Analysing the effects of anaemia on local recurrence of head and neck cancer when covariate values are missing

We present a case study in the analysis of the prognostic effects of anaemia and other covariates on the local recurrence of head and neck cancer in patients who have been treated with radiation therapy. Because it is believed that a large fraction of the patients are cured by the therapy, we use a failure time mixture model for the outcomes, which simultaneously models both the relationship of the covariates to cure and the relationship of the covariates to local recurrence times for subjects who are not cured. A problematic feature of the data is that two covariates of interest having missing values, so that only 75 per cent of the subjects have complete data. We handle the missing-data problem by jointly modelling the covariates and the outcomes, and then fitting the model to all of the data, including the incomplete cases. We compare our approach to two traditional methods for handling missingness, that is, complete-case analysis and the use of an indicator variable for missingness. The comparison with complete-case analysis demonstrates gains in efficiency for joint modelling as well as sensitivity of some results to the method used to handle missing data. The use of an indicator variable yields results that are very similar to those from joint modelling for our data. We also compare the results obtained for the mixture model with results obtained for a standard (non-mixture) survival model. It is seen that the mixture model separates out effects in a way that is not possible with a standard survival model. In particular, conditional on other covariates, we find strong evidence of an association between anaemia and cure, whereas the evidence of an association between anaemia and time to local recurrence for patients who are not cured is weaker.