Simultaneous confidence bands for low‐dose risk estimation with quantal data

Abstract

Risk assessment studies where human, animal or ecological data are used to set safe low dose levels of a toxic agent are challenging as study information is limited to high dose levels of the agent. Simultaneous hyperbolic confidence bands for low-dose risk estimation with quantal data have been proposed in the literature. In this paper, a new method using three-segment confidence bands to construct simultaneous upper confidence limits on extra risks and simultaneous lower bounds on the benchmark dose for quantal data is proposed. The proposed method is illustrated with a real data application and simulation studies.

A Review of Recent Advances in Benchmark Dose Methodology

“…In most of the literature, estimation is based on relatively few parametric dose–response models, such as the multistage, log‐logistic, Weibull, Hill, and gamma models (Buckley & Piegorsch, ; Buckley, Piegorsch, & West, ; Fox, Hogan, & Davis, ; Kerns, ; Kopylev & Fox, ; Moon, Kim, Chen, George, & Kodell, ; Peng, Robichaud, & Alsubie, ; Shao & Small, ; Taft & Hines, ; West et al., ; Wheeler & Bailer, ). These models are biologically plausible and partly validated in the sense that they have been shown to fit and predict well in many cases.…”

Simultaneous confidence sets for several effective doses

“…Logistic regression has wide applications in dichotomous response studies, relating various stimuli to the probability of observing a response in a subject; see its application to medicine and biology statistics in Finney (), to quantitative risk and hazard assessment in Piegorsch, West, Pan and Kodell () and Peng, Robichaud and Alsubie (), and to drug dose response curves in Carter et al. () and Bretz, Hsu, Pinheiro and Liu ().…”

“…Logistic regression has wide applications in dichotomous response studies, relating various stimuli to the probability of observing a response in a subject; see its application to medicine and biology statistics in Finney (1971), to quantitative risk and hazard assessment in Piegorsch, West, Pan and Kodell (2005) and Peng, Robichaud and Alsubie (2015), and to drug dose response curves in Carter et al (1986) and Bretz, Hsu, Pinheiro and Liu (2008). A key goal in any such study is to identify the stimulus, usually the dose of a substance, needed to elicit a particular probability of response in a subject based on the logistic model, known as the Effective Dose (ED) or Lethal Dose.…”

Simultaneous confidence bands for log‐logistic regression with applications in risk assessment

“…Under the same model assumption, Peng et al. () studied the use of simultaneous three‐segment confidence bands on extra risk. Buckley et al.…”

“…Al-Saidy et al (2003) proposed the use of simultaneous hyperbolic confidence bands for low-dose risk estimation under the Armitage-Doll multistage model (Armitage and Doll, 1954) to ensure a valid 100(1 − α)% simultaneous inference due to the method's underlying simultaneity. Under the same model assumption, Peng et al (2015) studied the use of simultaneous three-segment confidence bands on extra risk. Buckley et al (2008) applied the method of hyperbolic bands in risk assessment under two other forms of dose-response model, the Abbott-adjusted Weibull model and the Abbottadjusted log-logistic model.…”