Background/aims: The analyses of randomised controlled trials with missing data typically assume that, after conditioning on the observed data, the probability of missing data does not depend on the patient's outcome, and so the data are 'missing at random' . This assumption is usually implausible, for example, because patients in relatively poor health may be more likely to drop out. Methodological guidelines recommend that trials require sensitivity analysis, which is best informed by elicited expert opinion, to assess whether conclusions are robust to alternative assumptions about the missing data. A major barrier to implementing these methods in practice is the lack of relevant practical tools for eliciting expert opinion. We develop a new practical tool for eliciting expert opinion and demonstrate its use for randomised controlled trials with missing data.
Methods: We develop and illustrate our approach for eliciting expert opinion with the IMPROVE trial (ISRCTN 48334791), an ongoing multi-centre randomised controlled trial which compares an emergency endovascular strategy versus open repair for patients with ruptured abdominal aortic aneurysm. In the IMPROVE trial at 3 months post-randomisation, 21% of surviving patients did not complete health-related quality of life questionnaires (assessed by EQ-5D-3L). We address this problem by developing a web-based tool that provides a practical approach for eliciting expert opinion about quality of life differences between patients with missing versus complete data. We show how this expert opinion can define informative priors within a fully Bayesian framework to perform sensitivity analyses that allow the missing data to depend upon unobserved patient characteristics.
Results: A total of 26 experts, of 46 asked to participate, completed the elicitation exercise. The elicited quality of life scores were lower on average for the patients with missing versus complete data, but there was considerable uncertainty in these elicited values. The missing at random analysis found that patients randomised to the emergency endovascular strategy versus open repair had higher average (95% credible interval) quality of life scores of 0.062 (-0.005 to 0.130). Our sensitivity analysis that used the elicited expert information as pooled priors found that the gain in average quality of life for the emergency endovascular strategy versus open repair was 0.076 (-0.054 to 0.198).
Conclusion: We provide and exemplify a practical tool for eliciting the expert opinion required by recommended approaches to the sensitivity analyses of randomised controlled trials. We show how this approach allows the trial analysis to fully recognise the uncertainty that arises from making alternative, plausible assumptions about the reasons for missing data. This tool can be widely used in the design, analysis and interpretation of future trials, and to facilitate this, materials are available for download.
Keywords: Bayesian analysis; Missing data; clinical trials; expert elicitation; pattern-mixture models; quality of life; sensitivity analysis.