Addressing Loss of Efficiency Due to Misclassification Error in Enriched Clinical Trials for the Evaluation of Targeted Therapies Based on the Cox Proportional Hazards Model

A key feature of precision medicine is that it takes individual variability at the genetic or molecular level into account in determining the best treatment for patients diagnosed with diseases detected by recently developed novel biotechnologies. The enrichment design is an efficient design that enrolls only the patients testing positive for specific molecular targets and randomly assigns them for the targeted treatment or the concurrent control. However there is no diagnostic device with perfect accuracy and precision for detecting molecular targets. In particular, the positive predictive value (PPV) can be quite low for rare diseases with low prevalence. Under the enrichment design, some patients testing positive for specific molecular targets may not have the molecular targets. The efficacy of the targeted therapy may be underestimated in the patients that actually do have the molecular targets. To address the loss of efficiency due to misclassification error, we apply the discrete mixture modeling for time-to-event data proposed by Eng and Hanlon [8] to develop an inferential procedure, based on the Cox proportional hazard model, for treatment effects of the targeted treatment effect for the true-positive patients with the molecular targets. Our proposed procedure incorporates both inaccuracy of diagnostic devices and uncertainty of estimated accuracy measures. We employed the expectation-maximization algorithm in conjunction with the bootstrap technique for estimation of the hazard ratio and its estimated variance. We report the results of simulation studies which empirically investigated the performance of the proposed method. Our proposed method is illustrated by a numerical example.