Semi-parametric accelerated failure time mixture cure model with partly interval-censored data

The accelerated failure time (AFT) model is an important alternative to the proportional hazards model in survival analysis. To accommodate a subpopulation who are not susceptible to the event of interest, an AFT mixture cure model can be used. Common limitations with existing research are that they are focused on right-censored survival data only and cannot estimate the baseline hazard function. This thesis uses Gaussian basis functions to approximate the nonparametric baseline hazard. By using maximum penalised likelihood (MPL) estimation, smooth estimates of the baseline hazard function can be obtained whilst estimating the regression parameters. The derived asymptotic properties also allow largesample inference to be made on regression parameters and hazard related quantities. Simulation studies are conducted to evaluate the model performance, which includes a comparative study with an existing method from the smcure R package. The results show that the MPL method generally performs better in the survival model across all sample sizes, whilst the smcure produces less outliers in the cure model when the sample size is small. A real case study involving melanoma recurrence is also carried out which illustrates the usage of the model and an R package is developed to implement the proposed method.