Efficient statistical inference for a parallel study with missing data by using an exact method

ABSTRACT

In a parallel group study comparing a new treatment with a standard of care, missing data often occur for various reasons. When the outcome is binary, the data from such studies can be summarized into a 2 × 3 contingency table, with the missing observations in the last column. When the missingness is neither related to the outcome of interest nor related to other outcomes from the study but it is covariate dependent with the sole covariate being treatment, this type of missing data mechanism is considered as missing at random. In 2016, Tian et al.  proposed three statistics to test the hypothesis that the response rate is equivalent for a parallel group study with missing data. The asymptotic limiting distributions of these test statistics were used for statistical inference. However, asymptotic approaches for testing proportions generally do not have satisfactory performance with regard to type I error rate control for a clinical trial with the sample size from small to medium. For this reason, we consider an exact approach based on maximization to provide valid and efficient statistical inference for a parallel group study with missing data. Exact approaches can guarantee the type I error rate and they are computationally feasible in this setting. We conduct extensive numerical studies to compare the performance of the exact approach based on the three statistics for a one-sided hypothesis testing problem. We conclude that the exact approach based on the likelihood ratio statistic is more powerful than the exact approach based on the other two statistics. Two real clinical trial data sets are used to illustrate the application of the proposed exact approach.

KEYWORDS:

• Data generating mechanism
• exact test
• one-sided test
• parallel study
• unconditional test

Acknowledgments

The authors are very grateful to Editor, Associate Editor, and referee for their insightful comments that helped to improve the manuscript. Dr. Shan’s research is partially supported by grants from the National Institute of General Medical Sciences from the National Institutes of Health: P20GM109025. Dr. Tian’s research was partially supported by a grant from National Natural Foundation of China (No. 11771199).

Additional information

Funding

Dr. Shan’s research is partially supported by grants from the National Institute of General Medical Sciences from the National Institutes of Health: [P20GM109025]. Dr. Tian’s research was partially supported by a grant from National Natural Foundation of China No. [11771199].