  Bayes' Theorem confers inherent limitations on the accuracy of screening
tests as a function of disease prevalence. We have shown in previous work that
a testing system can tolerate significant drops in prevalence, up until a
certain well-defined point known as the $prevalence$ $threshold$, below which
the reliability of a positive screening test drops precipitously. Herein, we
establish a mathematical model to determine whether sequential testing
overcomes the aforementioned Bayesian limitations and thus improves the
reliability of screening tests. We show that for a desired positive predictive
value of $\rho$ that approaches $k$, the number of positive test iterations
$n_i$ needed is: $ n_i =\lim_{\rho \to
k}\left\lceil\frac{ln\left[\frac{\rho(\phi-1)}{\phi(\rho-1)}\right]}{ln\left[\frac{a}{1-b}\right]}\right\rceil$
where $n_i$ = number of testing iterations necessary to achieve $\rho$, the
desired positive predictive value, a = sensitivity, b = specificity, $\phi$ =
disease prevalence and $k$ = constant. Based on the aforementioned derivation,
we provide reference tables for the number of test iterations needed to obtain
a $\rho(\phi)$ of 50, 75, 95 and 99$\%$ as a function of various levels of
sensitivity, specificity and disease prevalence.
