We are provided with stroke audit data containing patient baseline measures and
5-year follow-up data for patients admitted to two Liverpool based hospitals with acute stroke between January and June 1996. Motivated by this data, we overview previous research on risk factors for survival post-stroke, and review methods for survival analysis and handling missing data.

Multiple imputation accounts for the additional uncertainty when handling
missing data, however following analysis of multiple imputed data, assessment
of model fit is complicated. We derive and justify formal and visual assessment
techniques for the proportional hazards assumption of a Cox regression model
fitted to multiply imputed data.

Multiple imputation using chained equations is a flexible approach for handling missing data, however misspecification of imputation model form can lead
to biased and restricted analyses. There is minimal research on handling nonproportional hazards within an imputation framework. We derive suitable imputation model forms to incorporate survival outcomes appropriately in the presence of non-proportional hazards, and ensure approximate compatibility with the analysis model.

On correcting analyses to account for non-proportional hazards, model fit is
rarely re-assessed in practice, with standard techniques inappropriate for nonstandard models. We develop formal and visual assessment techniques of the proportional hazards assumption for a survival model with a time-split, extending the work of Grambsch and Therneau (1994) and Winnett and Sasieni (2001).

Finally, we illustrate the methodological developments achieved within this thesis through application to the stroke audit data. Our analyses identify important risk factors for time to death following stroke, aiding in identification of stroke patients most at risk of death, both in the acute phase and long-term.