Bayesian statistical decision theory.

Analyzing life-time data with long-term survivors is an important topic in
medical application. Cure models are usually used to analyze survival data with the
proportion of cure subjects or long-term survivors. In order to include the propor-
tion of cure subjects, mixture and non-mixture cure models are considered. In this
dissertation, we utilize both maximum likelihood and Bayesian methods to estimate
model parameters. Simulation studies are carried out to verify the nite sample per-
formance of the estimation methods. Real data analyses are reported to illustrate
the goodness-of- t via Fr echet, Weibull and Exponentiated Exponential susceptible
distributions. Among the three parametric susceptible distributions, Fr echet is the
most promising.
Next, we extend the non-mixture cure model to include a change point in a covariate
for right censored data. The smoothed likelihood approach is used to address the
problem of a log-likelihood function which is not di erentiable with respect to the
change point. The simulation study is based on the non-mixture change point cure
model with an exponential distribution for the susceptible subjects. The simulation
results revealed a convincing performance of the proposed method of estimation.