Abordagem bayesiana para um delineamento Crossover 2 × 2 com medidas repetidas: um estudo de simulação e dados reais

Abstract

In the designs crossover, the subjects receive all treatments from the study at different periods, according to the groups of sequences formed. Because the subjects act as their own control, carryover effects may be present in the model, making inferences about the effects of treatment difficult. In addition, repeated measures of the response variable can be taken over time, which allows the trends of responses to be examined and compared. However, measures taken in the same subject may be correlated thus, the objective of this work was to analyze the crossover design 2 × 2, with repeated measurements within the treatment period, the Bayesian approach to mixed models. The following were considered as fixed effects: treatments, periods, sequences, time, and simple interaction between time and treatment, the effect of the subject was considered as random through the mixed marginal model. A simulation study was conducted, considering three repeated measurements (Time effects) within each period, sample sizes of 20 and 100 subjects, two different coefficients of variation (5% and 20%), a difference between treatments of 1 and 2 standard errors (SE) between means and effects carryover equal to zero for each treatment. In addition, four scenarios were simulated considering effects carryover equal to 4SE Thus, 28 scenarios were simulated with 1000 repetitions in each one. Also, an application was also performed with real data from the area of pathophysiology, considering the median frequency of the right lateral gastrocnemius muscle to assess whether an exergaming protocol improves muscle activity in cancer patients. Bayesian estimates a posteriori of the model’s unknown parameters were obtained a priori under non- informative distributions, using the Gibbs sampler. The error type I rate about effects carryover difference test carryover was close to 10%, being smaller in most subject scenarios. The test of the effects of time tends to be liberal with samples of 20 subjects, while samples of 100 subjects it becomes exact at the level of significance of 5% and the power of the test were approximately 99% in the scenarios where it was considered 6SE of this effect. The proposed model presented good performance concerning the accuracy, mean square error, and accuracy of carryover effects estimates differences carryover in treatment and time effects, especially with samples of 100 subjects. In turn, when the carryover effects were equal to 4SE of the difference between means, the estimates were unbiased and there is no loss of accuracy, although there was estimates biased period effect. The result with the real data was consistent, approaching the simulated scenarios with treatment differences of 1SE and effect times of 0 and 1.