Date of Award


Document Type

Open Access Dissertation




The Norman J. Arnold School of Public Health

First Advisor

Jiajia Zhang


The proportional hazards (PH) model and the accelerated failure time (AFT) model are the two most popular survival models in fitting the right-censored data. The AFT model is a useful alternative to the PH model, particularly when the PH assumption is not satisfied. Usually, the linear association is assumed with logarithm of survival time in the AFT model. However, the nonlinear association may exist in practice. The first project aims to handle the nonlinear component in the AFT model, which is called the semiparametric additive partial accelerated failure time (AP-AFT) model. Two estimation methods based on the rank-smooth method and the profile likelihood method are proposed, along with the variance estimation.

The other interest situation in practice is heterogeneity among subjects, which may lead to the different baseline distribution of patients with different characteristics. The AFT mixture model with latent subgroup is investigated in the second project. The semiparametric estimation method is improved by the expectation-maximization (EM) algorithm with the profile likelihood estimation method.

In practice, there exists the cases where either the PH model or the AFT model is appropriate to capture the data characteristic. The extended hazards (EH) model is developed to capture more general forms in survival data, which includes the PH and AFT models as its special cases. With the development of medical research, more and more diseases can be cured. Thus, patients may not die from the disease even with enough follow up time. Mixture cure model is developed to handle the survival data with possible cure fraction. The concepts of mixture model have been adapted to the PH and AFT models. However, there are limited studies on its extension to the EH model.

The third and fourth projects aim to estimate the EH and EH mixture cure models with the monotone splines. The advantage of the monotone spline is that it can capture any shape of the survival function with the appropriate knots and degrees. The estimated survival curve is parametric, and the inference is easy.

All the above projects are studied through the comprehensive simulation studies. The appropriate data are used for illustration purposes. For example , Mayo primary biliary cirrhosis (PBC) data is used in the AP-AFT model, pregnancy data is applied in the AFT mixture model, Stanford heart transplant data is used in the EH model, the melanoma data from the ECOG phase III clinical trial E1684, and the leukemia data from bone marrow transplant study are used in the EH mixture cure model.

Included in

Biostatistics Commons