The Permutation Distancing Test for dependent single-case observational AB-phase design data: A Monte Carlo simulation study

The Permutation Distancing Test (PDT) is a nonparametric test for evaluating treatment effects in dependent single-case observational design (SCOD) AB-phase data without linear trends. Monte Carlo methods were used to estimate the PDT power and type I error rate, and to compare them to those of the Single-Case Randomization Test (SCRT) assuming a randomly determined intervention point and the traditional permutation test assuming full exchangeability. Data were simulated without linear trends for five treatment effect levels (- 2, - 1, 0, 1, 2), five autocorrelation levels (0, .15, .30, .45, .60), and four observation number levels (30, 60, 90, 120). The power was calculated multiple times for all combinations of factor levels each generating 1000 replications. With 30 observations, the PDT showed sufficient power (≥ 80%) to detect medium treatment effects up to autocorrelation ≤ .45. Using 60 observations, the PDT showed sufficient power to detect medium treatment effects regardless of autocorrelation. With ≥ 90 observations, the PDT could also detect small treatment effects up to autocorrelation ≤ .30. With 30 observations, the type I error rate was 5-7%. With 60 observations and more, the type I error rate was ≤ 5% with autocorrelation < .60. The PDT outperformed the SCRT regarding power, particularly with a small number of observations. The PDT outperformed the traditional permutation test regarding type I error rate control, especially when autocorrelation increased. In conclusion, the PDT is a useful and promising nonparametric test to evaluate treatment effects in dependent SCOD AB-phase data without linear trends.