Sensitivity models for missing covariates in the analysis of survival data from multiple surveys

Using individual patient data from five independent surveys, we evaluate regional variations in survival in cerebral palsy. The influence of four important variables measuring disability, which are only partially observed for many cases, are analysed. Results are compared between a naive complete case analysis; a full likelihood model in which the covariates are assumed to be missing at random and in which each of the binary predictor variables are modelled as independent Bernoulli random variables; a model in which the covariates are modelled by a conditionalwise sequence, accommodating dependencies between the likelihoods of having various mixtures of disabilities; and a model in which the likelihood of a predictor variable being observed is allowed to depend on the value of the covariate itself (NMAR). Fully parametric survival regression models are used and analysis carried out in BUGS. Results suggest that proportions recorded as having severe visual or cognitive impairments are substantially lower than the actual proportions severely impaired. Associations between the likelihood of a particular covariate being recorded and the likelihood of a more severe disability imply that life expectancies for those who are very severely impaired may be up to 20% less than inferences based on complete case analyses.