### Abstract

Mixed-effects linear regression models have become more widely used for analysis of repeatedly measured outcomes in clinical trials over the past decade. There are formulae and tables for estimating sample sizes required to detect the main effects of treatment and the treatment by time interactions for those models. A formula is proposed to estimate the sample size required to detect an interaction between two binary variables in a factorial design with repeated measures of a continuous outcome. The formula is based, in part, on the fact that the variance of an interaction is fourfold that of the main effect. A simulation study examines the statistical power associated with the resulting sample sizes in a mixed-effects linear regression model with a random intercept. The simulation varies the magnitude (Δ) of the standardized main effects and interactions, the intraclass correlation coefficient (ρ), and the number (k) of repeated measures within-subject. The results of the simulation study verify that the sample size required to detect a 2×2 interaction in a mixed-effects linear regression model is fourfold that to detect a main effect of the same magnitude.

Original language | English (US) |
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Pages (from-to) | 603-608 |

Number of pages | 6 |

Journal | Computational Statistics and Data Analysis |

Volume | 53 |

Issue number | 3 |

DOIs | |

State | Published - Jan 15 2009 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Computational Mathematics
- Computational Theory and Mathematics
- Statistics and Probability
- Applied Mathematics

### Cite this

*Computational Statistics and Data Analysis*,

*53*(3), 603-608. https://doi.org/10.1016/j.csda.2008.06.010

**Sample sizes required to detect interactions between two binary fixed-effects in a mixed-effects linear regression model.** / Leon, Andrew C.; Heo, Moonseong.

Research output: Contribution to journal › Article

*Computational Statistics and Data Analysis*, vol. 53, no. 3, pp. 603-608. https://doi.org/10.1016/j.csda.2008.06.010

}

TY - JOUR

T1 - Sample sizes required to detect interactions between two binary fixed-effects in a mixed-effects linear regression model

AU - Leon, Andrew C.

AU - Heo, Moonseong

PY - 2009/1/15

Y1 - 2009/1/15

N2 - Mixed-effects linear regression models have become more widely used for analysis of repeatedly measured outcomes in clinical trials over the past decade. There are formulae and tables for estimating sample sizes required to detect the main effects of treatment and the treatment by time interactions for those models. A formula is proposed to estimate the sample size required to detect an interaction between two binary variables in a factorial design with repeated measures of a continuous outcome. The formula is based, in part, on the fact that the variance of an interaction is fourfold that of the main effect. A simulation study examines the statistical power associated with the resulting sample sizes in a mixed-effects linear regression model with a random intercept. The simulation varies the magnitude (Δ) of the standardized main effects and interactions, the intraclass correlation coefficient (ρ), and the number (k) of repeated measures within-subject. The results of the simulation study verify that the sample size required to detect a 2×2 interaction in a mixed-effects linear regression model is fourfold that to detect a main effect of the same magnitude.

AB - Mixed-effects linear regression models have become more widely used for analysis of repeatedly measured outcomes in clinical trials over the past decade. There are formulae and tables for estimating sample sizes required to detect the main effects of treatment and the treatment by time interactions for those models. A formula is proposed to estimate the sample size required to detect an interaction between two binary variables in a factorial design with repeated measures of a continuous outcome. The formula is based, in part, on the fact that the variance of an interaction is fourfold that of the main effect. A simulation study examines the statistical power associated with the resulting sample sizes in a mixed-effects linear regression model with a random intercept. The simulation varies the magnitude (Δ) of the standardized main effects and interactions, the intraclass correlation coefficient (ρ), and the number (k) of repeated measures within-subject. The results of the simulation study verify that the sample size required to detect a 2×2 interaction in a mixed-effects linear regression model is fourfold that to detect a main effect of the same magnitude.

UR - http://www.scopus.com/inward/record.url?scp=56349157861&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=56349157861&partnerID=8YFLogxK

U2 - 10.1016/j.csda.2008.06.010

DO - 10.1016/j.csda.2008.06.010

M3 - Article

AN - SCOPUS:56349157861

VL - 53

SP - 603

EP - 608

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

SN - 0167-9473

IS - 3

ER -