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

Roland C. Deutsch, Brian Habing, Walter W Piegorsch

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)2545-2556
Number of pages12
JournalJournal of Statistical Computation and Simulation
Volume84
Issue number12
DOIs
StatePublished - 2014

Fingerprint

Asymptote
Dose-response
Adjacent
Binary Response Model
Estimate
Weibull Model
Logistic Model
Maximum Likelihood Estimation
Demonstrate
Parameter Estimation
Dose
Simulation Study
Model
Specification
Maximum likelihood estimation
Formulation
Parameter estimation
Logistics
Specifications
Class

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

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title = "A pool-adjacent-violators-algorithm approach to detect infinite parameter estimates in one-regressor dose-response models with asymptotes",
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.",
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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.

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