Missing covariate data in parametric survival analysis : modelling the missing data mechanism

Aims and Motivation To examine the effect of level of disability on the survival of children with cerebral palsy using a cohort taken from Bristol. The data is subject to, possibly not missing at random (NMAR), unobserved covariate data. Methods A joint survival model for the log-survival times and missing data mechanism is introduced. This approach enables us to model the missing data mechanism. This is then used to model the effect of level of ambulatory disability on survival in the cerebral palsy data. Extensions to the model are discussed to include continuous and multiple covariates. Results Analysis suggests that the effect of severe ambulation on survival in individuals with cerebral palsy is underestimated if no account is taken of the missing data mechanism. Simulations show that this model, under various distribution assumptions, performs well in comparison to basic exclusion techniques. Conclusions It is very important to consider the mechanism behind any missing data when studying survival. Slight deviances from the less restrictive assumptions can effect parameter estimates in survival models. In our data, we see an increased effect of severe ambulation on survival in those with cerebral palsy. A severe level of ambulatory disability causes a decrease in survival.