43. Repeated Measures Binary Data (Cochran’s Q Test), (139 Patients)

With repeated observations in one patient, the paired property of the observations has to be taken into account because of the, generally, positive correlation between paired observations in one person. with two repeated observations Mc Nemar’s test is adequate (Chap. 41). However, with three or more observations Cochran’s Q test should be applied.

Is there a significant difference between the numbers of responders who have been treated differently three times.

In 139 patients three treatments are given in a three period crossover design. The scientific question was: is there a significant difference between the numbers of responders who have been treated differently three times.

The above table gives three paired observations in each patient (each row). The paired property of these observations has to be taken into account, because of the, generally, positive correlation between paired observations. Cochran’s Q test is appropriate for that purpose.

The data file is in extras.springer.com, and is entitled “chapter43repeatedmeasuresbinary”. Start by opening the data file in SPSS. For analysis the statistical model K Related Samples in the module Nonparametric Tests is required.

The above tables, in the output sheets show that the test is, obviously, highly significant with a p-value of 0,006. This means, that there is a significant difference between the treatment responses. However, we do not yet know where: between the treatments 1 and 2, 2 and 3, or between 1 and 3. For that purpose three separate McNemar’s tests have to be carried out.

The above output table shows that the difference between treatment 1 and 2 is statistically significant at p = 0,036. Subsequently, treatment 1 and 3, and 2 and 3 have to be tested against one another.

The above three separate McNemar’s tests show, that there is no difference between the treatments 2 and 3, but there are significant differences between 1 and 2, and 1 and 3. If we adjust the data for multiple testing, for example, by using p = 0,01 instead of p = 0,05 for rejecting the null-hypotheses, then the difference between 1 and 2 loses its significance, but the difference between treatment 1 and 3 remains statistically significant.

With repeated observations in one patient, the paired property of the observations has to be taken into account. With two repeated observations Mc Nemar’s test is adequate. However, with three or more observations Cochran’s Q test should be applied.

McNemar’s test for comparing two repeated binary outcomes is reviewed in the Chap. 41.