Cutoff Value for Wilcoxon-Mann-Whitney Test by Minimum P-value: Application to COVID-19 Data

Toru Ogura and Chihiro Shiraishi

International Journal of Statistics and Probability, 2022, vol. 11, issue 3, 1

Abstract: Dependent and independent variables may appear uncorrelated when analyzed in full range in medical data. However, when an independent variable is divided by the cutoff value, the dependent and independent variables may become correlated in each group. Furthermore, researchers often convert independent variables of quantitative data into binary data by cutoff value and perform statistical analysis with the data. Therefore, it is important to select the optimum cutoff value since performing statistical analysis depends on the cutoff value. Our study determines the optimal cutoff value when the data of dependent and independent variables are quantitative. The piecewise linear regression analysis divides an independent variable into two by the cutoff value, and linear regression analysis is performed in each group. However, the piecewise linear regression analysis may not obtain the optimal cutoff value when data follow a non-normal distribution. Unfortunately, medical data often follows a non-normal distribution. We, therefore, performed theWilcoxon-Mann-Whitney (WMW) test with two-sided for all potential cutoff values and adopted the cutoff value that minimizes the P-value (called minimum P-value approach). Calculating the cutoff value using the minimum P-value approach is often used in the log-rank and chi-squared test but not the WMW test. First, using Monte Carlo simulations at various settings, we verified the performance of the cutoff value for the WMW test by the minimum P-value approach. Then, COVID-19 data were analyzed to demonstrate the practical applicability of the cutoff value.

Date: 2022
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