Pattern mixture models for clinical validation of biomarkers in the presence of missing data.

Targeted therapies for cancers are sometimes only effective in a subset of patients with a particular biomarker status. In clinical development, the biomarker status is typically determined by an investigational-use-only/laboratory-developed test. A market ready test (MRT) is developed later to meet regulatory requirements and for future commercial use. In the USA, the clinical validation of MRT showing efficacy and safety profile of the targeted therapy in the biomarker subgroups determined by MRT is needed for pre-market approval. One of the major challenges in carrying out clinical validation is that the biomarker status per MRT is often missing for many subjects. In this paper, we treat biomarker status as a missing covariate and develop a novel pattern mixture model in the setting of a proportional hazards model for the time-to-event outcome variable. We specify a multinomial regression model for the missing biomarker statuses, and develop an expectation-maximization algorithm by the Method of Weights (Ibrahim, Journal of the American Statistical Association, 1990) to estimate the parameters in the regression model. We use Louis' formula (Louis, Journal of the Royal Statistical Society. Series B, 1982) to obtain standard errors estimates. We examine the performance of our method in extensive simulation studies and apply our method to a clinical trial in metastatic colorectal cancer.