Topics on estimating equations approaches for longitudinal binary outcomes with report bias
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Cocaine use is an important public health problem in the United States and throughout the world. It is associated with many medical consequences and psychosocial characteristics. Cognitive behavioral therapy (CBT) is an effective counseling intervention for supporting cocaine-dependent individuals through recovery and relapse prevention or reducing their cocaine use by improving patient's motivation and enabling them to recognize risky situations. Our motivating example from the Self-reported Cocaine use with Urine test (SCU) data was based on a study of the effect of Cognitive behavioral therapy (CBT) on cocaine dependence at the Primary Care Center of Yale-New Haven Hospital. To evaluate the impact of adding CBT to physician management on cocaine dependent patients receiving buprenorphone, patients were randomly assigned to the treatment group and the control group. Collected outcomes included self-reported daily drug uses and weekly urine test results. To date, Generalized Estimating Equations (GEE) are considered to be a reasonable approach to analyze the data with repeated measures binary outcomes. However, due to the existence of report bias in self-reported daily drug use, a direct application of GEE may not be valid for the SCU data. On the other hand, the less frequently measured urine test is considered more accurate. Therefore, we proposed Mean Corrected Generalized Estimating Equations (MCGEE) to estimate the treatment effect on self-reported binary outcomes. The urine test is used to detect the contamination and correct the model's mean in the equation. We demonstrated that the proposed approach yields consistent and asymptotically normally distributed estimators with unbiased contamination probability. However, we also noticed that when the time period for cocaine to be cleared from urine increased, the bias of the estimators of the MCGEE approach increased. Thus, we proposed to include a weight function of the contamination probability into the MCGEE and build Mean Corrected Weighted Generalized Estimating Equations (MCWGEE) to further control the potential bias of the estimators. Additionally, we also investigated the impacts of patients' dropouts in the SCU data using MCWGEE with an extra weight from the estimated probability of dropout at the time of attrition.