An Application of retrospective sampling in the analysis of a very large clustered data set

Abstract

Analysts may wish to expedite the analysis of a very large data set by examining a subsample of it. Such an analysis may seem relatively straightforward even when the data set consists of clusters of individuals with polytomous responses, together with covariates measured on the individuals and on the clusters. However, complications arise when a small fraction of these clusters contains rare, but important, responses. In this paper, we use retrospective sampling of the clusters to facilitate the analysis of the large data set while at the same time obtaining considerable information about rare outcomes. The data are then modelled employing weighted generalized estimating equations and a correspondingly weighted robust covariance structure. The analysis of a large set of data containing information on individuals in car accidents is used to demonstrate these techniques.

Keywords:

• Response-based sampling
• choice-based sampling
• case-control sampling
• marginal models
• overdispersion
• proportional-odds model
• robust estimator