A Priori Determination of the Pretest Probability

TL;DR

This work tackles the problem of estimating disease pretest probability $\phi$ a priori for accurate screening interpretation. It extends McGee's posttest heuristic into a logit-based framework, linking $\phi$ to the product of individual sign/ symptom likelihood ratios via $\phi \approx \frac{1}{5}\ln\left[\prod_{\theta} \kappa_\theta\right]$ and situating it within a Bayesian context that accommodates known and unknown test parameters. The paper surveys Bayesian and heuristic approaches to pretest probability, introduces a beta-binomial conjugate framework for uncertain $\phi$, and derives practical bounds (minimal and maximal) that can guide clinicians in evaluating the likelihood of disease before testing. The proposed a priori estimation aims to improve diagnostic decision-making by providing prevalence-independent, interpretable bounds that bridge pretest and posttest probabilities, potentially reducing misinterpretation of screening results in clinical practice.

Abstract

In this manuscript, we present various proposed methods estimate the prevalence of disease, a critical prerequisite for the adequate interpretation of screening tests. To address the limitations of these approaches, which revolve primarily around their a posteriori nature, we introduce a novel method to estimate the pretest probability of disease, a priori, utilizing the Logit function from the logistic regression model. This approach is a modification of McGee's heuristic, originally designed for estimating the posttest probability of disease. In a patient presenting with $n_θ$ signs or symptoms, the minimal bound of the pretest probability, $φ$, can be approximated by: $φ\approx \frac{1}{5}{ln\left[\displaystyle\prod_{θ=1}^{i}κ_θ\right]}$ where $ln$ is the natural logarithm, and $κ_θ$ is the likelihood ratio associated with the sign or symptom in question.