NationalLibraryOfScotland/medical-history-of-british-india huggingface dataset:
SIZE OF EXPERIMENTS FOR TESTING SERA OR
VACCINES
BY
P. V. SUKHATME
Imperial Council of Agricultural Research, New Delhi
AND
V. G. PANSE
Institute of Plant Industry, Indore
(Received for publication on 20 March 1942)
I N veterinary research experiments designed to test the efficacy of vaccine or
serum treatments are commonly required to be undertaken and the question
arises as to how many animals should be experimented with before a research
worker can conclude that the vaccine in question is effective. The question
is one of practical value owing principally to the difficulties which arise in
securing a large number of suitable animals, and it is consequently necessary to
know the minimum number of animals required to ascertain with a known
degree of confidence that the result observed is due to the treatment-effect
and not chance causes. The object of this note is to illustrate the principles
involved in determining the number of animals required in such experiments.
Suppose it is known that the normal rate of infection of a certain disease
in cattle is, say, 25 per cent. Further suppose that an average healthy animal
is injected against infection with a newly discovered serum and is found to be
free from infection. Can the evidence be considered adequate to support
the claim in favour of the serum ? Common-sense would tell us ' no ', for
even without the application of the serum there is more likelihood that the
animal would remain free from infection than that it would catch infection.
How can we then accept the claim about the efficacy of the serum treatment ?
Suppose that another experiment is made with two animals and it is found that
both animals are free from infection. Would the evidence be now adequate
to support the claim of the serum treatment ?
As in the case of one animal the answer would depend on the probability
of the event happening, if the serum treatment was without effect. This
probability is easily found. The event happened is that both animals are found
to be free from infection. According to past experience the probability of
an animal remaining free from infection is ¾ and of it catching infection is ¼.
The probability that one animal may remain free from infection is ¾ ; the
probability that the other may remain free is also ¾ ; therefore the probability
that both will remain free, which is the event actually observed, is the product
of these two independent probabilities, i.e. ¾ × ¾ = 9/16 The only alter-
natives to the event that has taken place are (i) one animal may catch infection
and the other may not (ii) both may catch infection. The probability that
75
76
Size of Experiments for Testing Sera or Vaccines
one may catch infection is ¼ the probability that the other may not catch
infection is ¾ ; the probability that this combined event may happen is there-
fore ¼ × ¾ ; but the one animal that may catch infection can be either of the
two experimented with and therefore this value of the probability for the
combined event has to be multiplied by 2. The probability therefore that one
may catch infection and one may remain free from infection is 2 × (¼ × ¾) =
6/16 Finally the probability of each catching infection is ¼ and consequently of
both catching infection is ¼ × ¼ =1/16 We can tabulate the results as follows:—
Event observed
Both animals free from infection
.....
Probability
. 9/16 = 0.5625
Alternative events—
(i) One animal is free from infection and the other is not
(ii) Neither is free from infection
....
6/16 = 0.3750
1/16 = 0.0625
The sum of the probabilities is 1 as it should be since we have dealt with
all the three possible events. It will be seen that the probability of the event
observed is not only large but is more than the sum of probabilities of all the
alternatives to the event observed and thus there is a greater chance that the
two animals would remain free from infection than that one or both of two
would catch infection even if the treatment had no real effect. With only
two animals the fact that both remain free from infection cannot therefore
be regarded as conclusive evidence supporting the claim of the efficacy of
the treatment.
Let us increase the size of our experiment to three animals and suppose that
none caught infection. Does the result observed in any way suggest that the
serum treatment is effective in checking the infection ? Following the
procedure given above let us calculate the probability of the event observed
and of all the other alternative events. The probability of the result observed
is obviously the product of the probabilities that each animal may remain
free from infection and is therefore (¾) 3 = 27/64 The alternatives to the
event observed are (i) two may remain free from infection, the third may
not; (ii) one may remain free from infection, the other two not and (iii)
all the three may catch infection. If A, B and C are the three animals in the
experiment, the event that two may remain free from infection and the third
may not can happen in any of the following three ways with the probabi-
lities noted against them :—
A and B remaining free from infection, C not —(¾ ) 2 × ¼
A and C remaining free from infection, B not — (¾ ) 2 × ¼
B and C remaining free from infection, and A not — (¾ ) 2 × ¼
The probability, therefore, that two may remain free from infection and the
third may not, is 3 × 9/64 = 27/64 In precisely the same way we can show
that the event that one remains free from infection and the other two do not
can happen in three different ways and therefore the probability of the event
happening is 3 × ¾ × ¼ × ¼ = 9/64. Lastly, the probability that all three
P. V. SUKHATME AND V. G.
PANSE
79
a sample of this size the probability required is larger than 0.05 as will be seen
from the following table :—
Sample size
17
18
19
20
21
22
23
Probability required.
(¾) 17 + 17(¼) (¾) 16 = 0.0501
(¾) 18 + 18(¼) (¾) 17 = 0.0395
(¾) 19 + 19(¼) (¾) 18 = 0.0310
(¾) 20 + 20(¼) (¾) 19 + 20×19/2 (¼) 2 (¾) 18 =0.0913
(¾) 21 + 21(¼) (¾) 20 + 21×20/2 (¼) 2 (¾) 19 =0.0714
(¾) 22 + 22(¼) (¾) 21 + 22×21/2 (¼) 2 (¾) 20 =0.0606
(¾) 23 + 23(¼) (¾) 22 + 23×22/2 (¼) (¾) 21 =0.0492
For all sizes of 23 and larger, however, the probability of observing a rate of
10 per cent infection or less is always less than 0.05 and we therefore conclude
that (barring the isolated cases of 18 and 19) a minimum of 23 number of
animals is necessary to reach a conclusive verdict.
The procedure of making the test of significance and of calculating the
minimum number of animals explained above is straightforward but laborious.
For, the calculation of the probability that a departure as large or larger will
occur, becomes increasingly heavy with large samples and also several cases
have to be examined before arriving at the minimum number of animals
required. A short-cut approach would seem, therefore, to be desirable in
practice and one is fortunately available in the circumstance that the probability
required can be expressed as a function of the ratio of the observed departure
to a quantity called its standard error. The standard error is a measure of
sampling variation. For the problem of infected numbers that we are consid-
ering here, it gives the measure of variation in th eexpected number of infected
animals in repeated samples of the same size. It is given by the expression,
√nQ (1—Q) where Q is the normal rate of infection and n is the number
of animals or the size of the experiment. Thus, when n = 12 and the normal
rate of infection is 25 per cent as in our first example, the standard error of the
expected infected number will be √12 × ¼ × ¾ or 1.5. Or again for the same
rate of normal infection, but n — 24 as in our second example, the standard
error will be √ 24 ×¼ × ¾ for 2.12. It means that on the basis of past
experience we should expect six out of every 24 animals to catch infection but
in different samples of 24, the numbers observed will be scattered around six
with a standard deviation of 2.12. The knowledge of standard error at once
gives us the proportion of samples (or the probability) showing a
departure as large as the one observed or larger. In general when the departure
of the observed number from the expected value is larger than twice the stand-
ard error, the probability of the departure as large or larger arising by pure
chance is smaller than 0.05. When the departures in a given direction only
(+ ve or — ve) are considered, as would be the case in ascertaining whether an
experimental treatment gives a rate of infection lower than the normal in-
fection, the value of probability is halved and the departure as large as twice
the standard error or larger will obtain with a probability smaller than 0.025.
In order that the probability should be less than 0.05 the departure in one
P. V. SUKHATME AND V. G.
PANSE
81
where Q 1 is the normal rate of infection whose estimates are q 1 and q 2 . Ac-
cording to the normal theory we should observe a positive difference q 1 — q 2
exceeding 1.645 times its standard error in just 5 out of 100 cases so that
we have
d = 1.646 ×√2Q 1 (1—Q 1 )/n
and hence n corresponding to known values of d and Q 1 Thus in the case
where the norml rate of infection Q 1 is 25 per cent, and we are interested in
reducing the rate by 20 per cent (or in other words d = 20 per cent) we get on
substituting in the above equation n = 25. This means that the experimenter
should have a minimum of 25 pairs of animals to ascertain whether the experi
mental treatment is efficacious to the extent of reducing the normal rate by
20 per cent, or more. A table is given below giving the values of n corres
ponding to various values of per cent Q and d for the direct use of the ex
perimental worker. The table shows the minimum number of pairs of
animals required to reach a conclusive verdict at the 5 per cent level of signi
ficance, corresponding to different values of the normal rate of infection and
of the margin of difference it is desired to test. It will be seen that the
number of pairs required is decreased as the margin of difference desired to be
tested becomes larger and as the normal rate approaches 50. To determine
with the help of this table the minimum number of animals necessary for an
experiment an approximate knowledge of the normal rate of infection from past
experience and of the difference desired to result from the treatment is clearly
essential.
Sometimes the experimental worker may know apriori that the popula
tion value of Q 2 of the experimental treatment is less than the population value
Q 1 of the normal treatment by a known and fixed margin D. The practical
problem in such cases is more specific than the one we have been discussing so
far in that the hypothesis now to be tested is that the experimental treatment
reduces the normal rate of infection by a definite margin D. The experimenter
cannot now expect the difference d in the observed rates of infection in the two
samples to be distributed around zero but around D, the known and fixed
value. He also cannot have the same value as above for the standard error of
the difference but instead a value of √Q 1 (1—Q 1 )/n +√Q 2 (1—Q 2 )/n. It follows then
that the values of n appropriate to such cases would be given by the
equation—
d - D = 1. 645 × √Q 1 (1—Q 1 )/n +√Q 2 (1—Q 2 )/n
Corresponding- to different values of D, there will be different tables of the
type given above giving values of n. It is not our intention to give these
tables, as they are unlikely to be of much use to practical research workers.
It will be observed that the case we have tabulated is the one which corres
ponds to zero value of D.
In using our table a research worker may often find that the numbers of
animals recommended are larger than it might be possible to obtain in practice
especially when the experiments are concerned with bigger animals. In such
82
Size of Experiments for Testing Sera or "Vaccines
cases we must frankly agree that there is no alternative but to work with
whatever number of suitable animals one can manage to get, always remem-
bering that larger the number of animals the larger will be the chance of
testing conclusively the difference between the normal and the experimental
treatment. When the number of animals obtainable is less than what is
statistically required, the experiment can only serve to give an indication of
the treatment effect but is unlikely to lead to any conclusive inference until
the results are confirmed by some other independent evidence or by repeti-
tion.
Table showing the minimum member of pairs of animals in experiments with
sera or vaccines
Normal rate of infection
Margin of difference desired
between the experimental
and the normal treatment
d/Q
10
15
20
25
15
69
31
...
...
20
87
38
22
...
25
101
45
25
16
30
114
51
28
18
35
123
55
31
20
40
130
58
32
21
45
134
60
33
21
50
135
60
34
22
55
134
60
33
21
60
130
58
32
21
65
123
55
31
20
70
114
51
28
18
75
101
45
25
16
80
87
38
22
14
85
69
31
17
11
REVIEW
Spontaneous and Experimental Leukaemia in Animals. By JULIUS
ENGELBRETH-HOLM, M. D. (Translated from Danish by C. L. Heel:
Oliver and Boyd, Edinburgh, 1942, pp. xxiii & 245, 15s.)
I T is the aim of this book, published on behalf of the Scientific Advisory
Committee of the Lady Tata Memorial Trust, to review the collected
knowledge of spontaneous and experimental leukaemias in animals and
to discuss the relationship which these conditions bear to the problem of leu-
kaemia in man.
The greater part of the volume is devoted to the animal leukaemias
on which most of the literature is widely scattered or otherwise inaccessible
to the veterinary worker; much of it is also so controversial that confusion
and not enlightenment is the lot of the worker whose studies lie in this highly
specialized field of knowledge. Dr Engelbreth-Holm has performed a work
of distinction and high value in presenting in one small volume a lucid ex-
position of the problem. This is supported by an admirably arranged biblio-
graphy extending to over 400 references freely drawn on in the text.
A classification of the leukaemias is included in a short historical intro-
duction. If much of this is old ground, the crisp and comprehensive manner
in which it is covered will be appreciated. The main subject matter is his-
torically arranged. This enables the reader systematically to grasp the
thoughts and achievements of the earlier workers on the subject, the scope
and the nature of present day research, and the probable directions in which
future research tends. This logical sequence is maintained in five headings
dealing with (a) Spontaneous leukaemia in animals (b) Transmission experi-
ments (c) The role of heredity in animal leukaemias (d) Attempts to produce
leukaemia experimentally (e) Relationship between human and animal
leukaemias. The various types of leukaemias that have been discovered in
animals are enumerated, although one finds no mention made of Hodgkin's
disease which, if not the commonest, is certainly one of the most interesting
of the animal leukaemias. Much attention is given to the transmissible leukae-
mia of the domestic fowl and the mouse and the virus aetiology of these
affections is very fully discussed. The aetiological dissimilarity of human
leukaemias is rightly mentioned. The role of heredity in susceptibility and
immunity in the experimentally transmissible leukaemias is recent work that
touches controversial ground : the known facts are, however, clearly stated.
The author contests the claims that leukaemia can be produced by carcino-
genic agents and differentiates between the ' leukaemoid state' and frank
leukaemia. He considers, however, that most leukaemias in animals are of
neoplastic origin, and that they have much in common with leukaemias of
the human subject, although not all the latter fulfil the criteria of the neo-
plastic state. This is a book which the worker on animal leukaemias and
cognate problems cannot afford to be without. [ J. F. S.]
93
GIPD—Sl—325 IC of AR—12-5-43—500.
CONTENTS
(VOL. XIII, PART I)
March 1943
The Editorial Committee of the Imperial Council of Agricultural Research,
India, takes no responsibility for the opinions expressed in this Journal
Original Articles
STUDIES ON NEWCASTLE (RANIKHET) DISEASE
VIRUS (WITH PLATES I—IV)
BRUCELLOSIS IN INDIA
.
.
.
.
.
STUDIES ON THE EFFECT OF VARIOUS FACTORS
ON THE VITAMIN C CONTENT OF THE MILK
OF COWS AND BUFFALOES
PLEUROPNEUMONIA IN GOATS WITH SPECIAL
REFERENCE TO PASTEURELLA INFECTION
(WITH PLATES V AND VI)
AN OUTBREAK OF BOVINE ENCEPHALOMYELITIS
INVESTIGATIONS ON THE TOXICITY OF CRINUM
DEFIXUM KER-GAWL, I (WITH PLATE VII)
TUBERCULOSIS AMONGST GOATS AT THE GOVERN-
MENT CATTLE FARM, HISSAR
SIZE OF EXPERIMENTS FOR TESTING SERA OR
VACCINES
S. Ganapathy Iyer
.
J. B. Polding . .
Zal R. Kothavalla and
Harnand Singh Gill
P. G. Pande
S. R. Hassan and J. A.
Idnani
M. R.
Subramania
Sastry, C. K. Vela-
yudhan Nayar, R.
Ramaswamy and K.
Venkatachalam
P. N. Nanda and Gopal
Singh
P. V. Sukhatme and
V. G. Panse
Abstracts . . . . . . . . . . . .
Review . . . . . . . . . . . .
PAGE
1
27
35
44
59
65
70
75
83
93
B. N. MAJUMDAR, S. N. RAY AND K. C.
SEN
9
Indian J. Vet. Sci. & Anim, Husb., Vol. XIII, Part II ]
PLATE
VIII
FIG. 1. Animal on high fluorine diet. Note emaciated condition. The left hind leg is kept raised
above the ground and shows a striking similarity to the so called ' rheumatic arthritis'.
On post mortem examination, the femur was found fractured (see Plate IX)
FIG. 2. Side view of a foot from an
animal on high fluorine diet.
Note the overlapping of hoofs
and the crack.
PLATE IX
[Indian J. Vet. Sci. & Amin. Husb., Vol. XIII, Part II
FIG. 1. Left :—Metatarsus showing exostoses.
Right:—Section through the same bone.
Note the periosteal deposit causing
thickening of the shaft.
FIG. 2. Fractured femur from the animal shown
in Plate
VIII.
B. N. MAJUMDAR, S. N. RAY AND K. C.
SEN
103
Table V
Analysis of bones and teeth of the experimental animals
No. and age
of animal
89 . . .
(5½ years) .
368 . . .
(6½ years) .
39 . . .
(6 years) .
88 . . .
(5 years) .
178 . . .
(6 years) .
391 . . .
(5½ years) .
167 . . .
(4½ years) .
180 . . .
(4½ years) .
402 . . .
(7 years) .
Group and length
of period under
experiment
Control
.
(9 months)
.
Control . .
(11 months)
.
Low fluorine .
(10½ months) .
Low fluorine .
(12 months) .
Calcium . .
(9½ months) .
Calcium . .
(11½ months) .
High fluorine .
(7½ months) .
High fluorine .
(8½ months) .
High fluorine .
(8½ months) .
Material
Femur .
Pelvis .
Vertebra .
Molar .
Incisor .
Femur .
Pelvis .
Vertebra .
Molar .
Incisor .
Femur .
Pelvis .
Vertebra .
Molar .
Incisor .
Femur .
Pelvis .
Vertebra .
Molar .
Incisor .
Femur .
Pelvis .
Vertebra .
Molar .
Incisor .
Femur .
Pelvis .
Vertebra .
Molar .
Incisor .
Femur .
Pelvis .
Vertebra .
Molar .
Incisor .
Exostosis .
Femur .
Pelvis .
Vertebra .
Femur .
Pelvis .
Vertebra .
Molar .
Incisor .
Ash per
cent of
f.f.m.
69.2
63.4
56.1
82.7
81.7
72.8
63.6
60.8
80.7
78.7
71.8
62.1
59.9
81.3
80.7
72.9
62.2
58.0
85.1
85.0
66.7
63.7
59.5
81.7
79.2
73.1
59.6
58.4
82.0
78.3
67.7
67.2
62.4
85.4
82.8
67.5
66.8
62.5
53.0
69.5
63.4
52.1
79.8
79.3
CO 2 per
cent of
f.f.m.
3.97
3.81
4.38
3.96
3.42
3.29
3.65
3.10
3.66
3.75
Calcium
gm./100
gm. ash
41.0
42.0
40.0
39.3
38.5
41.5
41.0
40.5
40.5
40.5
42.3
41.8
40.5
40.5
41.0
40.0
40.3
39.8
39.8
39.4
41.0
40.8
41.0
41.5
41.0
39.8
41.3
40.3
39.3
39.0
41.5
42.3
42.0
39.0
39.0
41.3
40.0
39.3
39.5
39.5
40.5
40.8
39.5
41.0
Phosphorus
gm./100
gm. ash
17.3
17.2
17.7
17.7
17.7
17.6
17.3
17.3
17.7
17.6
17.9
17.3
17.7
18.2
17.9
18.0
17.9
17.9
18.3
18.8
17.5
17.5
17.5
17.7
17.7
18.2
17.9
18.4
18.0
18.2
17.3
17.1
16.4
17.7
18.1
17.1
17.3
17.3
17.3
17.4
17.2
17.1
18.1
18.0
Magnesium
gm./100
gm. ash
1.95
1.92
1.93
2.13
2.02
1.83
1.82
1.83
2.01
2.36
2.08
2.14
2.23
2.30
2.20
2.18
2.23
2.19
2.10
2.24
2.03
1.81
1.81
1.80
1.99
1.80
1.80
1.81
1.78
1.90
1.94
2.20
2.24
2.14
2.29
2.00
2.10
2.08
2.13
1.90
2.01
2.00
2.09
2.25
Fluorine
mg./10
gm. f.f.m.
38.2
73.9
132.8
35.7
34.3
34.9
78.4
105.4
33.9
31.2
126.8
271.2
287.5
40.7
37.1
140.5
269.5
303.5
30.1
30.5
478.0
686.0
686.2
53.1
58.1
443.5
820.3
829.0
124.6
138.8
564.1
1115.5
992.2
93.9
104.8
1392.7
578.9
720.8
784.4
528.2
851.6
739.8
156.9
113.0
Calcium and phosphorus were estimated according to the method of Talapatra, Ray and Sen [1940] and
magnesium by a modified Holzapfel method [1934].
f.f.m. = fat-free material.
concentration of the molars and incisors is much in fluorine, the concentration being 2.5 times
lower, being in the nature of 2-3 times that of higher than that of the femur from which it was
normal teeth. The exostosis is exceptionally rich taken.
B. N. MAJUMDAR, S. N. RAY AND K. C.
SEN
107
McCrudden, F. H. (1910). Archiv Int. Med. 5, 596
Mahajan, M. R. (1934-35). Ann, Rep. V. I. O., Hydera-
bad State, 3, Imp. Coune. Agri. Res., New Delhi
Mahajan, M. R. (1935-30). Ann. Rep. V. I. O., Hydera-
bad Stale, 3, Imp. Coune. Agri. Res., New Delhi
Mahajan, M. R. (1938-39). Ann. Rep. V. I. O., Hydera-
bad State, 7, Imp. Coune. Agri. Res., New Delhi
Malan, A. I., Green, H. H. and Du Toit, P. J. (1928).
J. Agric. Sci. 18, 376
Miles, L. M. and Feng, C. T. (1925). J. Exp. Med. 41,
137
Pierce, A. W. (1939). Nutrition Abs. and Rev. 9, 253
Phillips, P. H., Hart, E. B. and Bohstedt, G. (1934).
Agri. Exp. Sta. Wisconsin, Res. Bull. 123, 30
Ramiah, P. Y. (1939-40). Rep. Animal Nutrition, Work,
Coimbatore, Imp. Coune. Agri. Res., New Delhi
Ramiah, P. V. (1940-41). Rep. Animal Nutrition Work,
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Reed, O. E. and Huffman, C. F. (1930). Agri, Exp. Sta.
Michigan, Technical Bull. 105
Roholm, K. (1937). Fluorine Intoxication, H. K. Lewis
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Sahai, L. (1937-38). Ann. Rep., V. I. O., Bihar, 8
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Sen, K. C. (1935). Agric. & Livestock in India 5, 115
Shortt, H. E„ McRobert, G. R. ; Bernard, T. W. and
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Smith, H. V. and Davey (1939). Agri. Exp. Sta. Arizona
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A. J. MACDONALD AND S.
BOSE
109
parts was fed to all the groups. During the first
six weeks the grain ration consisted of equal parts
of yellow broken maize, jowar and cheena and from
six weeks onward the grain ration consisted of
equal parts of yellow broken maize, wheat and
paddy. Tables I and II give the average compo-
sition of the mashes and grains used in each
experiment.
TABLE I
Percentage composition of foods—Experiment 1
Feeding-stuff
Group 1—
Basal mash—Parts—
Wheat bran
.
.
.
.
Yellow maize . . . .
Ground oats
.
.
.
.
Group 2—
Basal mash . . . .
Soya bean
.
.
.
.
Salt
.
.
.
.
Group 3—
Basal mash . . . .
Extracted soya bean . . . .
Salt . . . .
Group 4—
Basal mash . . . .
Heated extracted soya bean .
Salt
.
.
.
.
.
Chicks grain—
Yellow maize . . . .
Jowar
.
.
.
.
Cheena
.
.
.
.
Growers grain—
Yellow maize . . . .
Wheat
.
.
.
.
Paddy
.
.
.
.
50
30}
20
81.5
18.0} 0.5
84.0
15.5}
0.5
84.0
15.5}
0.5
1
1}
1
1
1}
1
Moisture
9.5
9.0
8.9
8.5
9.6
9.1
Crude
protein
11.4
16.0
16.0
15.9
9.8
9.8
Ether
extract
5.1
6.9
5.2
5.1
3.1
4.0
Fibre
10.1
9.0
9.2
9.3
4.1
5.2
Nitrogen
free
extract
57.8
52.7
54.2
54.7
70.7
69.5
Ash
6.1
6.4
6.5
6.5
2.7
2.4
TABLE II
Percentage coin-position of foods—Experiment
2
Feeding-stuff
Group 5—
Basal mash—Parts—
Wheat bran
.
.
.
.
Yellow maize . . . .
Ground oats . . . .
Group 6—
Basal mash
.
.
.
.
Soya bean . . . .
Salt
.
.
.
.
Group 7—
Basal mash . . . .
Extracted soya bean . . . .
Salt . . . .
Group 8—
Basal mash . . . .
Heated extracted soya bean .
Salt . . . .
50
30}
20
75.0
24.0}
1.0
77.0
22.0}
1.0
77.0
22.0}
1.0
Moisture
8.9
8.7
8.7
8.5
Crude
protein
9.5
15.9
16.0
15.9
Ether
extract
4.7
6.8
5.2
5.0
Fibre
11.3
10.1
10.1
10.2
Nitrogen
free
extract
59.0
52.6
54.1
54.4
Ash
6.6
5.9
5.9
6.0
C