Dynamic Amplification of Risk-Estimate Bias Through Differential Detection: A Markov Model for History-Based Covariates

Abstract

History-based risk factors, such as known family history, recorded personal history, and documented regional history, are often treated as covariates. Because these variables depend on testing, diagnosis, and recording, their observed values are influenced by detection. However, monitoring data are often unavailable, making it difficult to distinguish true history effects from detection-driven associations. We study the feedback loop that arises when observed history affects future monitoring and future monitoring affects which histories become observed. Prostate cancer screening serves as a case in point: knowing a family history may raise awareness and increase testing compared with having no known history. We develop Markov models for true and observed history states and show that differential detection can distort both observed risk ratios and the distribution of the observed history variable, and can create an apparent history effect even when true event risk does not depend on history. With history-dependent true risk, the observed history process is generally not Markovian, although the joint true-observed process is. Uniform incomplete detection can attenuate true history effects by shifting individuals with missed events into less recent observed-history states. We also develop an inverse sensitivity-analysis framework that combines a published observed association, a baseline event probability, and plausible detection probabilities to obtain the implied true risk contrast. Numerical analyses illustrate the distortions, and a prostate cancer family-history example demonstrates the sensitivity calculation using external calibration values. The framework is intended for registry, electronic health record, and surveillance studies that use documented history as a risk factor.