Informed Bayesian survival analysis

Abstract

Background We provide an overview of Bayesian estimation, hypothesis testing, and model-averaging and illustrate how they benefit parametric survival analysis. We contrast the Bayesian framework to the currently dominant frequentist approach and highlight advantages, such as seamless incorporation of historical data, continuous monitoring of evidence, and incorporating uncertainty about the true data generating process. Methods We illustrate the application of the outlined Bayesian approaches on an example data set, retrospective re-analyzing a colon cancer trial. We assess the performance of Bayesian parametric survival analysis and maximum likelihood survival models with AIC/BIC model selection in fixed-n and sequential designs with a simulation study. Results In the retrospective re-analysis of the example data set, the Bayesian framework provided evidence for the absence of a positive treatment effect of adding Cetuximab to FOLFOX6 regimen on disease-free survival in patients with resected stage III colon cancer. Furthermore, the Bayesian sequential analysis would have terminated the trial 10.3 months earlier than the standard frequentist analysis. In a simulation study with sequential designs, the Bayesian framework on average reached a decision in almost half the time required by the frequentist counterparts, while maintaining the same power, and an appropriate false-positive rate. Under model misspecification, the Bayesian framework resulted in higher false-negative rate compared to the frequentist counterparts, which resulted in a higher proportion of undecided trials. In fixed-n designs, the Bayesian framework showed slightly higher power, slightly elevated error rates, and lower bias and RMSE when estimating treatment effects in small samples. We found no noticeable differences for survival predictions. We have made the analytic approach readily available to other researchers in the RoBSA R package. Conclusions The outlined Bayesian framework provides several benefits when applied to parametric survival analyses. It uses data more efficiently, is capable of considerably shortening the length of clinical trials, and provides a richer set of inferences.

A general approximation to nested Bayes factors with informed priors

“…Next, we compare the Savage-Dickey normal approximation to Laplace's method and bridge sampling for an informed Bayesian parametric survival analysis (Bartoš et al, 2022). We repeat Bartoš et. al.…”

“…The Savage-Dickey normal approximation is not without limitations. Specifically, the approximation does not apply to nonnested model comparison (e.g., different parametric families as in Bartoš et al, 2022). Also, the approximation assumes that the prior distributions on the nuisance parameters do not strongly impact the posterior distribution of the focal parameter.…”

“…al. (2022) full sample and sequential reanalysis of a colon cancer treatment trial that examined the potential increase in disease‐free survival due to adding Cetuximab to the standard sixth version of a FOLFOX regimen (Alberts et al, 2012).…”

“…The data set obtained from Project Data Sphere (Re3data.Org, 2019) contains 22.9% recurrences across 1247 participants in the standard treatment group and 22.9% recurrences across 1251 participants in the enhanced treatment group. We perform two analyses: (1) we specify an uninformed standard normal distribution on the log acceleration factors, , and (2) we specify an informed directional hypotheses test, , as performed by Bartoš et al (2022). Laplace's method should perform relatively well in the first scenario, with weak prior information, and relatively poorly in the second scenario, with strong prior information.…”

“…We focus solely on a log‐normal survival model that received the highest posterior model probability in the reanalysis. For the nuisance parameters, we use informed prior distributions as specified in Table 1 in Bartoš et al (2022).…”