A Dual Cox Model Theory And Its Applications In Oncology

Abstract

Given the prominence of targeted therapy and immunotherapy in cancer treatment, it becomes imperative to consider heterogeneity in patients' responses to treatments, which contributes greatly to the widely used proportional hazard assumption invalidated as in several clinical trials. To address the challenge, we develop a Dual Cox model theory including a Dual Cox model and a fitting algorithm. As one of the finite mixture models, the proposed Dual Cox model consists of two independent Cox models based on patients' responses to one designated treatment (usually the experimental one) in the clinical trial. Responses of patients in the designated treatment arm can be observed and hence those patients are known responders or non-responders. From the perspective of subgroup classification, such a phenomenon renders the proposed model as a semi-supervised problem, compared to the typical finite mixture model where the subgroup classification is usually unsupervised. A specialized expectation-maximization algorithm is utilized for model fitting, where the initial parameter values are estimated from the patients in the designated treatment arm and then the iteratively reweighted least squares (IRLS) is applied. Under mild assumptions, the consistency and asymptotic normality of its estimators of effect parameters in each Cox model are established. In addition to strong theoretical properties, simulations demonstrate that our theory can provide a good approximation to a wide variety of survival models, is relatively robust to the change of censoring rate and response rate, and has a high prediction accuracy and stability in subgroup classification while it has a fast convergence rate. Finally, we apply our theory to two clinical trials with cross-overed KM plots and identify the subgroups where the subjects benefit from the treatment or not.