A robust analysis of crossover designs using multisample generalized L-statistics

In a crossover study, some or all subjects receive more than one treatment sequentially. Using a clinical example as motivation, we develop multisample generalized L-statistics (GL-statistics) to estimate and test for treatment effects in crossovers when the distribution of the response data deviates from normality. The basic idea is to adapt simple L-statistics, such as the trimmed mean and median, to data with dependencies. GL-statistics may be applied to crossovers with more than two periods and/or sequences. These designs are useful for experiments with two treatments in which carryover and treatment effects might be aliased in the commonly used two-period, two-sequence design, as well as for experiments with more than two treatments. For data analysis with large samples, the asymptotic properties of the GL-statistics suggest that the generalized trimmed mean and generalized median often should be strongly consistent and normal. A simulation study of a four-sequence, two-period crossover design found little loss in efficiency relative to a least squares approach when the trimmed mean or median is used with normal data, and substantial gains when the data are nonnormal, particularly for large sample sizes.