Survival modelling, missing values and frailty with application to cervical cancer data / Nuradhiathy Abd Razak

Data of cervical cancer patients treated in Hospital Universiti Sains Malaysia are analysed using the Cox proportional hazards regression analysis to model the prognostic factors. Since there is a non-proportional hazards covariate, the analysis is extended to the stratified Cox model. Also, parametric survival models including the Weibull, lognormal and log-logistic models are performed on the data. Among these parametric models, Weibull is the best. Then, a stratified Weibull model is performed because the proportional hazards assumption is violated. A comparison between the stratified Cox and stratified Weibull models shows that the stratified Cox model gives a better fit. Commonly, a complete case analysis is considered when there are missing values in a data set. This approach may reduce the sample size and power of the study. The performance of several methods for handling missing values is studied including the Expectation-Maximization (EM) algorithm by method of weight, hot deck, multiple imputation by chained equation with predictive mean matching (MICE-PMM) and complete case analysis methods for the Weibull data. The values are assumed missing at random (MAR). Simulation studies are performed, and the cervical cancer data is used for illustration. Overall, the EM algorithm by method of weight performs well compared to other methods. In survival data, there may exist unmeasured factors that also influence the survival and cause heterogeneity among individuals. This unobserved random effect is known as frailty. This study also focuses on the test for detecting frailty in a positive stable Gompertz model. The Zhu’s score test (Zhu, 1998), modified score test and ln s based test (Sarker, 2002) may also be derived from such a model. Thus, this study investigates the tests properties, and found that the modified score test performs better than the other tests based on the convergence rate and power of the test via simulation