Imputing missing time-dependent covariate values for the discrete time Cox model

We describe a procedure for imputing missing values of time-dependent covariates in a discrete time Cox model using the chained equations method. The procedure multiply imputes the missing values for each time-period in a time-sequential manner, using covariates from the current and previous time-periods as well as the survival outcome. The form of the outcome variable used in the imputation model depends on the functional form of the time-dependent covariate(s) and differs from the case of Cox regression with only baseline covariates. This time-sequential approach provides an approximation to a fully conditional approach. We illustrate the procedure with data on diabetics, evaluating the association of their glucose control with the risk of selected cancers. Using simulations we show that the suggested estimator performed well (in terms of bias and coverage) for completely missing at random, missing at random and moderate non-missing-at-random patterns. However, for very strong non-missing-at-random patterns, the estimator was seriously biased and the coverage was too low. The procedure can be implemented using multiple imputation with the Fully conditional Specification (FCS) method (MI procedure in SAS with FCS statement or similar packages in other software, e.g. MICE in R). For use with event times on a continuous scale, the events would need to be grouped into time-intervals.