### Abstract

In clinical trials one traditionally models the effect of treatment on the mean response. The underlying assumption is that treatment affects the response distribution through a mean location shift on a suitable scale, with other aspects of the distribution (shape/dispersion/variance) remaining the same. This work is motivated by a trial in Parkinson's disease patients in which one of the endpoints is the number of falls during a 10-week period. Inspection of the data reveals that the Poisson-inverse Gaussian (PiG) distribution is appropriate, and that the experimental treatment reduces not only the mean, but also the variability, substantially. The conventional analysis assumes a treatment effect on the mean, either adjusted or unadjusted for covariates, and a constant dispersion parameter. On our data, this analysis yields a non-significant treatment effect. However, if we model a treatment effect on both mean and dispersion parameters, both effects are highly significant. A simulation study shows that if a treatment effect exists on the dispersion and is ignored in the modelling, estimation of the treatment effect on the mean can be severely biased. We show further that if we use an orthogonal parametrization of the PiG distribution, estimates of the mean model are robust to misspecification of the dispersion model. We also discuss inferential aspects that are more difficult than anticipated in this setting. These findings have implications in the planning of statistical analyses for count data in clinical trials.

Language | English |
---|---|

Pages | 333-342 |

Number of pages | 10 |

Journal | Biometrical Journal |

Volume | 61 |

Issue number | 2 |

Early online date | 12 Jul 2018 |

DOIs | |

Publication status | Published - Mar 2019 |

### Fingerprint

### Keywords

- Count data
- Dispersion modelling
- Parameter orthogonality
- Poisson-inverse Gaussian regression
- Profile likelihood confidence interval

### Cite this

*Biometrical Journal*,

*61*(2), 333-342. https://doi.org/10.1002/bimj.201700218

}

*Biometrical Journal*, vol. 61, no. 2, pp. 333-342. https://doi.org/10.1002/bimj.201700218

**Beyond mean modelling : bias due to misspecification of dispersion in Poisson-inverse Gaussian regression.** / Heller, Gillian Z.; Couturier, Dominique-Laurent; Heritier, Stephane R.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Beyond mean modelling

T2 - Biometrical Journal

AU - Heller, Gillian Z.

AU - Couturier, Dominique-Laurent

AU - Heritier, Stephane R.

PY - 2019/3

Y1 - 2019/3

N2 - In clinical trials one traditionally models the effect of treatment on the mean response. The underlying assumption is that treatment affects the response distribution through a mean location shift on a suitable scale, with other aspects of the distribution (shape/dispersion/variance) remaining the same. This work is motivated by a trial in Parkinson's disease patients in which one of the endpoints is the number of falls during a 10-week period. Inspection of the data reveals that the Poisson-inverse Gaussian (PiG) distribution is appropriate, and that the experimental treatment reduces not only the mean, but also the variability, substantially. The conventional analysis assumes a treatment effect on the mean, either adjusted or unadjusted for covariates, and a constant dispersion parameter. On our data, this analysis yields a non-significant treatment effect. However, if we model a treatment effect on both mean and dispersion parameters, both effects are highly significant. A simulation study shows that if a treatment effect exists on the dispersion and is ignored in the modelling, estimation of the treatment effect on the mean can be severely biased. We show further that if we use an orthogonal parametrization of the PiG distribution, estimates of the mean model are robust to misspecification of the dispersion model. We also discuss inferential aspects that are more difficult than anticipated in this setting. These findings have implications in the planning of statistical analyses for count data in clinical trials.

AB - In clinical trials one traditionally models the effect of treatment on the mean response. The underlying assumption is that treatment affects the response distribution through a mean location shift on a suitable scale, with other aspects of the distribution (shape/dispersion/variance) remaining the same. This work is motivated by a trial in Parkinson's disease patients in which one of the endpoints is the number of falls during a 10-week period. Inspection of the data reveals that the Poisson-inverse Gaussian (PiG) distribution is appropriate, and that the experimental treatment reduces not only the mean, but also the variability, substantially. The conventional analysis assumes a treatment effect on the mean, either adjusted or unadjusted for covariates, and a constant dispersion parameter. On our data, this analysis yields a non-significant treatment effect. However, if we model a treatment effect on both mean and dispersion parameters, both effects are highly significant. A simulation study shows that if a treatment effect exists on the dispersion and is ignored in the modelling, estimation of the treatment effect on the mean can be severely biased. We show further that if we use an orthogonal parametrization of the PiG distribution, estimates of the mean model are robust to misspecification of the dispersion model. We also discuss inferential aspects that are more difficult than anticipated in this setting. These findings have implications in the planning of statistical analyses for count data in clinical trials.

KW - Count data

KW - Dispersion modelling

KW - Parameter orthogonality

KW - Poisson-inverse Gaussian regression

KW - Profile likelihood confidence interval

UR - http://www.scopus.com/inward/record.url?scp=85050541313&partnerID=8YFLogxK

U2 - 10.1002/bimj.201700218

DO - 10.1002/bimj.201700218

M3 - Article

VL - 61

SP - 333

EP - 342

JO - Biometrical Journal

JF - Biometrical Journal

SN - 0323-3847

IS - 2

ER -