Robust Methods for Estimating the Intraclass Correlation Coefficient and for Analyzing Recurrent Event Data

Abstract

Robust statistics have emerged as a family of theories and techniques for estimating parameters of a model while dealing with deviations from idealized assumptions. Examples of deviations include misspecification of parametric assumptions or missing data; while there are others, these two deviations are the focus of this work. When unaccounted for, naive analysis with existing techniques may lead to biased estimators and/or undercovered confidence intervals. At the same time, research poured into clustered/correlated data is extensive and a large body of methods have been developed. Many works have already connected topics within robust statistics and correlated data, but a plethora of open problems remain. This dissertation investigates a few of these open problems. Chapter 1 combines second-order generalized estimating equations (GEE2), inverse probability weighting (IPW), and semiparametric theory in order to estimate the intraclass correlation coefficient (ICC) in the presence of informative missing data. Chapter 2 approaches linear models with correlated outcomes from the mixed models (MM) perspective instead of GEE. In addition to the estimation of 2nd moments, this framework also allows estimation of the skewness and kurtosis of the distributions of the random effects/subject-specific error terms and tests for normality in both the random effects and the error terms. Chapter 3 addresses analytical challenges in the unique structure of "evolving clustered randomized trials'' in HIV prevention trials. In evolving CRTs, subjects are socially/sexually linked to an index partner, provided intervention based on the randomized arm this index partner is assigned to, and followed until HIV infection occurs or the end of study. We view phylogenetically-linked partners over time as recurrent events to the index and assess the intervention effect through the use of recurrent event analysis. However, subjects may refuse to participate or drop-out, leading to a statistical problem of potentially informative missing and/or censored events in a recurrent event process. We address this issue with embedding IPW within the recurrent event estimating equations.