Sample size determination for assessing equivalence based on proportion ratio under a randomized trial with non-compliance and missing outcomes.

When a generic drug is developed, it is important to assess the equivalence of therapeutic efficacy between the new and the standard drugs. Although the number of publications on testing equivalence and its relevant sample size determination is numerous, the discussion on sample size determination for a desired power of detecting equivalence under a randomized clinical trial (RCT) with non-compliance and missing outcomes is limited. In this paper, we derive under the compound exclusion restriction model the maximum likelihood estimator (MLE) for the ratio of probabilities of response among compliers between two treatments in a RCT with both non-compliance and missing outcomes. Using the MLE with the logarithmic transformation, we develop an asymptotic test procedure for assessing equivalence and find that this test procedure can perform well with respect to type I error based on Monte Carlo simulation. We further develop a sample size calculation formula for a desired power of detecting equivalence at a nominal alpha-level. To evaluate the accuracy of the sample size calculation formula, we apply Monte Carlo simulation again to calculate the simulated power of the proposed test procedure corresponding to the resulting sample size for a desired power of 80 per cent at 0.05 level in a variety of situations. We also include a discussion on determining the optimal ratio of sample size allocation subject to a desired power to minimize a linear cost function and provide a sensitivity analysis of the sample size formula developed here under an alterative model with missing at random.