Estimation of proportion ratio in non-compliance randomized trials with repeated measurements in binary data

It is not uncommon to encounter a randomized clinical trial (RCT) in which each patient is treated with several courses of therapies and his/her response is taken after treatment with each course because of the nature of a treatment design for a disease. On the basis of a simple multiplicative risk model proposed elsewhere for repeated binary measurements, we derive the maximum likelihood estimator (MLE) for the proportion ratio (PR) of responses between two treatments in closed form without the need of modeling the complicated relationship between patient’s compliance and patient’s response. We further derive the asymptotic variance of the MLE and propose an asymptotic interval estimator for the PR using the logarithmic transformation. We also consider two other asymptotic interval estimators. One is derived from the principle of Fieller’s Theorem and the other is derived by using the randomization-based approach suggested elsewhere. To evaluate and compare the finite-sample performance of these interval estimators, we apply the Monte Carlo simulation. We find that the interval estimator using the logarithmic transformation of the MLE consistently outperforms the other two estimators with respect to efficiency. This gain in efficiency can be substantial especially when there are patients not complying with their assigned treatments. Finally, we employ the data regarding the trial of using macrophage colony stimulating factor (M-CSF) over three courses of intensive chemotherapies to reduce febrile neutropenia incidence for acute myeloid leukemia patients to illustrate the use of these estimators.