Nonparametric Benchmark Dose Estimation with Continuous Dose‐Response Data. (18th December 2014)

• Record Type: Journal Article
• Authors: Lin, Lizhen; Piegorsch, Walter W.; Bhattacharya, Rabi
• Is Part Of: Scandinavian journal of statistics. Volume 42:Number 3(2015:Sep.)
• Page Start: 713
• Page End: 731
• Publication Date: 2014-12-18
• Subjects: Statistics -- Periodicals; 310
• DOI: 10.1111/sjos.12132
• Languages: English
• ISSNs: 0303-6898

Abstract

<abstract abstract-type="main" id="sjos12132-abs-0001"> <title>Abstract</title> <p id="sjos12132-para-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 <italic>d</italic>, the observation <italic>X</italic>(<italic>d</italic>) is assumed to follow a normal distribution: <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj2ffwx15k" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:sjos:media:sjos12132:sjos12132-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi><mml:mrow><mml:mo fence="true" mathsize="1.19em">(</mml:mo><mml:mrow><mml:mi>μ</mml:mi><mml:mo>(</mml:mo><mml:mi>d</mml:mi><mml:mo>)</mml:mo><mml:mo>, </mml:mo><mml:msup><mml:mrow><mml:mi>σ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mo fence="true" mathsize="1.19em">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>. No specific parametric form is imposed upon the mean <italic>μ</italic>(<italic>d</italic>), however. Instead, nonparametric maximum likelihood estimates of <italic>μ</italic>(<italic>d</italic>) and <italic>σ</italic> are obtained under a monotonicity constraint on <italic>μ</italic>(<italic>d</italic>). For purposes of quantitative risk assessment, a 'hybrid' form of risk function is defined for any dose <italic>d</italic> as <italic>R</italic>(<italic>d</italic>) = <italic>P</italic>[<italic>X</italic>(<italic>d</italic>) < <italic>c</italic>], where <italic>c</italic> > 0 is a constant independent of <italic>d</italic>. The BMD is then determined by inverting the <italic>additional risk function</italic><italic>R</italic><sub><italic>A</italic></sub>(<italic>d</italic>) = <italic>R</italic>(<italic>d</italic>) − <italic>R</italic>(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.</p> </abstract>