Proportional Hazard Regression Model Under Partly Interval-Censoring Assumption with Application to Prison Data

Abstract

In this thesis the analysis of well-known model in survival study that is Cox proportional hazard regression model via prison Partly Interval Censored (PIC) data is used. The maximum likelihood estimate was considered to obtain the estimated of the model parameter and the survival function and then the results were compared. In this model several imputation techniques are used that is; left point, mean and median. In contrast, the data needed to be modified to PIC data for the proposed of the researcher’s needs. Likewise, simulation data was generated where the failure rates were taken based on prison PIC data was also used to further compare these three imputation methods of estimation. From the prison data set and simulation study for this particular case, we can conclude that the Cox model proved to be feasible and works well in terms of estimation the survival function, likelihood ratio test and their P-value. In additional to that, based on imputation techniques, the mean and median showed better results with respect to estimate of the survival function.