Assessing equivalence or non-inferiority in screening tests with paired and independent binomial endpoints through confidence intervals for the odds ratio

The confidence interval (CI) on the population average (PA) odds ratio (OR) is a useful measure of agreement among different diagnostic methods when no gold standard is available. It can be calculated by the repeated measures logistic regression procedure (GENMOD, SAS). We compare the width of CIs from paired and independent samples with an identical number of measurements and an identical probability of positive response among them. For two and three diagnostic methods with binomial endpoints, the best performing sampling strategy is analytically described. The asymptotic formulae of the ratio of the CI widths for paired and independent samples are provided. We numerically study the dependence of the width of the CIs on the number of positive concordant outcomes. The width of CIs from independent samples is an increasing function of the sample size with a saturation asymptote and rather weak dependence on the argument. The width of CIs from paired samples is a decreasing function of the sample size with a saturation asymptote and significant dependence on the argument when the sample size is small. If curves for paired and independent samples intersect, a critical sample size exists. At this point, a small change in the sample size can reverse the choice of the best performing sampling policy. We numerically validated the robustness of the critical point to variations of the conditional OR. Published in 2005 by John Wiley & Sons, Ltd.