Flexible parametric survival models with time-dependent covariates for right censored data

Abstract

In survival studies the values of some covariates may change over time. It is natural to incorporate such time dependent covariates into the model to be used in the survival analysis. A standard approach is to use the semi parametric extended Cox proportional hazard model. An alternative is to extend a standard parametric model, such as a Weibull regression model, to include time-dependent covariates. However, the use of such simple parametric models may be too restrictive. Therefore in this thesis we further extend the Weibull regression model with time dependent covariates by using splines to give greater flexibility. The use of Cox, simple parametric and Weibull spline models is illustrated with and without time dependent covariates on two large survival data sets supplied by NHS Blood and Transplant. One data set involves times to graft failure of patients who have undergone a corneal transplant and contains many fixed covariates and one time-dependent covariate with at most one change point. The other data set concerns time to death of heart transplant patients and contains many fixed covariates and a time-dependent covariate with possibly many change points. A simulation study is used to evaluate and compare likelihood-based methods of inference for the competing models. In the first stage attention is focused on selection of the number of knots in the Weibull spline model in the simple case with no covariates. Stage two examines the results of inferences from the Weibull splines model with fixed covariates. Stage three compares the results of inferences for parameters in the extended Cox model and two simple parametric models with time-dependent covariates. Finally, stage four examines the Weibull splines model with time-dependent covariates.

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