Background Missing data are an unavoidable problem in clinical trials. Most existing missing data approaches assume the missing data are missing at random. However, the missing at random assumption is often questionable when the real causes of missing data are not well known and cannot be tested from observed data. Methods We propose a specific missing not at random assumption, which we call masked missing not at random, which may be more plausible than missing at random for masked clinical trials. We formulate models for categorical and continuous outcomes under this assumption. Simulations are conducted to examine the finite sample performance of our methods and compare them with other methods. R code for the proposed methods is provided in supplementary materials. Results Simulation studies confirm that maximum likelihood methods assuming masked missing not at random outperform complete case analysis and maximum likelihood assuming missing at random when masked missing not at random is true. For the particular missing at random model where both of missing at random and masked missing not at random are satisfied, theory suggests that maximum likelihood assuming missing at random is at least as efficient as maximum likelihood assuming masked missing not at random. However, maximum likelihood assuming masked missing not at random is nearly as efficient as maximum likelihood assuming missing at random in our simulated settings. We also applied our methods to the TRial Of Preventing HYpertension study. The missing at random estimated treatment effect and its 95% confidence interval are robust to deviations from missing at random of the form implied by masked missing not at random. Conclusion Methods based on the masked missing not at random assumption are useful for masked clinical trials, either in their own right or to provide a form of sensitivity analysis for deviations from missing at random. Missing at random analysis might be favored on grounds of efficiency if the estimates based on masked missing not at random and missing at random are similar, but if the estimates are substantially different, the masked missing not at random estimates might be preferred because the mechanism is more plausible.