Inference on the marginal distribution of clustered data with informative cluster size

TL;DR

This paper addresses the challenge of making inference on the marginal distribution of clustered data with informative cluster sizes, emphasizing nonparametric and robust methods, and providing a testing procedure with real-world application.

Contribution

It formally defines the problem of inference with informative cluster sizes and develops nonparametric, robust approaches along with a general testing procedure.

Findings

Developed a formal framework for informative cluster size inference.

Proposed a robust, nonparametric testing procedure for marginal distributions.

Illustrated methods with an example on spinal cord injury patients.

Abstract

In spite of recent contributions to the literature, informative cluster size settings are not well known and understood. In this paper, we give a formal definition of the problem and describe it from different viewpoints. Data generating mechanisms, parametric and nonparametric models are considered in light of examples. Our emphasis is on nonparametric and robust approaches to the inference on the marginal distribution. Descriptive statistics and parameters of interest are defined as functionals and they are accompanied with a generally applicable testing procedure. The theory is illustrated with an example on patients with incomplete spinal cord injuries.