Generalized survival models as a tool for medical research

In medical research, many studies with the time-to-event outcomes investigate the effect of an exposure (or treatment) on patients’ survival. For the analysis of time-to-event or survival data, model-based approaches have been commonly applied. In this thesis, a class of regression models on the survival scale, termed generalized survival models (GSMs previously described in Appendix A of [1]), and full likelihood-based estimation methods were presented along with four papers. The overall aim was to provide a rich and coherent framework for modelling either independent or correlated survival data.

Our main contributions to GSMs and related estimation approaches were as follows: First, we refined the mathematical and statistical backgrounds of the model components, including the link function, log-time, and smooth univariate functions. Second, we broadened the class to include generalized additive functional forms for representing covariate effects, such as non-linear forms, time-dependent effects, joint time-dependent and non-linear effects for age, and multivariate regression splines. Third, we introduced the thin plate regression splines [2], which can use knot free bases, as an alternative regression tool to knot-based regression splines into GSMs. Fourth, under a penalized likelihood framework, we integrated the process of parametric estimation and model selection for the number of spline basis functions. These refinements, extensions, and related assessments were undertaken in the first three papers. These newly proposed features of GSMs and estimation methods were implemented and integrated into the rstpm2 package in R.

This thesis consists of four research papers for modeling either independent or correlated survival data, together with either overall or net survival to be the measure of interest. In Paper I, the outcomes under study were independent time-to-death due to any cause (or time-to-any recurrence of disease). Parametric and penalized GSMs were introduced with extensions, simulation studies and applications. In Paper II, the outcome of interest was correlated time-to-some specific event due to any cause, such as time-to-event data collected from patients in the same clinics. It is reasonable to consider that the subjects within a cluster may share some unmeasured environmental or genetic risk factors, which are commonly modeled by a random effect b (or frailty U) and assumed to be independent of given baseline covariates. In this paper, GSMs with novel extensions were proposed to analyze correlated time-to-event data. In Paper III, we extended GSMs with novel features for relative survival analysis; the outcome of interest was time-to-death due to the disease under study. In Paper IV, we analyzed time-to-repeated event within the same subject using the proposed methods in Paper II and described the time-dependent cumulative risks of subsequent outcomes for men in different states since study entry.

In summary, these proposed methods performed well in extensive simulation studies under the investigated setting, with good point estimates and coverage probabilities. Through the analysis of example data sets, similar results can also be observed using the proposed methods and other well-established approaches, under proportional hazards or proportional odds models settings. Moreover, novel features were also illustrated in both simulations and applications. Generally, the combination of GSMs and full-likelihood based estimation methods can provide alternative tools for the analysis of survival data in medical research.

List of scientific papers

I. Xing-Rong Liu, Yudi Pawitan, Mark Clements. Parametric and penalized generalized survival models. Statistical Methods in Medical Research. 2016. [Accepted]
https://doi.org/10.1177/0962280216664760

II. Xing-Rong Liu, Yudi Pawitan, Mark Clements. Generalized survival models for correlated time-to-event data. Statistics in Medicine. [Accepted]
https://doi.org/10.1002/sim.7451

III. Xing-Rong Liu, Yudi Pawitan, Arvid Sjölander, Mark Clements. Use of knot-free splines in one and two dimensions for relative survival. 2017. [Manuscript]

IV. Xing-Rong Liu, Jan Adolfsson, Andreas Karlsson, Thorgerdur Palsdottir, Fredrik Wiklund, Henrik Grönberg, Mark Clements. Patterns of prostate-specific antigen (PSA) testing and subsequent outcomes. 2017. [Manuscript]