Testing for marginal covariate effect when the subgroup size induced by the covariate is informative

In many cluster-correlated data analyses, informative cluster size poses a challenge that can potentially introduce bias in statistical analyses. Different methodologies have been introduced in statistical literature to address this bias. In this study, we consider a complex form of informativeness where the number of observations corresponding to latent levels of a unit-level continuous covariate within a cluster is associated with the response variable. This type of informativeness has not been explored in prior research. We present a novel test statistic designed to evaluate the effect of the continuous covariate while accounting for the presence of informativeness. The covariate induces a continuum of latent subgroups within the clusters, and our test statistic is formulated by aggregating values from an established statistic that accounts for informative subgroup sizes when comparing group-specific marginal distributions. Through carefully designed simulations, we compare our test with four traditional methods commonly employed in the analysis of cluster-correlated data. Only our test maintains the size across all data-generating scenarios with informativeness. We illustrate the proposed method to test for marginal associations in periodontal data with this distinctive form of informativeness.