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Operational Characteristics of Hierarchical Generalized Pairwise Comparisons Test in the Presence of Missing Data (309952)

Keywords: Clinical trials, hierarchical endpoints, net benefit, statistical power, type-I error probability

The method of generalized pairwise comparisons (GPC) is a multivariate extension of the well-known non-parametric Wilcoxon-Mann-Whitney test that allows comparing two groups of observations based on multiple hierarchically ordered endpoints, regardless of their number or type (e.g., discrete, continuous, time to event). It provides a general measure of the difference between the groups called the ``net benefit', which quantifies the difference between the probabilities that a random observation from one group is doing better than an observation from the opposite group. The method offers a ``natural' way of handling missing data: whenever a comparison of two subjects is not possible for a higher-priority outcome due to missingness, the comparison is made using the next outcome in the hierarchy. However, it is unclear how this naïve way of dealing with missing data influences the type-I error probability and power of the test based on GPC. Theoretical considerations show that the expected value and the variance of the net benefit statistic depend, in a complicated manner, on the entire variance-covariance structure of the set of the outcomes and thresholds of clinical relevance. This presentation will look into the patterns in which all of these parameters, as well as various missingness mechanisms, influence the operational characteristics of the test.