Bayesian Survival Analysis Using the rstanarm R Package

Abstract: Survival data is encountered in a range of disciplines, most notably health and medical research. Although Bayesian approaches to the analysis of survival data can provide a number of benefits, they are less widely used than classical (e.g. likelihood-based) approaches. This may be in part due to a relative absence of user-friendly implementations of Bayesian survival models. In this article we describe how the rstanarm R package can be used to fit a wide range of Bayesian survival models. The rstanarm package facilitates Bayesian regression modelling by providing a user-friendly interface (users specify their model using customary R formula syntax and data frames) and using the Stan software (a C++ library for Bayesian inference) for the back-end estimation. The suite of models that can be estimated using rstanarm is broad and includes generalised linear models (GLMs), generalised linear mixed models (GLMMs), generalised additive models (GAMs) and more. In this article we focus only on the survival modelling functionality. This includes standard parametric (exponential, Weibull, Gompertz) and flexible parametric (spline-based) hazard models, as well as standard parametric accelerated failure time (AFT) models. All types of censoring (left, right, interval) are allowed, as is delayed entry (left truncation), time-varying covariates, time-varying effects, and frailty effects. We demonstrate the functionality through worked examples. We anticipate these implementations will increase the uptake of Bayesian survival analysis in applied research.

• The paper demonstrates how Bayesian methods, via the rstanarm package, provide robust handling of survival data with complex censoring and time-varying effects.
• It highlights the use of various baseline hazard functions, such as exponential, Weibull, Gompertz, and spline-based models for flexible survival modeling.
• The study shows improved model fit and predictive accuracy using Hamiltonian Monte Carlo and leave-one-out cross-validation in real-world survival analyses.

Overview of Bayesian Survival Analysis Using the rstanarm R Package

The paper "Bayesian Survival Analysis Using the rstanarm R Package" by Samuel L. Brilleman, Eren M. Elci, Jacqueline Buros Novik, and Rory Wolfe presents a comprehensive guide to leveraging the Bayesian framework for survival analysis using the rstanarm package within the statistical environment R. As survival data is prevalent in health and medical research, the paper emphasizes the advantage of Bayesian methods over classical approaches, such as likelihood-based inference, typically employed in these analyses.

The foundation of the paper is the rstanarm package, which simplifies Bayesian regression modeling via an intuitive R syntax and the powerful Stan software for back-end estimation. This user-friendly interface allows researchers to specify models using standard R formula syntax, making Bayesian survival analysis more accessible. Stan operates via Hamiltonian Monte Carlo for full Bayesian inference, enhancing computational efficiency and robustness in posterior sampling.

Key Functionalities

The rstanarm package supports a broad range of survival models encapsulated by different baseline hazard functions. Parametric options include exponential, Weibull, and Gompertz models, alongside flexible parametric models using spline functions. The flexibility of rstanarm to accommodate various censoring types—left, right, interval—and delayed entry is particularly beneficial for applied survival research.

Model Specifications

One distinguishing characteristic of the package is its handling of time-varying covariates and effects. Time-varying effects are modeled via spline functions, enabling the depiction of non-proportional hazards, which are typically restrictive in classical models. The integration of multilevel survival models addresses clustering and frailty effects, crucial for data such as patient outcomes aggregated by hospitals or geographic regions.

Practical and Theoretical Implications

The paper's authors argue that the application of Bayesian methods in survival analysis provides intuitive probability statements and better handling of parameter uncertainty. For practical applications, the flexibility to model complex survival data structures, including clustering and time-varying effects, makes rstanarm a potent tool. The package's ability to generate survival predictions—from individual-specific predictions to standardised survival curves—shows its readiness for direct application in research involving prognostication and risk assessment.

Numerical Results and Comparison

The paper includes detailed examples showing the use of rstanarm to fit survival models, comparing various model specifications based on different baseline hazards and assessing model fit through metrics such as approximate leave-one-out cross-validation. These demonstrations illustrate the practical implementation of Bayesian survival analysis and further substantiate the utility of rstanarm in applied research, especially highlighting differences over classical models with numerical results.

Future Directions

The acknowledgement of ongoing developments within rstanarm, including joint modeling of longitudinal and survival data, forecasts continued evolution of the package. The authors point toward other potential expansions such as recurrent event models and competing risks, which would further enhance the package's capability to tackle diverse and complex datasets encountered in real-world survival analyses.

In conclusion, the paper effectively advocates for increased adoption of Bayesian survival analysis facilitated by rstanarm, encouraging researchers to leverage its expansive functionality to address sophisticated modeling challenges in survival data while benefiting from the interpretational clarity and robustness inherent in Bayesian methods.