Two-part statistics with paired data

In epidemiology, we often study data from a mixed distribution, i.e. with a clump of observations at zero and positive continuous data. Lachenbruch developed statistics for this kind of data for independent samples. These tests are the sum of one test for equality of proportions of zero values and one conditional test for the continuous distribution. This paper concerns the adaptation of these tests to paired samples. Like Lachenbruch, we developed two statistics, which tend to a two-degree-of-freedom chi2 distribution. These two-part statistics are the sum of McNemar's test for testing the equality of proportions of zero values, and the Wilcoxon signed-rank test or the paired Student's test for testing the equality of the distribution of positive values. We studied the behaviour of these tests for various proportions of zeros, and mean values of the continuous distribution. All tests are efficient when the smaller proportion of zero values corresponds to the population with the larger mean. In all other situations, the two-part statistics are superior to the others. These methods are applied to a matched case-control study of lower limb venous insufficiency.