Power analysis in randomized clinical trials based on item response theory

Patient relevant outcomes, measured using questionnaires, are becoming increasingly popular endpoints in randomized clinical trials (RCTs). Recently, interest in the use of item response theory (IRT) to analyze the responses to such questionnaires has increased. In this paper, we used a simulation study to examine the small sample behavior of a test statistic designed to examine the difference in average latent trait level between two groups when the two-parameter logistic IRT model for binary data is used. The simulation study was extended to examine the relationship between the number of patients required in each arm of an RCT, the number of items used to assess them, and the power to detect minimal, moderate, and substantial treatment effects. The results show that the number of patients required in each arm of an RCT varies with the number of items used to assess the patients. However, as long as at least 20 items are used, the number of items barely affects the number of patients required in each arm of an RCT to detect effect sizes of 0.5 and 0.8 with a power of 80%. In addition, the number of items used has more effect on the number of patients required to detect an effect size of 0.2 with a power of 80%. For instance, if only five randomly selected items are used, it is necessary to include 950 patients in each arm, but if 50 items are used, only 450 are required in each arm. These results indicate that if an RCT is to be designed to detect small effects, it is inadvisable to use very short instruments analyzed using IRT. Finally, the SF-36, SF-12, and SF-8 instruments were considered in the same framework. Since these instruments consist of items scored in more than two categories, slightly different results were obtained.