  This work proposes a statistical model for crossover trials with multiple
skewed responses measured in each period. A 3 $\times$ 3 crossover trial data
where different drug doses were administered to subjects with a history of
seasonal asthma rhinitis to grass pollen is used for motivation. In each
period, gene expression values for ten genes were measured from each subject.
It considers a linear mixed effect model with skew normally distributed random
effect or random error term to model the asymmetric responses in the crossover
trials. The paper examines cases (i) when a random effect follows a skew-normal
distribution, as well as (ii) when a random error follows a skew-normal
distribution. The EM algorithm is used in both cases to compute maximum
likelihood estimates of parameters. Simulations and crossover data from the
gene expression study illustrate the proposed approach.
  Keywords: Crossover design, Mixed effect models, Skew-normal distribution, EM
algorithm.
