3 Optimal crossover designs

A note on misspecification in general linear models with correlated errors for the analysis of crossover clinical trials

Among various approaches to the repeated measures analysis in crossover clinical trials, the general linear models (GLMs) with correlated errors attract substantial attention due to their simplicity in model specification, implementation, and interpretation. The goal of this research note is to conduct simulation studies to numerically investigate the impact of model misspecification in the GLMs with correlated errors in the analysis of crossover trials. A series of synthetic two-treatment and three-treatment crossover trials were designed, and simulation studies were conducted to assess how treatment effect estimation, type I error rates, and power can be affected by misspecified period effects, carryover effects, and variance-covariance structures in the GLMs. Numerical studies confirm that (i) the GLMs with terms for both carryover and period effects and with an unstructured variance-covariance matrix can provide unbiased treatment effect estimates and control of Type I error rates and that (ii) misspecification in either period effects, carryover effects, or covariance structures in the GLMs can induce inflated type I error, declined power, or biased treatment effect estimates. Although methodologic contribution of this research note is minimal, we provide practical recommendations and advice to pharmaceutical sponsors and other investigational drugs and device applicants in designing and analyzing crossover trials using the GLMs with correlated errors.

Improving academic self-efficacy, school connectedness, and identity in struggling middle school girls: a preliminary study of the REAL girls program

Girls struggling to be successful in middle school are often dealing with negative life experiences that affect their ability to achieve academically. Frequently, their academic failures and problem behaviors are associated with feeling overwhelmed by difficult and challenging life circumstances. In the absence of intervention, these patterns may contribute to girls chronically underperforming in school, dropping out of school, and becoming involved in delinquent and high-risk behaviors. This article describes a quasi-experimental, mixed-methods study of the REAL Girls program. REAL Girls was designed to help struggling middle school girls develop resilience--particularly academic self-efficacy, school connectedness, and identity--and achieve successful outcomes in school and life. In this study, using a crossover design, 48 girls identified as experiencing academic failure, school behavior problems, or truancy participated in one of two implementations of this 3-day intervention. Findings based on both quantitative and qualitative data suggest that REAL Girls contributed to positive increases in academic self-efficacy, school connectedness, and identity. Repeated measures analysis of variance and paired t tests suggest significant increases in each outcome variable, both immediately after program delivery and 2 weeks later, and effect size estimates suggest moderate to large program impact. Focus groups conducted 90 days after implementation of the program confirmed the quantitative findings and support the efficacy of the REAL Girls program and approach.

The construction of multi-factor crossover designs in animal husbandry studies

For ethical reasons it is important to try to obtain as much useful information as possible from an animal experiment whilst minimizing the number of animals used. Crossover designs, where applicable, provide an ideal framework for achieving this. If two or more treatment factors are included in the crossover design then the reduction in total animal usage can be considerable. In this paper we consider such designs, defined as multi-factor crossover designs. The designs are applicable when there are several different treatment factors, each at t levels, to be applied to the experimental units. The motivation for investigating these designs was a study conducted at GlaxoSmithKline to determine the preference of male and female dogs for t=5 different types of bed and t=5 different bedding conditions. A construction method is given for forming universally optimal designs for t not too large. Also given is an example for the special case where the number of treatment levels t=6.