In many clinical trials for chronic conditions a run-in period is used prior to randomization. Often, only those participants who meet certain criteria during the run-in phase go on to get randomized. The others, along with the information that they might have provided, are excluded from the study. This exclusion of the relevant response data from any subsequent study analysis can be considered as resulting in missing data; although quite common in practice, this approach has expectedly been shown to create a bias in favor of the active treatment when this active treatment is used during the run-in. Hence, many randomized clinical trials report overly optimistic results, with the extent of the bias depending in large part on how many otherwise eligible subjects were excluded due to the use of the run-in. If these biased trials are to contribute valid information to medical decision making, then the biases need to be corrected, and this involves accounting for all participants who were intended to be randomized. We propose specific imputation methods for doing so.