Sample size recommendations for studies on reliability and measurement error: an online application based on simulation studies

Simulation studies were performed to investigate for which conditions of sample size of patients (n) and number of repeated measurements (k) (e.g., raters) the optimal (i.e., balance between precise and efficient) estimations of intraclass correlation coefficients (ICCs) and standard error of measurements (SEMs) can be achieved. Subsequently, we developed an online application that shows the implications for decisions about sample sizes in reliability studies. We simulated scores for repeated measurements of patients, based on different conditions of n, k, the correlation between scores on repeated measurements (r), the variance between patients' test scores (v), and the presence of systematic differences within k. The performance of the reliability parameters (based on one-way and two-way effects models) was determined by the calculation of bias, mean squared error (MSE), and coverage and width of the confidence intervals (CI). We showed that the gain in precision (i.e., largest change in MSE) of the ICC and SEM parameters diminishes at larger values of n or k. Next, we showed that the correlation and the presence of systematic differences have most influence on the MSE values, the coverage and the CI width. This influence differed between the models. As measurements can be expensive and burdensome for patients and professionals, we recommend to use an efficient design, in terms of the sample size and number of repeated measurements to come to precise ICC and SEM estimates. Utilizing the results, a user-friendly online application is developed to decide upon the optimal design, as 'one size fits all' doesn't hold.