Nonparametric Benchmark Dose Estimation with Continuous Dose-Response Data

Lizhen Lin, Walter W. Piegorsch and Rabi Bhattacharya

Scandinavian Journal of Statistics, 2015, vol. 42, issue 3, 713-731

Abstract: type="main" xml:id="sjos12132-abs-0001"> 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 ( μ ( d ) , σ 2 ) . No specific parametric form is imposed upon the mean μ(d), however. Instead, nonparametric maximum likelihood estimates of μ(d) and σ are obtained under a monotonicity constraint on μ(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.

Date: 2015
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