Estimating Response Ratios from Continuous Outcome Data

Several methods for imputing the number of responders from summary continuous outcome data in randomized controlled trials exist. A method by Furukawa and others was used in the quite common case that only such summary continuous outcome measures, but not the actual numbers of responders, are reported in order to estimate response rates (probabilities) for different treatments and response ratios between treatments in such trials. The authors give some empirical justification, but encourage search for theoretical support and further empirical exploration. In particular, a problem that needs to be addressed is that randomness in baseline score is not taken into consideration. This will be done in the present paper. Assuming a binormal model for the data, we compare theoretically the true response rate for a single treatment arm to the theoretical response rate underlying two versions of the suggested imputation method. We also assess the performance of the method numerically for some choices of model parameters. We show that the method works satisfactorily in some cases, but can be seriously biased in others. Moreover, assessing the uncertainty of the estimates is problematic. We suggest an alternative Bayesian estimation procedure, based directly on the normal model, which avoids these problems and provides more precise estimates when applied to simulated data sets.