Clinical trials in critical care: can a Bayesian approach enhance clinical and scientific decision making?

Abstract

Recent Bayesian reanalyses of prominent trials in critical illness have generated controversy by contradicting the initial conclusions based on conventional frequentist analyses. Many clinicians might be sceptical that Bayesian analysis, a philosophical and statistical approach that combines prior beliefs with data to generate probabilities, provides more useful information about clinical trials than the frequentist approach. In this Personal View, we introduce clinicians to the rationale, process, and interpretation of Bayesian analysis through a systematic review and reanalysis of interventional trials in critical illness. In the majority of cases, Bayesian and frequentist analyses agreed. In the remainder, Bayesian analysis identified interventions where benefit was probable despite the absence of statistical significance, where interpretation depended substantially on choice of prior distribution, and where benefit was improbable despite statistical significance. Bayesian analysis in critical care medicine can help to distinguish harm from uncertainty and establish the probability of clinically important benefit for clinicians, policy makers, and patients.

Figure 1 –. Example Plot of Prior, Likelihood, and Posterior Distribution Using the Guérin (2013) “PROSEVA” Trial

This figure shows the prior (red curve), likelihood of observed data (green curve), and posterior (blue curve) plotted together with absolute risk reduction on the x-axis and probability density on the y-axis. The prior distribution is skeptical, centered at an absolute risk reduction of 0, with variance equivalent to a 400-person trial. The likelihood is centered at the observed absolute risk reduction of the trial and has lower variance than the prior because the trial enrolled 466 patients. The posterior combines the prior and likelihood, resulting in a compromise between skepticism (perhaps based on previous proning trials, or the broader context of clinical trials in ventilation) and the observed mortality reduction. Although the posterior distribution is attenuated relative to the data, the resulting posterior probability of exceeding the 4% minimum clinically important difference (blue shaded area) is 98%, providing strong evidence that proning is beneficial even if one is skeptical before seeing the data from Guérin et al. Similar plots with user-specified MCID and prior distributions are available for every trial in the analysis through the accompanying interactive app.

Figure 2 –. Probability of Clinical Benefit Versus P-value

This figure shows the relationship between the p-value and the posterior probability that the absolute risk reduction exceeds the minimum clinically relevant effect for each study. Each dot corresponds to a particular study. The color of the dot denotes agreement (blue) or potential disagreement (red) between frequentist and Bayesian analyses for that particular prior. Note that the blue dots in the quadrant with p-value < 0.05 and posterior probability of clinical benefit < 50% correspond to studies with p-value < 0.05 that showed harm. The posterior probability of exceeding the MCID increases as prior distributions shift from skeptical (left) to enthusiastic (right) but the p-values stay the same.