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7/28/2019 Foot-And-mouth Disease Vaccine Potency Testing -Determination and Statistical Validation of a Model Using a Serol
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Vaccine 21 (2003) 32403248
Foot-and-mouth disease vaccine potency testing: determination andstatistical validation of a model using a serological approach
Paul V. Barnett a,, Robert J. Statham a, Wilna Vosloo b, Daniel T. Haydon c
a Institute for Animal Health, Pirbright Laboratory, Ash Road, Pirbright, Woking, Surrey GU24 0NF, UKb ARC-Onderstepoort Veterinary Institute, Exotic Diseases Division, Private Bag X5, Onderstepoort 0110, So uth Africa
c Department of Zoology, University of Guelph, Guelph, Ont., Canada N1G 2W1
Received 7 October 2002; received in revised form 13 February 2003; accepted 11 March 2003
Abstract
European foot-and-mouth disease vaccine manufacturers are required to quantify the efficacy of their product in accordance with the
European Pharmacopoeia (EP). The method used most often to establish the potency of foot-and-mouth disease vaccines requires viral
challenge of vaccinated cattle. Alternative approaches, such as challenge-free serological assessments have many advantages over existing
methods and could be used if robust statistical models could be developed that related antibody titres to protection from challenge. Logistic
regression analysis of data from two independent research laboratories, representing six of the seven main serotypes of FMD, permitted the
parameterisation of these models and indicated that a significant relationship existed between antibody titre and probability of protection.
Furthermore, no significant differences were observed in the parameters of logistic models fitted to different strains within the serotypes
A, O, and SAT-3, or when strains from serotypes A, O, and Asia-1, or SAT-1 and SAT-3, were combined. However, significant differences
in the model parameters did exist between different laboratories. Using these models a bootstrap analysis suggested that for vaccines that
induced consistently high titres, as few as six to eight individual animals could be used to establish with confidence the minimum protective
doses that would protect 50% of vaccinated animals. We conclude that a serologically evaluated truncated test that eliminates the need to
virus challenge cattle is a credible alternative for quantifying vaccine potency.
2003 Elsevier Science Ltd. All rights reserved.
Keywords: Foot-and-mouth disease; Vaccine; Potency; Challenge test; Logistic regression; Antibody titre
1. Introduction
Inactivated foot-and-mouth disease virus (FMDV) is used
in vaccine preparations to control foot-and-mouth disease
(FMD), one of the most economically important diseases
affecting livestock. These vaccines are used in many parts
of the world, particularly where the disease is endemic,
including South America, Africa, the Middle East and the
Far East. In disease free countries, concentrated inactivated
FMD virus antigens are also kept in strategic reserves,
so-called antigen banks, which can be rapidly formulated
into vaccine during an emergency should an outbreak re-
quire additional control measures.
In order to assess the quality of the vaccine, all FMD
vaccine producers are obliged to instigate a series of tests
to establish the safety and efficacy of their product. These
tests include a measurement of potency which in accordance
Corresponding author. Tel.: +44-1483-232441;
fax: +44-1483-232448.
E-mail address: [email protected] (P.V. Barnett).
with the European Pharmacopoiea (EP) requires that vaccine
batches be tested in groups of at least five cattle inoculated
with reduced dose volumes of vaccine so that potency can
be expressed in terms of 50% protective doses [1] (PD50, de-
fined as the factor by which the concentrate may be diluted
such that 50% of vaccinated animals are protected). This
method has practical and logistical problems, and disadvan-
tages from the perspective of animal welfare. For example, in
any extinction point test, approximately 50% of the animals
that are not protected will suffer the painful clinical man-
ifestations of the disease and even some protected animals
may show primary lesions at the site of challenge. Also, only
one valency can be tested in any given trial. Clinically in-
fected animals represent a disease security hazard requiring
expensive high security housing. Finally, given the financial
commitment of purchasing these animals and maintaining
them during the trial period the smallest permitted group
sizes are often used leading to lack of statistical power and
imprecision [2].
However, the European Pharmacopoiea has supported the
use of alternative testing methods provided a correlation
0264-410X/03/$ see front matter 2003 Elsevier Science Ltd. All rights reserved.
doi:10.1016/S0264-410X(03)00219-6
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P.V. Barnett et al. / Vaccine 21 (2003) 32403248 3241
can be established between them and the challenge test.
Serologically-based methods have certain advantages, not
least the relatively insignificant discomfort caused to the
animals as a result of vaccination and subsequent blood sam-
pling. They allow several FMD vaccines to be tested simul-
taneously and/or a number of serotypes to be examined in a
single polyvalent vaccine and can significantly improve theaccuracy of the result. For this reason many research work-
ers developed and evaluated a variety of serological tests and
assessed the correlation of the results with protection. These
have included the virus neutralisation test, plaque reduction
test, the metabolic inhibition test, mouse protection test and
different forms of the enzyme linked immunosorbent assay
(ELISA).
Although some disadvantages have been noted with these
tests, it is generally accepted by FMD research workers that
there is an excellent correlation between the virus neutral-
isation antibody titres of primo-vaccinated cattle and their
protection from virus challenge at 21 days post-vaccination
[36]. Stellman [7] developed this approach further by show-ing how such antibody titres could be used to statistically
assess vaccine and Pay and Parker [8] described a method
for relating log virus neutralisation titres of cattle sera to the
potency of a vaccine in antigen PD50 units. A correlation
was also established between the antigen dose in the vac-
cine, the virus neutralising antibody response and the level
of induced protection [9].
Certainly, there are strong arguments for replacing the
challenge test by in vitro serological assays, however, any
form of test would have to meet certain general criteria. The
test system must be consistent and reproducible, it must be
standardised and include standard reference reagents and pa-rameterised using substantial data sets from which the mod-
els relating titre to protection can be reliably established.
Two methods have primarily been used to calculate the de-
gree of protection in a group of vaccinated animals. Pay
and Hingley [2] and Ahl et al. [10] used mean serum anti-
body titres to calculate a PD50 or a percentage protection.
Bengelsdorff[11] and van Maanen and Terpstra [12] used a
second method in which an individual titre or index was as-
signed to protection and non-protection and the assessment
of a group was calculated from the passed and not-passed
individuals.
In this paper, we have accrued data from two laborato-
ries: The Institute for Animal Health, based at Pirbright in
the United Kingdom and the ARC-Onderstepoort Veterinary
Institute in South Africa, in which cattle challenge tests and
serology have been performed to establish the potency of
many different batches of FMD vaccine. At the Pirbright
Laboratory these tests were performed to either substanti-
ate that a given antigen could be formulated into a high
potency (10 PD50) vaccine for acceptance into the Inter-
national FMD Vaccine Bank[13], or to show stability of the
antigen during ultra-low temperature storage. Similarly, by
using a truncated version of that specified in the OIE man-
ual [14], involving just a single vaccine dilution group, the
laboratory at Onderstepoort performed cattle challenge tests
to ensure that their vaccines had potency values of 8 PD50.
Encompassing six different serotypes, the objective of this
analysis was to:
determine the relationship between virus neutralising titre
and protection;
quantify any variation in this relationship between labora-tories or as a result of the use of different vaccine strains
or serotypes;
provide a model that could be used to calculate the prob-
ability that vaccines achieve potency levels at or in excess
of a pre-specified requirement.
2. Methods
2.1. Data
The data comprised the results of vaccine potency tri-
als conducted in the two laboratories (Pirbright and Onder-
stepoort) on six different serotypes (O, A, Asia-1, SAT-1,
SAT-2, and SAT-3). The data is summarised in Table 1 and
Fig. 1. Animals were vaccinated (except control individuals)
with various dilutions of vaccine of varying valency, and the
neutralising antibody titre (log 10 SN50/100 TCID50) to the
vaccine virus strains estimated from serum samples taken at
21 days post-vaccination using the virus neutralisation test
(VNT). At this time animals were challenged with homolo-
gous virus to the vaccine strain by intradermal inoculation of
10,000 ID50 into the tongue. Animals were observed closely
for the subsequent reading period, normally 810 days, and
the occurrence of generalised lesions on any one or morefeet taken as evidence that the animal was not protected by
the vaccination.
2.2. Analysis
The data for each vaccinated animal thus constitutes: lab-
oratory, serotype, strain, log antibody titre from the VNT,
and protected or unprotected status. Logistic regression im-
plemented within MINITAB was used to determine the sig-
nificance of differences between strains within serotypes,
and between laboratories on the relationship between log an-
tibody titre and protection. The significance of all two-way
interactions was examined and those revealed to be insignif-
icant at the 5% level were omitted from subsequent analysis.
When no significant differences between strains or serotypes
were revealed the data were combined and parameters for a
single model estimated. Appropriate minimal models were
determined, and characterised by their intercepts and slopes
(with accompanying standard errors (S.E.)), the covariance
between the estimated slope and intercept, T50 (defined as
the titre at which animals are protected with probability
50%), the 95% confidence intervals (95% CI) on T50 as de-
termined using Fiellers theorem [15] and T95 (defined as the
titre at which animals are protected with probability 95%).
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Table 1
Summary of the data (P: Pirbright, O: Onderstepoort)
Serotype Challenge strains No. of animals challenged No. of animals protected (%) Average neutralising Ab titre
of vaccinated animals
Asia-1 P: India 46 37 (80) 2.44 (40)
O P: Manisa 36 31 (86) 2.34 (32)
P: Lausanne 26 19 (73) 2.36 (24)
A P: Cruzeiro 102 53 (52) 1.67 (92)
P: Thailand 36 32 (88) 2.25 (32)
P: Iraq 26 22 (85) 2.29 (24)
SAT-1 O: Sar/9/81 77 49 (64) 1.68 (55)
O: Bot/1/77 12 7 (58) 1.79 (10)
SAT-2 O: Zim/7/83 77 44 (57) 1.79 (55)
O: KNP/19/89 7 1 (14) 1.72 (5)
SAT-3 O: Bec/1/65 14 2 (14) 0.66 (10)
O: KNP/10/90 33 22 (67) 1.70 (25)
The number of animals challenged includes control unvaccinated animals.
The 95% confidence regions (95% CR) for adopted modelswere also determined using methods described in Sokal and
Rolf [16].
The expected probability of protection (i) for an individ-
ual animal with titre ti is given by:
i =exp(a0 + a1ti)
1 + exp(a0 + a1ti)(1)
where a0 and a1 are the intercept and slope of the associated
logistic regression model relating protection to titre. The ex-
pected proportion of protected cattle, , in a group compris-
ing n individuals, with log titres t1, t2, t3, . . . t n, is given by:
= 1/nn
i=1i. An estimate of whether or not this differssignificantly from 50% of the group can be approximated
by inspecting the quantity p =n/2
i=0
n
i
i(1 )(ni)
which constitutes a (one-tailed) test of the hypothesis that
0.5. If n cattle in a potency trial are vaccinated with
vaccine diluted X-fold and the hypothesis that 0.5 is
Table 2
Parameters corresponding to logistic regression models fitted to subsets of the data in which no significant heterogeneity could be detected at the 5% level
Model no. Virus/lab Vaccine/challenge strain n a0 S.E. a0 a1 S.E. a1 Covariance
(a0, a1)
T50 T50 (95% CI) T95
Onderstepoort
1 SAT-1 Sar/9/81 77 5.155 1.18 4.726 1.054 1.190 1.091 0 .932 1 .258 1.7142 SAT-1 Bot/1/77 12 15.200 12.96 9.780 8.008 102.020 1.554 Insufficient data 1.855
3 SAT-1 Sar/9/81 + Bot/1/77 89 4.780 1.02 4.157 0.840 0.820 1.150 0 .988 1 .307 1.858
4 SAT-2 Zim/7/83 77 6.002 1.30 4.482 0.934 1.162 1.339 1 .164 1 .517 1.996
5 SAT-2 KNP/19/89 7 Insufficient data
6 SAT-2 Zim/7/83 + KNP/19/89 84 5.760 1.18 4.065 0.805 0.912 1.417 1 .243 1 .594 2.141
7 SAT-3 Bec/1/65 + KNP/10/90 47 5.000 1.41 4.310 1.287 1.740 1.160 0 .965 1 .469 1.843
Pirbright
8 A Cruzeiro + Thailand + Iraq 164 6.920 1.14 4.773 0.728 0.807 1.450 1 .326 1 .560 2.067
9 O Manisa + Lausanne 62 8.889 3.43 5.673 1.967 6.668 1.567 1 .116 1 .749 2.086
10 Asia-1 India 46 10.123 5.31 5.803 2.634 13.860 1.744 0.409 1.977 2.252
11 All 3
combined
Cruzeiro + Thailand + Iraq
+ Manisa + Lausanne
+ India
272 6.923 0.957 4.658 0.581 0.540 1.486 1 .377 1 .581 2.118
rejected in favour of the hypothesis that > 0.5 then it canbe concluded that the PD50 of the vaccine is greater than X.
The test is conservative because the variance of a mixed bi-
nomial process (in which each trial succeeds or fails with
a different probability) isn
i=1i(1 i), which is always
greater than the variance for a homogenous process with the
same mean (in which each trial succeeds or fails with the
same probability)which is n(1 ) [17]. Thus, assum-
ing the process to be homogenous when it is in fact mixed
should lead to an overestimate of p.
We can, in principle, use a bootstrap analysis to inves-
tigate the relationship between the number of animals in
such challenge-free trials, and the probability that signifi-cantly more than half the animals in such trials would be
protected. We can randomly assign all vaccinated individu-
als in a trial of n animals a titre from the set of observed
titres for that serotype, and use the model combined over
all strains for that serotype reported in Table 2 to calculate
the mean and variance of the expected number of animals
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Fig. 1. Histograms showing the frequency distribution of titres induced by vaccines of different FMD serotypes.
protected, and the P-value indicative of whether significantly
more than half the animals were protected. Repeating this
process 500 times each for a range of different possible
sizes of trials, allows us to compute the probability that sig-
nificantly more than half the animals in a trial would be
protected as a function of the number of animals in the
trial.
3. Results
3.1. The relationship between virus neutralising titre
and protection
No significant interactions between neutralising anti-
body titre and serotype, or antibody titre and strain were
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detected in any of the analyses described below. Analysis
indicated a highly significant effect of laboratory on the
relationship between titre and protection, we therefore pro-
ceeded to analyse results from the different laboratories
separately. The parameter estimates, with standard errors,
covariances and T50 and T95 values are summarised in
Table 2.
3.2. ARC-Onderstepoort Veterinary Institute
Of the two strains of SAT-1 examined, significant differ-
ences in model intercept were established between Sar/9/81
and Bot/1/77 (P < 0.05): a significant relationship existed
between titre and probability of protection against Sar/9/81
(P < 0.001) but not against Bot/1/77 (presumably a con-
sequence of the small number of potency results available
for this strain). Similarly, a significant relationship between
titre and protection existed for the SAT-2 strain Zim/7/83
(P < 0.001) but insufficient data existed to establish such a
relationship for the other SAT-2 strain, KNP/19/89. No sig-
nificant differences between titre and protection could be es-
tablished for the SAT-3 strains Bec/1/65 and KNP/10/90 so
these were combined and a significant relationship between
titre and protection was apparent (P < 0.001). When strains
Sar/9/81, Zim/7/83, and (KNP/10/90 + Bec/1/65) represent-
ing the three SAT strains are compared, the Zim/7/83 was
found to be modelled by a lower intercept to the SAT-1 and
SAT-3 strains (which were not distinguishable) indicating
that this SAT-2 strain requires a higher titre to achieve the
same level of protection compared to Sar/9/81, KNP/10/90
and Bec/1/65. This is reflected in the T95 values for SAT-1,
SAT-2, and SAT-3 vaccines which were 1.858, 2.141, and1.843, respectively (for models with strains combined within
serotypes).
Fig. 2. The best fitting models to four different subsets of the data.
3.3. Institute for Animal Health, Pirbright
Significant relationships existed between antibody titre
and probability of protection for all strains for which data
were available for serotypes Asia-1, O, and A. In addition,
no significant differences were revealed in the intercepts of
logistic models fitted to the three strains of the A serotype,namely, A15 Thailand, A22 Iraq and A24 Cruzeiro, or the
two strains, Manisa and Lausanne, of the O strain. Analysis
of all three serotypes combined also revealed no significant
differences in intercepts between serotypes. T95 values for
serotypes A, O, and Asia-1 vaccines were 2.067, 2.086, and
2.252, respectively (once again for models with strains com-
bined within serotypes). An observation previously reported
using independent data from tests involving other O, A, and
C vaccine strains [18].
The probabilities of protection with different titres of anti-
body for different subsets of the data sets that are statistically
indistinguishable are indicated in Fig. 2. The estimates of
slope and intercept for the logistic regressions exhibit nega-
tive covariance (see Table 2). This means that uncertainty in
the estimated value of the intercept is negatively correlated
with uncertainty in the estimate of the slope. Therefore, the
confidence regions in parameter space which encapsulate the
true parameters governing the relationship between titre
and protection with 95% probability, are angled ellipses (see
Fig. 3a and b).
3.4. Determining the probability that a particular test
vaccine has a specified/required PD50
Suppose that a vaccine concentrate of serotype Asia-1from Pirbright was diluted X-fold and used to vaccinate eight
test animals. At 21 days post-vaccination, these animals were
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Fig. 3. The confidence regions for the models fitted to the data from vaccine potency trials for serotypes from the two laboratories. The confidence
regions are for models 3, 6, and 7 and 8, 9, and 10 (see Table 2). The angle in the orientation of these ellipses arises from the negative covariance
between estimates of slope and intercepts reported in Table 2.
bled, and log antibody titre determined. Suppose the eight
log titres, ti, were: 2.70, 2.15, 2.85, 2.85, 2.25, 3.15, 3.15, and
1.65. Using these titres and the estimated model (a0 and a1
model number 10) this laboratory from Table 2, we would
estimate that the expected proportion of animals protected
would be = (1/8)8
i=1(exp(a0 + a1ti))/(1 + exp(a0 +
a1ti)) = 0.90260 (in reality seven of eight (87.5%) of these
animals with these titres were protected from challenge).
The quantityn/2
i=0
n
i
i(1 )(ni) yields a P-value of
0.0046. If the PD50 of the test vaccine was Xthen we would
expect 50% of the animals to be protected, but from these
results we anticipate that over 90% would be protected, so
the probability that the PD50 really is Xor less is in this case
very small and we could be 99.54% confident that the PD50of the stored vaccine concentrate was greater than X.
As a second example suppose that 10 test animals had
been vaccinated with a SAT-1 vaccine from Onderstepoort,
diluted Y-fold. Suppose the 21-day log titres were: 1.80,
1.90, 1.40, 1.70, 2.10, 2.40, 2.10, 1.50, 1.30, and 1.60. Us-
ing these titres and the estimated model (number 3) for the
combined SAT-1 results from this laboratory from Table 2,
we would estimate that the expected proportion of animals
protected would be = (1/10)10
i=1(exp(a0 + a1ti))/(1 +
exp(a0 + a1ti)) = 0.882 (in reality 7 of the 10 (70%)
animals with these titres were protected from challenge).
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Fig. 4. The probability of being able to show that the PD50 is significantly greater than that used in these vaccine trials as a function of the number
of individuals used in the trial. Each point is the proportion of 500 re-sampled sets of titre values (from the indicated serotype) in which significantly
more than 50% of individuals in the set would be protected. The number of individuals (the number of re-sampled titres) in each trial is indicated on
the x-axis. Parameter values are those for the combined strains model for each serotype (numbers 3, 610).
If the PD50 of the test vaccine was Y then we would ex-
pect 50% of the animals to be protected, but from these re-
sults we anticipate that 88.2% would be protected, so the
probability that the PD50 really is Y or less is in this casen/2i=0
n
i
i(1 )(ni) = 0.0034 and in this case, we
could be 99.66% confident that the PD50 of the vaccinetested was greater than Y.
The number of animals required in a trial to establish with
95% confidence that the vaccine protected 50% of vacci-
nated animals obviously depends on the data used but some
examples using data analysed in this study are shown in
Fig. 4. If the titres from each serotype analysed here were
representative generally of those obtainable from vaccines
prepared from these serotypes then only modest numbers
of animals (as few as six) are required to establish that the
most effective and consistent vaccines (those of serotype O
and Asia-1) protect half the animals when diluted as they
were in these trials. For the more variable titres obtained
from SAT-1 and SAT-3 vaccines, even using as many as 18
animals would not necessarily indicate 50% protection with
any degree of confidence.
4. Discussion
This analysis reveals that the relationships documented
between vaccinally induced antibody titre and protection
against clinical foot-and-mouth disease differs between two
different laboratories. Whether this is because of method-
ological differences in the adopted procedures, or because
different relationships hold for the different serotypes stud-
ied in each of the different laboratories cannot be determined
from the data available. However, previous studies have also
documented differences in the test results between different
laboratories [19]. In general, it appears that so long as sam-
ple sizes were not too small, results from different strains
of the same serotype usually conformed to a single logis-tic model (this was the case for three serotypes represented
by more than one strain: A, O, and SAT-3). The parame-
terisation of these models for each serotype enables the use
of challenge-free trials to estimate the effectiveness of these
vaccines. We developed a simple statistical framework for
analysis of challenge-free trials for which existing data sug-
gests that for some serotypes, six to eight animals might
provide sufficient statistical power to confidently establish
required PD50 values. This is fewer animals than that cur-
rently stipulated by the European Pharmacopoiea.
Usually potency testing of inactivated vaccines is per-
formed on the target species. This takes into account not
only the active substance, i.e. antigen, but other compo-
nents such as the adjuvants which are incorporated to fur-
ther enhance the immunity of the vaccine. This is true for
foot-and-mouth disease vaccine as this vaccine always in-
corporates either aluminium hydroxide/saponin or mineral
oil-based adjuvants. This in vivo potency assessment usually
involves cattle, which makes the test very costly and involves
the examination of virus challenged animals to establish the
protective ability of the vaccines. The extremely infectious
nature of FMDV means that high level containment facilities
are required to perform such tests, which further limits ac-
cessibility and adds to the overall cost. The results are then
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P.V. Barnett et al. / Vaccine 21 (2003) 32403248 3247
based on whether generalisation of disease has occurred at
sites other than that of challenge. This of course means that
animals not protected will suffer the painful clinical man-
ifestations of FMD and even some protected animals may
undergo some pain due to the development of primary le-
sions at the site of challenge. Results are, therefore, either
black or white, with no intermediary level in which an an-imal could be perceived as being partially protected. These
results are then extrapolated into percentages of protected
animals within the vaccine dose groups and converted to a
PD50 value by the Krber method [20] or some similar pro-
cedure, to establish the lowest dilution of vaccine that would
protect 50% of the animals. Such tests are often based on
relatively small numbers of animals. For example, the Eu-
ropean Pharmacopoeia monograph for foot-and-mouth dis-
ease vaccines requires three vaccine dilution groups of five
animals per group. This test has been viewed as both statis-
tically weak and inaccurate with a 90% confidence interval
for the PD50 value lying anywhere between 45 and 220% of
the potency [21]. A further important consideration is thatoften FMD vaccines can be multivalent containing three or
four different strains of virus and it is not possible to under-
take a challenge test with more than a single strain of virus
at any one time.
A test approach that relies on large numbers of defined
sera that have an established correlation with potency and
protection in the target species therefore seems an attractive
alternative. By far the most explored area of investigation
has been the correlation between protection and serological
parameters such as neutralising antibody [2,7,2224]. The
data of this sort collected at Onderstepoort and Pirbright per-
mits a feasibility study of this approach. In order to developlogistic models it is important that the data span a wide range
of titres. Data for serotype C from Pirbright could not be
used in this analysis because no records of vaccinated but
unprotected animals existedthe vaccine always protected
vaccinates, and thus a logistic model could not be fitted.
The bootstrap analysis of the number of animals required
to conclude with reasonable confidence that significantly
more than half the animals in a group are protected (Fig. 4)
is only intended for illustratory purposes. Specifically, we
do not claim that the titres included in the analysis here are
representative of those that would be expected from field use
of market ready product. Data for some strains and serotypes
(very usefully) includes vaccine used at higher dilutions, and
thus induce a wider range of titres than would be expected
from non-experimental use. However, it does show, first, that
its very straightforward to use this kind of data to suggest the
number of animals required in such trials, and second, that
if a vaccine regularly induces high levels of protection then
this number could be quite modestpossibly as low as 68.
In summary, statistical analysis of serological and protec-
tion data accrued from challenge/potency tests performed
at two independent research laboratories and encompassing
vaccine strains representing six of the seven serotypes of
FMD indicates a significant effect of laboratory on the rela-
tionship between neutralising antibody titre and protection.
However, individual analysis of the data from each labora-
tory showed that, provided reasonable sample sizes are avail-
able, a significant relationship can be established between
antibody titre and probability of protection. Furthermore, no
significant differences were observed in the parameters of
logistic models fitted to combined strains within serotypesA, O, and SAT-3, or when the strains from serotypes A, O,
and Asia-1 or SAT-1 and SAT-3 are combined. These mod-
els permit the development of a truncated test, that avoids
the use of virus challenge and requires only a single group
of cattle administered with a vaccine diluted to a level equal
to or greater than the required potency value (PD50) potency,
providing an alternative method for evaluating the vaccine
potency required.
Acknowledgements
Daniel T. Haydon was supported by the Wellcome Trust.We thank Victoria Edge for helpful discussions.
References
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