Semiparametric Marginal Regression Analysis for Dependent Competing Risks Under an Assumed Copula

Summary Competing risks problems arise in many fields of science, where two or more types of event may occur on a subject, but only the event occurring first is observed together with its occurrence time, and other events are censored. The marginal and joint distributions of event times for competing risks cannot be identified from the observed data without assuming the relationship between events. The commonly adopted independent censoring assumption may be easily violated. An alternative is to assume that the joint distribution of event times follows a known copula, which is an explicit function of the marginal distributions. On the basis of the latter assumption, we consider marginal regression analysis for dependent competing risks, with the marginal regressions performed via semiparametric transformation models, including the proportional hazards and proportional odds models. We propose a non-parametric maximum likelihood analysis, which provides explicit expressions for the score functions and information matrix, and facilitates convenient computations. Large and finite sample properties are studied. We report an illustration with data from an acquired immune deficiency syndrome clinical trial where the censoring may be dependent. The proposal can be readily used as a sensitivity analysis for assessing effects of potential dependent censoring and can incorporate external information on the association of competing risks.