Mean corrected generalized estimating equations for longitudinal binary outcomes with report bias

Cocaine addiction is an important public health problem worldwide. Cognitive-behavioral therapy is a counseling intervention for supporting cocaine-dependent individuals through recovery and relapse prevention. It may reduce patients' cocaine uses by improving their motivations and enabling them to recognize risky situations. To study the effect of cognitive behavioral therapy on cocaine dependence, the self-reported cocaine use with urine test data were collected at the Primary Care Center of Yale-New Haven Hospital. Its outcomes are binary, including both the daily self-reported drug uses and weekly urine test results. To date, the generalized estimating equations are widely used to analyze binary data with repeated measures. However, due to the existence of significant self-report bias in the self-reported cocaine use with urine test data, a direct application of the generalized estimating equations approach may not be valid. In this paper, we proposed a novel mean corrected generalized estimating equations approach for analyzing longitudinal binary outcomes subject to reporting bias. The mean corrected generalized estimating equations can provide consistently and asymptotically normally distributed estimators under true contamination probabilities. In the self-reported cocaine use with urine test study, accurate weekly urine test results are used to detect contamination. The superior performances of the proposed method are illustrated by both simulation studies and real data analysis.