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Two-Tailed P-Values Calculation in Permutation-Based Tests: A Warning Against “Asymptotic Bias” in Randomized Clinical Trials

Fernando Pires Hartwig

The rapid developments in computer science worldwide are enabling the routine use of computation-intensive methods for statistical applications. Among such methods, the permutation method is of particular interest since it allows robust calculation (regarding test assumptions) of the P-value based on an empirical null distribution. Moreover, this approach fits well with the general design and rationale of randomized clinical trials, indicating the potential of such method for studies with this design. In this commentary, a discussion to clarify the inadequacy of applying asymptotic reasoning for calculating two-sided P-values for permutation-based tests is considered, since such mistake can be observed in modern teaching literature and is of great concern for cases when the empirical null distribution is asymmetric and/or the P-value is close to the pre-defined α level. Moreover, the suitability of permutation-based tests to analyze results from randomized clinical trials indicates that such mistake has to be stressed to the clinical research community in order to avoid incorrect analyses and misinterpretations of such studies.