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.

Keywords:

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

Acknowledgements

Thanks are due to the Editor and the Associate Editor for their helpful comments on an earlier draft of this manuscript.