Using Bayesian statistics to estimate the likelihood a new trial will demonstrate the efficacy of a new treatment

Abstract

Abstract Background The common frequentist approach is limited in providing investigators with appropriate measures for conducting a new trial. To answer such important questions and one has to look at Bayesian statistics. Methods As a worked example, we conducted a Bayesian cumulative meta-analysis to summarize the benefit of patient-specific instrumentation on the alignment of total knee replacement from previously published evidence. Data were sourced from Medline, Embase, and Cochrane databases. All randomised controlled comparisons of the effect of patient-specific instrumentation on the coronal alignment of total knee replacement were included. The main outcome was the risk difference measured by the proportion of failures in the control group minus the proportion of failures in the experimental group. Through Bayesian statistics, we estimated cumulatively over publication time of the trial results: the posterior probabilities that the risk difference was more than 5 and 10%; the posterior probabilities that given the results of all previous published trials an additional fictive trial would achieve a risk difference of at least 5%; and the predictive probabilities that observed failure rate differ from 5% across arms. Results Thirteen trials were identified including 1092 patients, 554 in the experimental group and 538 in the control group. The cumulative mean risk difference was 0.5% (95% CrI: −5.7%; +4.5%). The posterior probabilities that the risk difference be superior to 5 and 10% was less than 5% after trial #4 and trial #2 respectively. The predictive probability that the difference in failure rates was at least 5% dropped from 45% after the first trial down to 11% after the 13th. Last, only unrealistic trial design parameters could change the overall evidence accumulated to date. Conclusions Bayesian probabilities are readily understandable when discussing the relevance of performing a new trial. It provides investigators the current probability that an experimental treatment be superior to a reference treatment. In case a trial is designed, it also provides the predictive probability that this new trial will reach the targeted risk difference in failure rates. Trial registration CRD42015024176 .

Keywords

• Meta-analysis
• Bayesian statistics
• Cumulative
• Direct probability
• Posterior probability
• Predictive probability