Notes on misspecifying the random effects distribution regarding analysis under the AB/BA crossover trial in dichotomous data – a Monte Carlo evaluation

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Abstract
When patient responses are dichotomous under an AB/BA design, we commonly assume the normal random effects logistic regression model. This normality assumption for random effects is, however, unlikely to hold. Based on the maximum likelihood estimator, we apply Monte Carlo simulations to investigate the impact of misspecification on hypothesis testing and estimation because of the incorrect normal assumption for random effects. We find that Type I error is not affected by misspecifying the normal random effects distributions. We further find that the influence due to misspecifying distributions of random effects on power, bias and mean-squared-error, the coverage probability and the average length of the confidence interval is generally minimal when the variation of responses between patients is small and the number of patients per group is large. This influence can be substantial when the variation of responses between patients is large and the number of patients per group is small. Thus, the estimate of the required sample size or the accuracy of an interval estimator under the normal random effects assumption can be liberal. We use the data comparing a drug with placebo in treating cerebrovascular deficiency to illustrate the potential difference in inference between various random effects distributions considered here.

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