstein 2. Ogawa 3. Blood OAA 4. Dubos Special text to be punched 1n columns 63- 80 wit~n

day

30-31

Col. 32 Col. 33

Col. 34- 36 Col. 37-4 2 Col. 43- 44 Col. 45-62 Col . 63-80

Codes for col. 32 1. Tube 2. Legroux flask

3. 4. 5.

Petri dish Tube with screwcap Flat bottle with screwcap Special text to be punched in column.s 45- 62

9.

9.

WHO/TB/TECHNICAL GUIDE/77.9 page 38 APPEND IX II I

Notations for Dilution Levels

Cone entration 10- 2 10- 2 10- 2 1/2 • 10- 2 10- 2 1/4 10- 2 1/8 l0- 2 1/16 10-J 10- 3 10- 3 1/2 1/4 1/8 1/16 10-3 10- 3 10- 3 10- 3

Degree of dilution 25 50 100 200 400 800 1 600

Punchcode notation 25 0 05 1 01 2 02 2 04 2 08 2 16 2

4 2

4 2

250 500 1 000 2 000

25 1 05 2 01 3 02 3 04 3 08 3 16 3 25 2 05 3 01 4 02 4 04 4 08 4 16 4 25 3

4 000 8 000 16 000 2 500

10- 4 2 • 10-4 10- 4 10- 4 1/2 1/4 • 10- 4 4

5 000 10 000 20 000 40 000 80 000 160 000 25 000 50 000 100 000 200 000 400 000 800 000 1 600 000

1/8 1/16

10- 4 10- 4

2

4 • 10- 5 10-5 10-5 10- 5

OS 4 01 5 02 5 04 5 08 5 16 5

1/2

1/4 • 10-s 1/8 • 10-s 1/16 • 10-s

Testing laboratory:

Inoculation date: Diluent:

Reading date: Volume inoculated per container (v) : ml Degree of dilution (d)

Optimum (W): Limit

x2 -

2~

xl - (l2+

a,>

a)~ (~+X2 + ~) w.xl or b) 2W+ x -(l +~l

().) :

~ 2 3

1 2 ~ ~~x iii: + x n2 + n' ~ v

1

2

Production Lab. Batch No. ol Reconstitution Fluid

Shilll!lent Storage

Container: Medium (batch No.):

"'

Total No . of Average a} Jtl +Jl2 +21:} 2 Sum of concolony S(x+l) squares colony 2 b} x +a:, count to.J.ners $.--sx count 2 2 c) 2x~ Sx Sx n Sx

X·

U).Jt2 or c) 2iJ + x 2 or d) a)

<x>

x,

~

No. ot oulturab1e partiolea per ml. BCO 6 .10 6 .lo 6 .10 6 .10 . 10 6

&} b) c} Reconst1 tuted at : lnocule ted at : hrs hrs min min

b) c) d)

&) b)

a) b)

6 .10 6 .10 6 .lo 6 .10 6 .10

c) Reconstituted Inocu1st.ed at: a~ :

c) d)

hrs hrs

mln.

min .

.

&) b)

a) b)

--- Reconstituted at: Inoculated at: hrs min.

1-

c)

c) d)

.lo6 6 .10 6 .10 6 .10 6 .10 6 .10 6 > .., .10 Ill " ~ z ~~ 6 :::! ,.,......_ • 10 X

hrs

min . a) b)

&) b) c) d)

c) ~econst1t.uted at: ~noculated at t

hrs

min.

hrs

min. a)

a) b) c)

...

b)

c) Recon s~1tuted

<

...

... ..... ... n "'

.1l ' at:

hrs hrs

min. min.

d)

2 .... n > r

lnoculated a. t : Remarks1

6 .10

c

TB/70 . S

" 2 :.,

" ....

> ....,

0>

~

"" z 0 H

1'1

"" 0 r; ........... ~ C>

:;,--........ (")

X

..., ..., t"l

<

2 ......

(")

F: wHG QJALITY SJSPE~SIJIII CJ~T~OL

JF

oC~

PRODUCT.): OEPART~~~T ,

Jc1c~~~~ AT1JN

CF

CJLTU~ABL~

PARTI~L~S

...... 0

c:::

G")

NC

b3

lNV~STlGATED

BY BCG

CQPENNAGEN

GN 15 J Af~ 76

( 1J

.)\JoJ::l.T

lJ

~ -.J

.

-.J

PRODUCED BY STRAI~

..0

JANISH 1331

LGT NJ 3J7

Sc~l~~

1 ~l CONTAIN~

3JJ . JJ

~G

~Ol~T

~E!GHf

DILUTE D

9 HRS 23 MIN BY KS JN

SAUT~N

(1+3) ~uNfAINI N G

PFEP. Jo JAI\ 7b LOEwENSTEIN M~l)

0.10 ML INOCULATED PER TuB: I NOCUL~TEO

IUM

PM~>.

08

J~~

7o

9 HRS 45

~IN

BY KL ~?

CJLGNi tS CuuN TEO 34 DAYS AFTER INOCULATION BY

LIMIT OF COJNT 100

COLONI~S

()1uJ

SHGW~

A~

+I

DEGREE OF OIL.

co u :~T S

1

1ST SER . 2 3 37 4~

")q

ONLY SER. 5 53

N

4 49

C>-i! S..J

T

AVt:RAGE

CQUNT 0 . 52 -J . 07 45 . 6 21.6* lJ.~

l60JOJJ 320 \JJO~

6400000 W E IGIH ::D

4S 24 13 8 ~EAN

23

7 7 ( *)

Iq 11 8

a 9

20 18

5 5

4.Jl ::> . 8J 11.64

13

15

10

22 . 19

CULTU ~ABLE

PARTICL~S

71J.J72.

MlLLI OI~

?

:=;;

ML

WHO QUALITY CONTROL JF dCG PRUDUCTS: Su~PENSID~

DETc~~lNATIJ~

OF

CULTUhABL~

PAkTILLt~

NO

201

I~VEST!GATcO

hY

~CG

LABu~AT1Rt,

aUCHAREST

JN

Jo JAN 7o

(lj

~ut;Jt::T

71

FKCDUCLJ eY

!NST!TUT PASTEUR, GAKAR, SENEGAL

STRAIN Sc~T

FkENCH 1173 P 2 ll

LOT NC' 75-36...J R~CEIVcO rl~S

FROM BRUXELLES ~ECONSTITUTEu

AT

2

AMPS

AT 52 TURE

~

23 MIN BY JP IN ? H~~

S.J ML SAUTON ~1N

( 1+~1

P~t:P. P~tP.

lit JUL

75

D!LUTE[ 1ST T!ME

9

~RS P~~

MI~

2ND TIME

57

bY LB IN SAUTON l1+31

15 .JtL 75

0.10 Ml :NJCULATED

MEJlUM J Ml"4

p;:...,:p .

J6 JAN 76

l>J(•CULATC:O 1ST TIME 10 HRS

2ND Tl"\!:

U

H"S

b

MIN BY RB LIMIT DF COJNT 100 COLONI::::, 1>100 SrlJW•~

CJLONIES CCUNTEu 28 OAYS AFTER INQCuLAI.ON bY AS

AS

+-)

Dl: GREE

COUtHS 1ST SEF<.. 1

OF OIL. 50JO 10001) 20000

z

(Jil

Ll ·~ L Y .:>~ K •

~

l.Hl s~

I

AVERAGi: :auNT 6d.3

COUl11TS ZNG 1 65 2

s c.;;; • j

N

Crll

T

4111:-{AGo:: C.CJNT

3

4

5 3

)Q

68 41 17 16 (:;:)

68 34 15

69

25 20 18

3 6

J.Jl 3 . d6

0.15

33 . 3* 17 . ::1 33 . 74

32 1:~

-0.14 J . 94

16

17

oJ 2? l<t 15

64

27 14 17

3 3 6

v.zz J . 93

o3.0 J . od L8.0*

-O.bJ 0.61 15.3 29 . tHI

WE!GHTED "\EAN CULTURABLE

PARTICL~S

3.374 MiLLION Pi:R ML :.

2.9d8 MllliON PER Ml

., )>

'"0

LOG (1ST SER . l

-

LOG (2Ni) Sf R. I

0.053

z 0 ..... X

'"0 t"'l

()Q

t:l>

"'""''-l &:-t:e t"'l C1

0

~

...... '-..... o-l

<:

cr

...... C1 )>

2

r

c: ...... 0 t"'l

C)

......... .....

..... . .c

WHO/TB/TECHNICAL GUIDE/77.9 page 42 APPENDIX Vl

DERIVATION OF COMPUTATIONAL PROCEDURES FOR ESTIMATING THE NUHBER OF CULTURABLE PARTICLES PER MILLILITRE OF VACCINE As indicated 1n the ma1n text, the average counts x , x , and x are accumulated as 1 3 2 follows:

and these "cumulative values" are compared with 2w or twice the "optimum'' count.

A

cumulative

value of 2Whas been chos en because it will correspond , in the l1miting cases, to one of the following three sets of values : (l)

xl

= W;

x2 x3

1w. 2 , XJ

= 4 W·,

1

?x hence xl + x2 + ~ 3 = 2W

2W

(2) (3)

x2 = U); x3 =W;

l w. 2 '

hence x2 + 2x 3 2W

hence 2x

3

There are four possibilities : l. Even the final cumulative value, x 1 +

x

2

+

2x , may not exceed 3

2~.

In this case, the ~olume

fLnal cumulative value is the basis for further calculations.

If v is the

(e.g. 0.2 ml)

inoculated in each container, and d , d , and d represent the d1lution factors 2 1 3 (e.g. 20 000, 40 000 , and 80 000), the cumulative value corresponds to an amount of vacc1ne w hich (as d 2

= 2d , and d = 4d ) equals 2~ ; 1 3 1 1

and if 2~ ml of vaccine gives dl

colonies, one m1llilitre of vaccine must contain cullurable particles. 2. If x 1 +

v

x

2

+

2x

-

3

is the only cumulative value to exceed 1

2~,

further computations are based

upon the separate values of x weight. The term x

and (x

2

+ 2;. ) .

3

The latter term, (~

2

+

2~ ) is given "full"

3

1

is given a we ight dependent on the numbe r by which (x

2

+ 2x ) falls short

3

of 2w, as follows.

WHO/TB/TECHNICAL GUIDE/77.9 page 43 Appendix VI

The computations are formulated in terms of finding the dose of vaccine that will yield 2W colonies, An amount of vaccine of ~ + 2 ~

2~ 3

2 An additional 2~- (x

2

has given the first (x 2w-

2

+ 2i ) colonies.

3

2

+ 2x ) colonies constitutes a fraction

cx 2 • 2x3)

3

of the x

1

co l onies on the average obtained from

v d 1

2Y millilitre of vaccine. A total of 20) colonies d2

is thus obtained as ci + 2x ) colonies from 2Y ml plus 2(.,)- (x + 2x ) colonies· from 2 2 3 3 d2 2W- (x2 • 2x ) 2<..>- (i2 • 2x ) 3 3 2~ (1 + millilitre of vaccine. 2~ ml. This equals d2 xl d2 xl

.

Thus one colony (rather than 2Wcolonies)

is obtained from

1 ~

millilitre; d2 v

and the estimate of the number of culturable particles in one millilitre is G.)

2W- (x2 + 2x ) 3 1+

or

d2 v

w 2w+ x

. -

xl (i2 + 2x3 )

1

xl 3. If (x 2 + 2x ), though not 2x , exceeds 2(.o), the computations proceed as follows:

3

3

a total of 2 W colonies is obtained as 2x colonies from ~ • d2 2W- 2x • (1 +

3

colonies from zY ml of vaccine plus (2 w- 2x ) 3 d3

2W- 2x 3 ------~ ml of vaccine, equalling (since vd x2 2

3

) ml of vaccine.

x2 The estimate of the number of culturable particles in one millilitre of vaccine is: d3 v 1 + CoL)

2w- 2x

or 3

d3 v

(A)

. 2

x2 - 2x 3

2(A)+ x

x2

WHO/TB/TECHNICAL GUIDE/77.9 page 44 Appendix VI

4. x 2

Even the first cumu1ative value, 2x and x

-

3

may exceed twice the optimum.

In this case.

1

2

are disregarded and the computations proceed as follows. has given an average of 2x colonies.

The amount of vaccine

3

One millilitre of vaccine must contain

v

x

3

of culturable particles.

WHOjTBjTECHNICAL GUIDE/77.9 page 45 APPENDIX VII

The distribution of log difference Counts averaging oo/v 6~

colonies are distributed according to the Poisson formula with a The estimate of culturable particles,

standard deviation (sampling error) of ~·

= 6oo/( 6v) ,

thus has a standard deviation (from the sampling error alone) that ~ be

indicated through the formula: E

= (6w !

\{{;W) • d/( 6-v·) (1

= (1 :!:

1/ \[6W)

•

IIXl/v

with a logari.thm of:

log E

= log

! 1/ '{6c.l;) + log

~ + log d - log v

We may now define a variable f = (1 and standard deviation (l/l/6w). variable takes the values f 1

:!:

1/ 1.{6;) that is normally distributed with mean 1

If for two d.ilution series of the same suspension this

and f , we have: 2

or, since

~

is a predetermined constant and t ;he values of d and v are the same for both dilu-

tion series, subject to experimental errors o•f course but not to sampling error, we have for sampling error alone: El fl E = -f or log E1 - log E 2 2 2

= log

f 1 - log f 2

While E is normally distributed, log E and log f have slightly skewed distributions. Thus for ~

= 40,

log (1 + 1/ ~)

= 0.0272

while log (1 - 1/ ~)

=-

0.0290.

Yet the

approximation to a normal distribution is good enough to permit significance tests derived from the normal distribution to be considered. reasonably accurate. log f may thus be taken to be approximately The standard error of

J1oi (1 and the standard error of log f 1

+ ;

1

if6W) ; 1oi (1 - ; '/§) approximately

1

- log f

2

since the variance of a difference is equal to the sum of the variances of the terms. this formula confidence limits have been derived for specific values of ~.

From

*

*

*