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 multisampl e generalized L-statistics (GL-statistics) to estimate and test for treatme nt effects in crossovers when the distribution of the response data deviate s from normality. The basic idea is to adapt simple L-statistics, such as t he trimmed mean and median, to data with dependencies. GL-statistics may be applied to crossovers with more than two periods and/or sequences. These d esigns are useful for experiments with two treatments in which carryover an d treatment effects might be aliased in the commonly used two-period, two-s equence design, as well as for experiments with more than two treatments. F or data analysis with large samples, the asymptotic properties of the GL-st atistics suggest that the generalized trimmed mean and generalized median o ften should be strongly consistent and normal. A simulation study of a four -sequence, two-period crossover design found little loss in efficiency rela tive to a least squares approach when the trimmed mean or median is used wi th normal data, and substantial gains when the data are nonnormal, particul arly for large sample sizes.