Contributions to Nonparametric Testing in Clustered Data

Clustered data refers to a specific kind of correlated data where units within the same cluster are correlated while units from different clusters are independent. The number of units in each cluster, known as the cluster size, can be associated with the cluster’s outcome. This is known as the informative cluster size (ICS) and affects the inference drawn from clustered data. Recently, a hypothesis testing method has been developed to detect the presence of ICS. However, considering ICS alone may not be sufficient when comparing outcomes across multiple groups of units within clustered data. The size of a group within a cluster (intra-cluster group size) can also be correlated with the outcomes of that group within the cluster, leading to an informative intra-cluster group size (IICGS). IICGS can occur even without the presence of ICS in the data. In this dissertation, a statistical hypothesis testing method specifically designed to test for IICGS in clustered data is developed. Another chapter of this dissertation involves statistical method development for clustered ordinal data. There does not exist any method to test the association between two ordinal variables in a clustered data with ICS. To address this gap, a statistical hypothesis testing procedure is developed utilizing a marginalization principle. Through simulated and real data applications, the usefulness of the proposed methods is established.