MSc Stats Defence: Inference for cure fractions in process-based models

CANDIDATE:  RADIA TAISIR

ABSTRACT:

The first hitting time of a Wiener process to a boundary naturally leads to a lifetime model with cures and is known to follow an inverse Gaussian distribution. This thesis focuses on a first hitting time regression model for lifetime data with cures based on the defective inverse Gaussian distribution. Maximum likelihood estimation (MLE) of the model parameters is performed using the EM algorithm on the incomplete likelihood, which is written as a mixture model between those cured and those susceptible. Confidence intervals are obtained using two different methods: (i) delta method on the cure rate directly; and (ii) delta method on the log odds of being cured. Through simulation, the performance of the MLE and the confidence intervals is evaluated. The study results demonstrate that model parameters and the cure rate can be estimated with low bias, but confidence intervals for the cure rate had coverage probabilities below the nominal level of confidence.