## Introduction

Although not as popular as continuous and binary variables, count outcomes arise quite often in clinical research. For example, number of hospitalisations, number of suicide attempts, number of heavy drinking days and number of packs of cigarettes smoked per day are all popular count outcomes in mental health research. Studies yielding paired outcomes are also popular. For example, to evaluate new eye-drops, we can treat one eye of a subject with the new eye-drops and the other eye with a placebo drop. To evaluate skin cancer for truck drivers, we can compare skin cancer on the left arm with the right arm, since the left arm is more exposed to sunlight. To evaluate the stress of combat on Veterans’ health, we may use twins in which one is exposed to combat and the other is not, as differences observed with respect to health are likely attributable to combat experience. In a pre-post study, the effect of an intervention is evaluated by comparing a subject’s outcomes before (pre) and after (post) receiving the intervention. In all these studies, each unit of analysis has two outcomes arising from two different conditions. Interest is centred on the difference between the means of the two outcomes.

For continuous outcomes, the paired t-test is the standard statistical method for evaluating differences between the means. However, the paired t-test does not apply to non-continuous variables such as binary and count (frequency) outcomes. For binary outcomes, McNemar’s test is the standard. For count or frequency outcomes, there is not much discussion in the literature. Many use Wilcoxon’s signed-rank test because this method is applicable to paired non-continuous outcomes such as count responses. One major weakness of the signed-rank test is its limited power. As observations are converted to ranks and only ranks are used in the test statistic, the signed-rank test does not use all available information in the original data, leading to lower power when compared with tests that use all data. This is why t-tests are preferred and widely used to compare two independent groups for continuous outcomes.

With recent advances in statistical methodology, there are more options for comparing paired count responses. In this paper, we discuss some alternative procedures that use all information in the original data and thus generally provide more power than the signed-rank test. In the second section, we first provide a brief review of paired outcomes and methods for comparing continuous and binary paired outcomes. We then discuss the classic signed-rank test and modern alternatives for comparing paired count outcomes. In the third section, we compare different methods for comparing paired count outcomes using simulation studies. In the fourth section, we present our concluding remarks.