Expert prior elicitation and Bayesian analysis of the Mycotic Ulcer Treatment Trial I

Abstract

Purpose: To perform a Bayesian analysis of the Mycotic Ulcer Treatment Trial I (MUTT I) using expert opinion as a prior belief.

Methods: MUTT I was a randomized clinical trial comparing topical natamycin or voriconazole for treating filamentous fungal keratitis. A questionnaire elicited expert opinion on the best treatment of fungal keratitis before MUTT I results were available. A Bayesian analysis was performed using the questionnaire data as a prior belief and the MUTT I primary outcome (3-month visual acuity) by frequentist analysis as a likelihood.

Results: Corneal experts had a 41.1% prior belief that natamycin improved 3-month visual acuity compared with voriconazole. The Bayesian analysis found a 98.4% belief for natamycin treatment compared with voriconazole treatment for filamentous cases as a group (mean improvement 1.1 Snellen lines, 95% credible interval 0.1-2.1). The Bayesian analysis estimated a smaller treatment effect than the MUTT I frequentist analysis result of 1.8-line improvement with natamycin versus voriconazole (95% confidence interval 0.5-3.0, P = 0.006). For Fusarium cases, the posterior demonstrated a 99.7% belief for natamycin treatment, whereas non-Fusarium cases had a 57.3% belief.

Conclusions: The Bayesian analysis suggests that natamycin is superior to voriconazole when filamentous cases are analyzed as a group. Subgroup analysis of Fusarium cases found improvement with natamycin compared with voriconazole, whereas there was almost no difference between treatments for non-Fusarium cases. These results were consistent with, though smaller in effect size than, the MUTT I primary outcome by frequentist analysis. The accordance between analyses further validates the trial results. (ClinicalTrials.gov number, NCT00996736.).

Keywords: Bayesian; clinical trial; corneal ulceration; fungal keratitis; statistics.

Figure 1

Plot of the individual and group expert prior distributions for the difference in 3-month visual acuity between topical natamycin and voriconazole for all filamentous (A), Fusarium (B), and non-Fusarium cases (C). Individual prior distributions were constructed from each individual's reported mean and 95% CrI (gray line). For display purposes, identical individual prior distributions were displaced slightly vertically in the figure. The group prior distribution was constructed by adding and then normalizing the 11 individual prior distributions using both the CrI method (red) and the histogram method (green). Individual prior distributions using the histogram method are not shown in the figure.

Figure 2

Plots of the prior distribution (red), the likelihood of MUTT I results (blue), and the posterior distribution (gold) for filamentous (A, B), Fusarium (C, D), and non-Fusarium (E, F) cases. The posterior distributions were calculated using Bayes' theorem by multiplying the prior distribution by the likelihood and normalizing. The subjective Bayesian analysis used the group prior distributions (A, C, E). The objective Bayesian analysis used priors derived from the Mycotic Ulcer Therapeutic Exploratory Trial results (B, D, F).