### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 1256-1262 |

Number of pages | 7 |

Journal | Journal of the American Statistical Association |

Volume | 95 |

Issue number | 452 |

DOIs | |

State | Published - Dec 1 2000 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

}

*Journal of the American Statistical Association*, vol. 95, no. 452, pp. 1256-1262. https://doi.org/10.1080/01621459.2000.10474325

**A Robust Analysis of Crossover Designs using Multisample Generalized L-Statistics.** / Putt, Mary E.; Chinchilli, Vernon M.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A Robust Analysis of Crossover Designs using Multisample Generalized L-Statistics

AU - Putt, Mary E.

AU - Chinchilli, Vernon M.

PY - 2000/12/1

Y1 - 2000/12/1

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=0442278004&partnerID=8YFLogxK

U2 - 10.1080/01621459.2000.10474325

DO - 10.1080/01621459.2000.10474325

M3 - Article

AN - SCOPUS:0442278004

VL - 95

SP - 1256

EP - 1262

JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

SN - 0162-1459

IS - 452

ER -