Date on Master's Thesis/Doctoral Dissertation


Document Type

Master's Thesis

Degree Name



Bioinformatics and Biostatistics

Committee Chair

Kong, Maiying

Author's Keywords

2 x 2; Crossover; Linear


Multivariate analysis; Longitudinal method


Crossover design is a type of longitudinal study with each subject receiving different treatments in different time periods. It has been used frequently in the pharmaceutical industry and other medical fields to investigate the safety and efficacy of new drugs or new treatments. For crossover studies, the treatment effects from the earlier period may be carried over to the later period, which is called the carry-over effect, the response may naturally change over different periods. How to assess treatment effect with accounting for all these features deserves further investigation. Linear mixed-effects (LME) model has been widely applied to analyze data resulted from longitudinal studies. In this project, we model treatment effects, period effects, and carryover effects using the LME for 2x2 crossover studies, where all subjects are randomly assigned to two sequences, and each subject is treated subsequently with two treatments, the order of the treatments depends on its sequence. We first investigated the simple 2x2 design, where each subject has only one response measurement under each treatment. Extensive simulations were carried out to compare the performance between LME and the traditional Grizzle's method. We extend the LME to the general 2x2 crossover studies, where the response under each treatment is taking over different time point. We applied our model to an endothelial progenitor cell (EPC) study, where each patient was exposed to either air (placebo) first then airborne particular matters (PM) or PM first then air. In each exposure condition, the EPC cells were measured right before the exposure (Pre), right after the exposure (Post), and the second day follow-up (FU). The results obtained from LME and traditional methods are compared.