Generalized Fiducial Inference for Threshold Estimation in Dose-Response and Regression Settings

In many biomedical experiments, such as toxicology and pharmacological dose-response studies, one primary goal is to identify a threshold value such as the minimum effective dose. This paper applies Fisher's fiducial idea to develop an inference method for these threshold values. In addition to providing point estimates, this method also offers confidence intervals. Another appealing feature of the proposed method is that it allows the use of multiple parametric relationships to model the underlying pattern of the data and hence, reduces the risk of model mis-specification. All these parametric relationships satisfy the qualitative assumption that the response and dosage relationship is monotonic after the threshold value. In practice, this assumption may not be valid but is commonly used in dose-response studies. The empirical performance of the proposed method is illustrated with synthetic experiments and real data applications. When comparing to existing methods in the literature, the proposed method produces superior results in most synthetic experiments and real data sets. Supplementary materials accompanying this paper appear on-line.