From Test Performance to Risk-Based Effect Sizes: A Unified Wald-Type Framework to Design Clinical Validation Studies for Binary and Survival Outcomes

Abstract

Clinical validation studies of predictive tests are usually designed to focus on sensitivity ($Se$) and specificity ($Sp$), while statistical power is often calculated on regression-effect scales (e.g., risk ratio, hazard ratio). However, these quantities are statistically connected. Here, we provide closed-form links from sensitivity, specificity, and disease prevalence ($\pi$) to predictive risks, risk contrasts, and Wald-type variance, power, and sample-size formulas for binary and fixed-horizon survival outcomes. Analyses of statistical efficiency via C- and D-optimal principles demonstrate how prevalence and threshold choices affect study efficiency, supporting rapid decisions in preliminary studies and informing the design of subsequent, larger studies. Simulations show good calibration across most realistic scenarios; when events are rare and test effects are simultaneously very large, continuity and minimum-event corrections are needed to stabilize the approximation. We illustrate the framework with a case study describing use of the coronary artery calcium score for predicting incident cardiovascular disease in patients with type 2 diabetes mellitus. The formulas let investigators check power and required enrollment directly from $(Se,Sp,\pi)$, without running a separate simulation for each design candidate.