Author ORCID Identifier

Year of Publication


Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation


Arts and Sciences



First Advisor

Dr. Solomon W. Harrar


In this dissertation, we investigate three distinct but interrelated problems for nonparametric analysis of clustered data and multivariate data in pre-post factorial design.

In the first project, we propose a nonparametric approach for one-sample clustered data in pre-post intervention design. In particular, we consider the situation where for some clusters all members are only observed at either pre or post intervention but not both. This type of clustered data is referred to us as partially complete clustered data. Unlike most of its parametric counterparts, we do not assume specific models for data distributions, intra-cluster dependence structure or variability, in effect addressing the so-called nonparametric Behrens-Fisher problem. A nonparametric measure of effect size is proposed. By constructing hypotheses based on the nonparametric effect size measure, the proposed test can eventually provide meaningful and interpretable probabilistic comparisons of treatments. The method accommodates continuous, ordered categorical and ordinal data seamlessly.

The second project focuses on nonparametric methods for multivariate data in a pre-post design where some of the samples are partially complete. This type of data can also be viewed as missing data where all the variables are missing at either pre or post intervention. Here also we derive asymptotic theory for estimating the vector of nonparametric effect size measures. The Wald-type statistic is proposed for large sample size and ANOVA-type statistic is proposed for small sample size. Apart from asymptotic evaluations, the Wald-type and ANOVA-type statistics are also shown to have good finite-sample performance in a variety of settings and missing patterns by a simulation study. The methods are further extended to the arbitrary missing pattern situation.

The third project is motivated by the Asthma Randomized Trial of Indoor Wood Smoke (ARTIS). The study involved a three-arm placebo controlled randomized trial on homes with wood burning stoves in a pre-post intervention design. The active treatments were aimed at improving functional, emotional and activity symptoms of children with asthma. In this project, nonparametric procedures are developed for the general pre-post clustered data collected in a factorial layout. Compared with the first project, the methods in this project are able to make comparisons across multiple treatments and between intervention periods. Here also, both complete and partially complete clusters are allowed. Simulation studies provide evidence that our method perform reasonably well in both large sample and small-sample settings. Therefore, the proposed nonparametric methods provide a new way of analyzing non-metric clustered data in factorial designs with repeated measures and is also a powerful competitor of the parametric mixed effects model for continuous outcomes.

Simulation studies provide evidence that our methods perform well in a wide variety of settings that involve small samples. Real datasets from two randomized trials are used to illustrate the application of the methods.

Digital Object Identifier (DOI)

Available for download on Sunday, September 04, 2022