A Bayesian non-inferiority approach using experts' margin elicitation - application to the monitoring of safety events

Abstract

Background: When conducing Phase-III trial, regulatory agencies and investigators might want to get reliable information about rare but serious safety outcomes during the trial. Bayesian non-inferiority approaches have been developed, but commonly utilize historical placebo-controlled data to define the margin, depend on a single final analysis, and no recommendation is provided to define the prespecified decision threshold. In this study, we propose a non-inferiority Bayesian approach for sequential monitoring of rare dichotomous safety events incorporating experts' opinions on margins.

Methods: A Bayesian decision criterion was constructed to monitor four safety events during a non-inferiority trial conducted on pregnant women at risk for premature delivery. Based on experts' elicitation, margins were built using mixtures of beta distributions that preserve experts' variability. Non-informative and informative prior distributions and several decision thresholds were evaluated through an extensive sensitivity analysis. The parameters were selected in order to maintain two rates of misclassifications under prespecified rates, that is, trials that wrongly concluded an unacceptable excess in the experimental arm, or otherwise.

Results: The opinions of 44 experts were elicited about each event non-inferiority margins and its relative severity. In the illustrative trial, the maximal misclassification rates were adapted to events' severity. Using those maximal rates, several priors gave good results and one of them was retained for all events. Each event was associated with a specific decision threshold choice, allowing for the consideration of some differences in their prevalence, margins and severity. Our decision rule has been applied to a simulated dataset.

Conclusions: In settings where evidence is lacking and where some rare but serious safety events have to be monitored during non-inferiority trials, we propose a methodology that avoids an arbitrary margin choice and helps in the decision making at each interim analysis. This decision rule is parametrized to consider the rarity and the relative severity of the events and requires a strong collaboration between physicians and the trial statisticians for the benefit of all. This Bayesian approach could be applied as a complement to the frequentist analysis, so both Data Safety Monitoring Boards and investigators can benefit from such an approach.

Keywords: Bayesian inference; Children; Clinical trial; Elicitation; Mixture model; Non-inferiority.

Conflict of interest statement

The authors declared declare that they have no competing interests with respect to the research, authorship, and/or publication of this article.

Figures

Fig. 1

General framework describing the two steps of the decision rule building. This figure summarizes the general framework, divided in two steps: 1 Fit margins from experts’ elicitation (Dj); 2 Sensitivity analysis to choose the prior and the decision thresholds

Fig. 2

Histogram of the acceptable difference of severe intraventricular haemorrhage between arms, and mixtures of Beta distributions fitted from experts’ elicitation, through 3 different methods, with their criteria for goodness of fit. The histogram represents the acceptable difference of IVH among the E experts (dj,e). The 3 lines represent the fits of this difference (Dj), obtained through the 3 different methods. The legend gives the parameters of the fits and their criteria for goodness of fit

Fig. 3

Plots of posterior class a and class b misclassifications according to the decision thresholds for each of the 13 pairs of priors for severe intraventricular haemorrhage. This figure represents the posterior rates of misclassifications for each pair of priors. Prior 1 is the non-informative prior, with α1,j=α0,j=β1,j=β0,j=1; Prior 2 to 13 are distinguished by (i) the means for the difference between the two arms: E(π1,j−π0,j)=0 for prior 2, 3, 4 and 5; E(π1,j−π0,j)=median(dj,e) for prior 6, 7, 8 and 9; and E(π1,j−π0,j)=π0,j for prior 10, 11, 12 and 13; (ii) their precision: 1 for prior 2, 6 and 10; 1/3 for prior 3, 7 and 11; 1/10 for prior 4, 8 and 12; and 1/20 for prior 5, 9 and 13. For each prior, the red solid line represents the number of posterior class a misclassifications (trials that conclude that the difference between arms is Unacceptable, while it is not true) at the final analysis, according to each final threshold. The blue solid line represents the number of posterior class b misclassifications (trials that conclude that the difference between arms is Acceptable, while it is not true)

Fig. 4

Distribution of the successive conclusions and errors, obtained by applying the decision rule to the 5000 simulated trials, at each interim analysis and in overall, for severe intraventricular haemorrhage. The left part of the plot represents the conclusions at each interim analysis. The right part represents the overall count of conclusions among the 11 analyses. The upper part of the plot represents the trials with an Acceptable difference between arms: orange area correspond to trials that conclude that the difference between arms is Acceptable, while it is true; red area correspond to trials that conclude that the difference between arms is Unacceptable, while it is not true (class a misclassifications). The bottom part of the plot represents the trials with an Unacceptable difference between arms: green area correspond to trials that conclude that the difference between arms is Unacceptable, while it is true; blue area correspond to trials that conclude that the difference between arms is Acceptable, while it is not true (class b misclassifications)

Fig. 5

Distribution of the overall conclusions and errors, obtained by applying the decision rule to the 5000 simulated trials, according to the event and the scenario. This plot presents the overall numbers or misclassifications obtained by applying this decision rule, according to the 5 scenario and to the 4 events. The left part of the plot represents the trials with an Acceptable difference between arms: orange area correspond to trials that conclude that the difference between arms is Acceptable, while it is true; red area correspond to trials that conclude that the difference between arms is Unacceptable, while it is not true (class a misclassifications). The right part of the plot represents the trials with an Unacceptable difference between arms: green area correspond to trials that conclude that the difference between arms is Unacceptable, while it is true; blue area correspond to trials that conclude that the difference between arms is Acceptable, while it is not true (class b misclassifications). IVH: Intraventricular haemorrhage; NEC: Necrotizing enterocolitis