### Abstract

Binary response models are often applied in dose-response settings where the number of dose levels is limited. Commonly, one can find cases where the maximum likelihood estimation process for these models produces infinite values for at least one of the parameters, often corresponding to the 'separated data' issue. Algorithms for detecting such data have been proposed, but are usually incorporated directly into in the parameter estimation. Additionally, they do not consider the use of asymptotes in the model formulation. In order to study this phenomenon in greater detail, we define the class of specifiably degenerate functions where this can occur (including the popular logistic and Weibull models) that allows for asymptotes in the dose-response specification. We demonstrate for this class that the well-known pool-adjacent-violators algorithm can efficiently pre-screen for non-estimable data. A simulation study demonstrates the frequency with which this problem can occur for various response models and conditions.

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

Pages (from-to) | 2545-2556 |

Number of pages | 12 |

Journal | Journal of Statistical Computation and Simulation |

Volume | 84 |

Issue number | 12 |

DOIs | |

State | Published - 2014 |

### Fingerprint

### Keywords

- Abbott adjustment
- dose-response modelling
- infinite estimates
- maximum likelihood
- PAV-algorithm
- separated data

### ASJC Scopus subject areas

- Applied Mathematics
- Statistics and Probability
- Modeling and Simulation
- Statistics, Probability and Uncertainty

### Cite this

*Journal of Statistical Computation and Simulation*,

*84*(12), 2545-2556. https://doi.org/10.1080/00949655.2013.793344

**A pool-adjacent-violators-algorithm approach to detect infinite parameter estimates in one-regressor dose-response models with asymptotes.** / Deutsch, Roland C.; Habing, Brian; Piegorsch, Walter W.

Research output: Contribution to journal › Article

*Journal of Statistical Computation and Simulation*, vol. 84, no. 12, pp. 2545-2556. https://doi.org/10.1080/00949655.2013.793344

}

TY - JOUR

T1 - A pool-adjacent-violators-algorithm approach to detect infinite parameter estimates in one-regressor dose-response models with asymptotes

AU - Deutsch, Roland C.

AU - Habing, Brian

AU - Piegorsch, Walter W

PY - 2014

Y1 - 2014

N2 - Binary response models are often applied in dose-response settings where the number of dose levels is limited. Commonly, one can find cases where the maximum likelihood estimation process for these models produces infinite values for at least one of the parameters, often corresponding to the 'separated data' issue. Algorithms for detecting such data have been proposed, but are usually incorporated directly into in the parameter estimation. Additionally, they do not consider the use of asymptotes in the model formulation. In order to study this phenomenon in greater detail, we define the class of specifiably degenerate functions where this can occur (including the popular logistic and Weibull models) that allows for asymptotes in the dose-response specification. We demonstrate for this class that the well-known pool-adjacent-violators algorithm can efficiently pre-screen for non-estimable data. A simulation study demonstrates the frequency with which this problem can occur for various response models and conditions.

AB - Binary response models are often applied in dose-response settings where the number of dose levels is limited. Commonly, one can find cases where the maximum likelihood estimation process for these models produces infinite values for at least one of the parameters, often corresponding to the 'separated data' issue. Algorithms for detecting such data have been proposed, but are usually incorporated directly into in the parameter estimation. Additionally, they do not consider the use of asymptotes in the model formulation. In order to study this phenomenon in greater detail, we define the class of specifiably degenerate functions where this can occur (including the popular logistic and Weibull models) that allows for asymptotes in the dose-response specification. We demonstrate for this class that the well-known pool-adjacent-violators algorithm can efficiently pre-screen for non-estimable data. A simulation study demonstrates the frequency with which this problem can occur for various response models and conditions.

KW - Abbott adjustment

KW - dose-response modelling

KW - infinite estimates

KW - maximum likelihood

KW - PAV-algorithm

KW - separated data

UR - http://www.scopus.com/inward/record.url?scp=84906351330&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84906351330&partnerID=8YFLogxK

U2 - 10.1080/00949655.2013.793344

DO - 10.1080/00949655.2013.793344

M3 - Article

AN - SCOPUS:84906351330

VL - 84

SP - 2545

EP - 2556

JO - Journal of Statistical Computation and Simulation

JF - Journal of Statistical Computation and Simulation

SN - 0094-9655

IS - 12

ER -