Optimal Crossover Designs for Generalized Linear Models

Abstract

We identify locally D-optimal crossover designs for generalized linear models. We use generalized estimating equations to estimate the model parameters along with their variances. To capture the dependency among the observations coming from the same subject, we propose six different correlation structures. We identify the optimal allocations of units for different sequences of treatments. For two-treatment crossover designs, we show via simulations that the optimal allocations are reasonably robust to different choices of the correlation structures. We discuss a real example of multiple treatment crossover experiments using Latin square designs. Using a simulation study, we show that a two-stage design with our locally D-optimal design at the second stage is more efficient than the uniform design, especially when the responses from the same subject are correlated.for crossover experiments with responses under univariate GLMs, including binary, binomial, Poisson, Gamma, Inverse Gaussian responses, etc.Among different types of experiments that are available for treatment comparisons with multiple periods, the crossover designs are among the most important ones. In these experiments, every subject is exposed to a sequence of treatments over different time periods, i.e., subjects crossover from one treatment to another. One of the most important aspects of crossover designs is that we can get the same number of observations as other designs but with less number of subjects. This is an important consideration since human participants are often scarce in clinical trials. The order in which treatments are applied to subjects is known as a sequence and the time at which these sequences are applied is known as a period. In most of the cases, the main aim of such experiments is to compare t treatments over p periods. In each period, each subject receives a treatment, and the corresponding response is recorded. In different periods, a subject may receive different treatments, but treatment may also be repeated on the same subject. Naturally, crossover designs also provide within-subject information about treatment differences.Most of the research in the crossover design literature dealt with continuous response variables (see, for example, Kershner and Federer (1981), Laska and Meisner (1985), Matthews (1987), Carriere and Huang (2000), and the references therein). The problem of determining optimal crossover designs for continuous responses has been studied extensively (see, for example, Bose and Dey (2009), for a review of results). For examples of practical cases where the responses are discrete in nature, such as binary responses, one may refer to Jones and Kenward (2014) and Senn (2003). Among many fixed effects models proposed in the literature, the following linear model is used extensively to formulate crossover designs.where Y ij is the observation from the jth subject in the ith time period, with i = 1, . . . , p and j = 1, . . . , n. Here d(i, j) stands for the treatment assignment to the jth subject at time peri...

The work environment pilot: An experiment to determine the optimal office design for a technology company

“…This observation suggests that simply running an experiment on office design with employees may have a positive effect on enjoyment of the space, engagement, and occupancy. While this experimental design is noted to be be not as efficient as other designs [117], the advantages in overcoming commercial and logistic challenges make it a valuable tool in the practitioners toolkit.…”