Evaluation and interpretation of results for three cross-over designs

Abstract

In cross-over designs, individual sequences of treatments are applied to the animals. Within such designs it is possible that every treatment could modify the effect of the subsequent treatment applied to the same animal. We compared three cross-over designs each with three treatments, three periods, and two blocks. This comparison was done with respect to the variance of the estimations of the effects and its biases caused by the interactions between the treatment and the carry over effect of the foregoing treatment. Moreover, different methods of estimating variance components and calculating the degrees of freedom were compared by means of simulation. If the animal variance component is small, then the bias of the REML estimator of the variance components is greater than one of the widespread ANOVA-estimator called 'TYPE3'. But nevertheless, the mean squared error of this estimation is smaller in the case of REML in comparison to ANOVA. Therefore, the REML method should be preferred. For calculating the degrees of freedom, the Kenward-Roger method should be used. After applying this method, the true significance level is almost equal to its required value, but if the Satterthwaite method is used, the true significance level will be too high. If the interaction (treatment × carry over) is ignored in the model although it exists, the standard error of the treatment effect estimation is too great, and, therefore, the true significance level is too small. The methods which have been evaluated are available in the SAS-procedure MIXED (<citeref rid="b9">SAS Institute, 1999a</citeref>). To assist the investigation of cross-over designs by using this software, we developed programs for data management and data analysis. These programs are available from the first author.