Contribution to the analysis of complex survey data and cluster-correlated biological data using inverse sampling

Abstract

This thesis addresses two main areas of statistical application. The first part of the thesis focuses on the analysis of complex survey data using inverse sampling. In the second part of the thesis some new ideas of analyzing cluster-correlated biological data are discussed. Part I of this thesis discusses various inverse sampling schemes, some theory of inverse sampling and explore its strengths and weaknesses. We propose an estimating equations approach for handling complex parameters, such as ratios and “census” regression parameters, which naturally extends to poststratification estimation. We also explore the use of inverse sampling analyses of categorical complex survey data. Inverse sampling methods for testing hypotheses using Wald and Quasi-score tests for complex survey data are also studied. The first part of Part II of this thesis discusses analyses of cluster-correlated biological data. We present some theory of the proposed methods and explore potential areas of application. In the second part of Part II of this thesis, we discuss some methods of analyzing cluster-correlated binary response data. Conditional logistic regression (CLR) method for analyzing cluster-correlated binary response data implicitly assumes that the dependence arising from random cluster effects is a nuisance and all unmeasured cluster-specific risk factors are aggregated into a cluster-specific baseline. It is however, invalid when these assumptions fail. We propose an alternative method to rectify these shortcomings: mean conditional estimating equation. Some properties and basic theory of the proposed method are discussed. The final chapter of Part II of this thesis discusses estimation methods for analyzing data having two types of correlation: within-cluster correlation and longitudinal correlation where the cluster sizes may be ignorable or nonignorable. We first study the effect on the efficiency of the regression parameter estimators when the assumed working correlation structures depart from the true correlation structure. Secondly, we demonstrate that methods that implicitly assume ignorable cluster sizes can lead to asymptotically invalid inferences when this assumption fails. We study properties of proposed alternative approaches that lead to asymptotically valid inferences when cluster sizes are ignorable or nonignorable. (Abstract shortened by UMI.)