Confidence Bands for Low‐Dose Risk Estimation with Quantal Response Data

Abstract

We study the use of simultaneous confidence bands for low-dose risk estimation with quantal response data, and derive methods for estimating simultaneous upper confidence limits on predicted extra risk under a multistage model. By inverting the upper bands on extra risk, we obtain simultaneous lower bounds on the benchmark dose (BMD). Monte Carlo evaluations explore characteristics of the simultaneous limits under this setting, and a suite of actual data sets are used to compare existing methods for placing lower limits on the BMD.

Simultaneous confidence bands for Abbott-adjusted quantal response models in benchmark analysis

“…This is particularly common under the cancer risk assessment paradigm highlighted by Al-Saidy et al [3]. When the data appear as proportions, say Y i /N i , it is common to assume that the parent distribution of each numerator Y i is binomial, with sample-size parameter N i (number of subjects tested).…”

“…The first form replaces F(d | β) with the Weibull c.d.f. yielding the following probability of response: (3) where 0 ≤β 0 < 1 and β 2 ≥ 1. This model is quite popular in cancer risk assessment and, expanding on the work of Al-Saidy et al [3], is a natural form to use within the context of our benchmark risk application.…”

“…yielding the following probability of response: (3) where 0 ≤β 0 < 1 and β 2 ≥ 1. This model is quite popular in cancer risk assessment and, expanding on the work of Al-Saidy et al [3], is a natural form to use within the context of our benchmark risk application. (The Weibull form is also popular in many non-cancer risk applications, however; see, e.g., [15] or [32].…”

“…In these cases, proper statistical practice obliges the user to apply some form of multiplicity correction in the calculation of the confidence limits (including adjustments for the case when decisions are made in a post hoc fashion), although to our knowledge this is not common. To overcome the multiplicity/post hoc problem, Al-Saidy et al [3] proposed methodology that allows a risk assessor to calculate a simultaneous (upper) 100(1 -α)% confidence band on an extra risk function and, using this band, to find simultaneous lower 100(1 -α)% confidence limits on any number of BMDs. That is, risk regulators can make a priori or a posteriori decisions on any number of benchmark responses for the agent under study and obtain simultaneous lower bounds on the exposure levels producing these benchmark responses.…”

“…In their study, Al-Saidy et al [3] focused on one specific form of dose-response model, the multistage model from carcinogenicity testing:…”