Bias correction via outcome reassignment for cross-sectional data with binary disease outcome

Cross-sectionally sampled data with binary disease outcome are commonly analyzed in observational studies to identify the relationship between covariates and disease outcome. A cross-sectional population is defined as a population of living individuals at the sampling or observational time. It is generally understood that binary disease outcome from cross-sectional data contains less information than longitudinally collected time-to-event data, but there is insufficient understanding as to whether bias can possibly exist in cross-sectional data and how the bias is related to the population risk of interest. Wang and Yang (2021) presented the complexity and bias in cross-sectional data with binary disease outcome with detailed analytical explorations into the data structure. As the distribution of the cross-sectional binary outcome is quite different from the population risk distribution, bias can arise when using cross-sectional data analysis to draw inference for population risk. In this paper we argue that the commonly adopted age-specific risk probability is biased for the estimation of population risk and propose an outcome reassignment approach which reassigns a portion of the observed binary outcome, 0 or 1, to the other disease category. A sign test and a semiparametric pseudo-likelihood method are developed for analyzing cross-sectional data using the OR approach. Simulations and an analysis based on Alzheimer's Disease data are presented to illustrate the proposed methods.