AUXILIARY COVARIATE DATA IN FAILURE TIME REGRESSION

We consider the problem of missing covariate data in the context of ce nsored failure time relative risk regression. Auxiliary covariate data , which are considered informative about the missing data but which ar e not explicitly part of the relative risk regression model, may be av ailable. Full covariate information is available for a validation set. An estimated partial likelihood method is proposed for estimating rel ative risk parameters, This method is an extension of the estimated li kelihood regression analysis method for uncensored data (Pepe, 1992; P epe and Fleming, 1991). A key feature of the method is that it is nonp arametric with respect to the association between the missing and obse rved, including auxiliary, covariate components. Asymptotic distributi on theory is derived for the proposed estimated partial likelihood est imator in the case where the auxiliary or mismeasured covariates are c ategorical. Asymptotic efficiencies are calculated for exponential fai lure times using an exponential relative risk model. The estimated par tial likelihood estimator compares favourably with a fully parametric maximum likelihood analysis. Comparisons are also made with a standard partial likelihood analysis which ignores the incomplete observations . Important efficiency gains can be made with the estimated partial li kelihood method. Small sample properties are investigated through simu lation studies.