Some contributions to nonparametric and semiparametric inference for clustered and multistate data.

This dissertation is composed of research projects that involve methods which can be broadly classified as either nonparametric or semiparametric. Chapter 1 provides an introduction of the problems addressed in these projects, a brief review of the related works that have done so far, and an outline of the methods developed in this dissertation. Chapter 2 describes in details the first project which aims at developing a rank-sum test for clustered data where an outcome from group in a cluster is associated with the number of observations belonging to that group in that cluster. Chapter 3 proposes the use of pseudo-value regression (Andersen, Klein, and Rosthøj, 2003) in combination with penalized and latent factor regression techniques for prediction of future state occupation in a multistate model based on high dimensional baseline covariates. Chapter 4 describes the development of an R package involving various rank based tests for clustered data which are useful in situations where the number of outcomes in a cluster or in a particular group within a cluster is informative. Chapter 5 explains the fouth project which aims at developing a covariate-adjusted rank-sum test for clustered data through alingned rank transformation

Robust Testing of Paired Outcomes Incorporating Covariate Effects in Clustered Data with Informative Cluster Size

Paired outcomes are common in correlated clustered data where the main aim is to compare the distributions of the outcomes in a pair. In such clustered paired data, informative cluster sizes can occur when the number of pairs in a cluster (i.e., a cluster size) is correlated to the paired outcomes or the paired differences. There have been some attempts to develop robust rank-based tests for comparing paired outcomes in such complex clustered data. Most of these existing rank tests developed for paired outcomes in clustered data compare the marginal distributions in a pair and ignore any covariate effect on the outcomes. However, when potentially important covariate data is available in observational studies, ignoring these covariate effects on the outcomes can result in a flawed inference. In this article, using rank based weighted estimating equations, we propose a robust procedure for covariate effect adjusted comparison of paired outcomes in a clustered data that can also address the issue of informative cluster size. Through simulated scenarios and real-life neuroimaging data, we demonstrate the importance of considering covariate effects during paired testing and robust performances of our proposed method in covariate adjusted paired comparisons in complex clustered data settings

Bundle formation in parallel aligned polymers with competing interactions

Aggregation of like-charged polymers is widely observed in biological and soft matter systems. In many systems, bundles are formed when a short-range attraction of diverse physical origin like charge-bridging, hydrogen-bonding or hydrophobic interaction, overcomes the longer- range charge repulsion. In this Letter, we present a general mechanism of bundle formation in these systems as the breaking of the translational invariance in parallel aligned polymers with competing interactions of this type. We derive a criterion for finite-sized bundle formation as well as for macroscopic phase separation (formation of infinite bundles).Comment: accepted for publication in Europhys Let