A count weighted Wilcoxon rank-sum test and application to medical data

The basic Wilcoxon rank-sum test is a nonparametric method that allows for the comparison of characteristics between two different populations. It is commonly used to analyze associations between a binary outcome (a population indicator) and the parameters of interest. However, when the binary outcome is transformed into a count variable (e.g. 0, 1, 2, 3…), the Wilcoxon test can still be applied to examine the association between the count variable and the dependent parameter in a nonparametric manner. This can be done by dichotomizing the count as zeros and non-zeros (or by using other thresholds). Nevertheless, this approach may result in a loss of information and potentially lower statistical power. To address this limitation, we propose a modification to the conventional test called the count weighted Wilcoxon test. This method utilizes all the available data without the need to create a binary variable. By assigning weights to the count variable, the count weighted method has the potential to increase the detection power of the test. In this way, we demonstrate the applicability of this new method to medical data, particularly when researchers are interested in analyzing associations between numerical and count variables.