Bayesian and Frequentist Approaches for Flexible Parametric Hazard-Based Regression Models with Generalized Log-logistic Baseline Distribution: An Application to Right-Censored Oncology Data Sets

Abstract

n general, parametric hazard-based regression models can be motivated by allow ing baseline distribution parameters to be affected by covariates. Furthermore, it is common practice to link covariates to a single parameter of interest; this method will be called a single parameter hazard-based regression (SPHBR) models. The role of the additional (covariate independent) parameters in these SPHBR models is frequently little more than to provide the model with enough generality to adjust to data. A more flexible technique is to regress these additional distributional pa rameters on covariates as well; this is referred to as multi-parameter hazard-based regression (MPHBR) models. The development of MPHBR models in the context of Bayesian survival analysis with particular interest towards application to right censored oncology data is the main focus of this thesis. Chapter 2 of this thesis examines the fundamentals of survival analysis as well as the methodologies employed to achieve the study’s objective; these are common and can be ignored by readers with familiarity with the field. A flexible generalized log logistic distribution that can incorporate both monotone and non-monotone hazard rates is developed in chapter 3 and examined using both Bayesian and classical in ference methods. Using the baseline distribution proposed in chapter 3, chapter 4 presents a flexible parametric proportional hazard (PH) model. The tractability of the PH model is shown, and the implications of the method are discussed, including how to interpret covariate effects (via the hazard ratio), how to perform proportion ality assumption checks on regression coefficients, and how to use Bayesian model selection techniques. To show how versatile the accelerated failure time (AFT) model is, chapter 5 presents an alternative parametric hazard-based regression model to the one presented in chapter 4. The parametric hazard-based regression mod els proposed in chapters 4 and 5 might not be accurate if crossovers exist in the xxxv hazard or survival functions. The accelerated hazard (AH) model, a novel flexi ble hazard-based regression model that can take into account survival data with crossover survival curves, is proposed in Chapter 6 of this thesis as a solution to this issue. The parameters of the proposed AH model are estimated using Bayesian and frequentist approaches. The need to enable parametric hazard-based regression models—and really any parametric survival regression model—more interpretable motivates the presentation of a general class of parametric hazard-based regression models in Chapter 7. Covariate effects on the baseline hazard are straightforward to interpret due to the proposed general class. The class also has the benefit of allowing for both proportional and time-independent effects of some covariates on baseline hazard and non-proportional and time-dependent effects of other covariates in the same model, unlike PH, AFT, or AH. For estimating the model parameters, both the Bayesian and frequentist approaches are applied. In chapter 8, the Amoud Class, a novel class of survival regression models that includes all hazard-based and odds-based models as special cases and is more flexible in modelling survival data, is introduced. The main advantage of the class is that it can provide users with a quantitative tool for selecting which of the seven often employed methods for hazard-based and odds-based regression models is more appropriate for a certain set of data. For each of the models proposed in chapters 3, 4, 5, 6, and 7, several simulations are run using a variety of parameter settings and data generation sce narios in order to evaluate the efficacy of the model’s estimators. To demonstrate the adaptability of the proposed survival regression models, applications of right censored oncology data sets are explored. Finally, in Chapter 9, we conclude the thesis with a discussion and mention of some future works.