Nonparametric Benchmark Dose Estimation with Continuous Dose-Response Data

摘要

We propose a new method for risk-analytic benchmark dose (BMD) estimation in a dose-response setting when the responses are measured on a continuous scale. For each dose level d, the observation X(d) is assumed to follow a normal distribution: N((d),sigma 2). No specific parametric form is imposed upon the mean (d), however. Instead, nonparametric maximum likelihood estimates of (d) and sigma are obtained under a monotonicity constraint on (d). For purposes of quantitative risk assessment, a hybrid' form of risk function is defined for any dose d as R(d) = P[X(d) < c], where c > 0 is a constant independent of d. The BMD is then determined by inverting the additional risk functionR(A)(d) = R(d) - R(0) at some specified value of benchmark response. Asymptotic theory for the point estimators is derived, and a finite-sample study is conducted, using both real and simulated data. When a large number of doses are available, we propose an adaptive grouping method for estimating the BMD, which is shown to have optimal mean integrated squared error under appropriate designs.