### Abstract

We compare and contrast several different methods for estimating the effect of treatment when responses are paired binomial observations. The ratio of binomial probabilities is the parameter of interest, while the binomial probabilities are nuisance parameters which may vary between pairs. The application is a meta-analysis of the treatment of rectal cancer, with observations in each study indicating the number of recurrences of the cancer in each of two groups, one with radiation therapy and one without. The ratio of the probabilities of recurrence in the radiation to non-radiation groups is of substantive interest, and is modelled as a logistic or complementary log-log function of an unknown linear combination of the covariates. The three methods we consider are maximum likelihood, a Bayesian approach and an approach based on estimating equations. For the MLE and Bayesian approach the potentially large number of nuisance parameters are estimated together with the parameters of interest, whereas for the estimating equation approach only the parameters of interest are estimated. A simulation study is performed to compare the methods and evaluate the impact of overdispersion.

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

Pages (from-to) | 3375-3390 |

Number of pages | 16 |

Journal | Statistics in Medicine |

Volume | 20 |

Issue number | 22 |

DOIs | |

State | Published - Nov 30 2001 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Epidemiology

### Cite this

*Statistics in Medicine*,

*20*(22), 3375-3390. https://doi.org/10.1002/sim.890

**Estimation for paired binomial data with application to radiation therapy.** / Taylor, Jeremy M G; Weiss, Robert E.; Li, Wenzhi; Hsu, Chiu-Hsieh; Suwinski, Rafal.

Research output: Contribution to journal › Article

*Statistics in Medicine*, vol. 20, no. 22, pp. 3375-3390. https://doi.org/10.1002/sim.890

}

TY - JOUR

T1 - Estimation for paired binomial data with application to radiation therapy

AU - Taylor, Jeremy M G

AU - Weiss, Robert E.

AU - Li, Wenzhi

AU - Hsu, Chiu-Hsieh

AU - Suwinski, Rafal

PY - 2001/11/30

Y1 - 2001/11/30

N2 - We compare and contrast several different methods for estimating the effect of treatment when responses are paired binomial observations. The ratio of binomial probabilities is the parameter of interest, while the binomial probabilities are nuisance parameters which may vary between pairs. The application is a meta-analysis of the treatment of rectal cancer, with observations in each study indicating the number of recurrences of the cancer in each of two groups, one with radiation therapy and one without. The ratio of the probabilities of recurrence in the radiation to non-radiation groups is of substantive interest, and is modelled as a logistic or complementary log-log function of an unknown linear combination of the covariates. The three methods we consider are maximum likelihood, a Bayesian approach and an approach based on estimating equations. For the MLE and Bayesian approach the potentially large number of nuisance parameters are estimated together with the parameters of interest, whereas for the estimating equation approach only the parameters of interest are estimated. A simulation study is performed to compare the methods and evaluate the impact of overdispersion.

AB - We compare and contrast several different methods for estimating the effect of treatment when responses are paired binomial observations. The ratio of binomial probabilities is the parameter of interest, while the binomial probabilities are nuisance parameters which may vary between pairs. The application is a meta-analysis of the treatment of rectal cancer, with observations in each study indicating the number of recurrences of the cancer in each of two groups, one with radiation therapy and one without. The ratio of the probabilities of recurrence in the radiation to non-radiation groups is of substantive interest, and is modelled as a logistic or complementary log-log function of an unknown linear combination of the covariates. The three methods we consider are maximum likelihood, a Bayesian approach and an approach based on estimating equations. For the MLE and Bayesian approach the potentially large number of nuisance parameters are estimated together with the parameters of interest, whereas for the estimating equation approach only the parameters of interest are estimated. A simulation study is performed to compare the methods and evaluate the impact of overdispersion.

UR - http://www.scopus.com/inward/record.url?scp=0035976599&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035976599&partnerID=8YFLogxK

U2 - 10.1002/sim.890

DO - 10.1002/sim.890

M3 - Article

C2 - 11746324

AN - SCOPUS:0035976599

VL - 20

SP - 3375

EP - 3390

JO - Statistics in Medicine

JF - Statistics in Medicine

SN - 0277-6715

IS - 22

ER -