TITLE:
Bayesian Interval Estimation of the Prevalence Rate Using Pool Testing Strategy with Retesting
AUTHORS:
Velmah Kiprop, Matiri George Munene, Luke Akongo Orawo
KEYWORDS:
Pool Testing, Specificity, Sensitivity, Trinomial Distribution, Posterior Distribution, Gridding Method, Credible Intervals, Coverage Probability
JOURNAL NAME:
Open Journal of Statistics,
Vol.15 No.3,
June
30,
2025
ABSTRACT: Accurate estimation of disease prevalence is crucial for effective public health intervention and resource allocation. Generating data by individual testing methods is often impractical and expensive for large populations, particularly when disease prevalence is low. Pool testing involves combining samples from multiple individuals into a pool and performing a single test, and offers a cost-effective and efficient alternative. In pool testing strategy with retesting, if a pool tests negative, it is classified as non-defective, whereas if it is positive, then a retest is needed. The retesting strategy mitigates the effects of initial test errors, thereby enhancing the accuracy of the estimation of the prevalence rate. Evidence in the literature indicates that the traditional Wald method has been used to construct approximate confidence intervals for the prevalence rate. However, this interval estimation method is based on the normality approximation and hence may not be accurate when the true prevalence rate is close to zero. In this paper, we propose a Bayesian interval estimation approach which is not affected by extreme values of the prevalence rate and allows for incorporating prior information about the prevalence rate. We assumed that the prior distribution for the unknown prevalence rate
p
is a Beta distribution with parameters
α
0
and
β
0
and based on pool testing outcomes for the
n
pools each of size
k
,
100(
1−α
)%
credible intervals were constructed from the resulting posterior distribution. Simulation studies were carried out to compare the efficiencies of the Bayesian and Wald interval estimation methods for various values of
p
.