Joint incorporation of randomised and observational evidence in estimating treatment effects

In evidence-based medicine, randomised trials are regarded as a gold standard in estimating relative treatment effects. Nevertheless, a potential gain in precision is forfeited by ignoring observational evidence. We describe a simple estimator that combines treatment estimates from randomised and observational data and investigate its properties by simulation. We show that a substantial gain in estimation accuracy, compared with the estimator based solely on the randomised trial, is possible when the observational evidence has low bias and standard error. In the contrasting scenario where the observational evidence is inaccurate, the estimator automatically discounts its contribution to the estimated treatment effect. Meta-analysis extensions, combining estimators from multiple observational studies and randomised trials, are also explored.