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.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty