Semiparametric accelerated failure time model estimation with time-varying covariates
The semiparametric accelerated failure time model is a potential alternative to the popular Cox proportional hazards model, especially when the proportional hazards assumption is violated. The expression of an accelerated failure time model is simply in the form of a classical log-linear model, and is generalised to incorporate censored data. It enables direct interpretation of covariate effects on the natural logarithm of the survival time. However, the estimation of a semiparametric accelerated failure time model is in general difficult, particularly in computation. In this thesis, we propose a penalised likelihood estimation method for semiparametric accelerated failure time models in two situations. The first situation is the semiparametric accelerated failure time model with right-censored time-to-event data and time-varying covariates. The second situation is a more generalised situation of the first one, which is the semiparametric accelerated failure time model with partly interval-censored time-to-event data and time-varying covariates. In the estimation procedures for both situations, the Gaussian basis functions are adopted to build a smooth approximation of the nonparametric baseline hazard function. A roughness penalty is incorporated to further guarantee the smoothness in the likelihood. The constrained optimisation problems are solved using a combination of two algorithms. We conduct comprehensive simulations to demonstrate the performance of the proposed method, and apply the method in one real data application corresponding to the two situations mentioned above. The conclusion and some remarks are given at the end of the thesis.