A finite sample comparison of nonparametric estimates of the effective dose in quantal bioassay

Abstract

To estimate the effective dose level ED α in the common binary response model, several parametric and nonparametric estimators have been proposed in the literature. In the present paper, we focus on nonparametric methods and present a detailed numerical comparison of four different approaches to estimate the ED α nonparametrically. The methods are briefly reviewed and their finite sample properties are studied by means of a detailed simulation study. Moreover, a data example is presented to illustrate the different concepts.

A Comparative Study of Parametric and Nonparametric Estimates of the Attributable Fraction for a Semi-continuous Exposure

“…The authors also compare their estimator with the LI estimator and found no clear ordering between the LI estimator and their estimator. Dette and Scheder (2010) conduct a detailed numerical comparison to estimate the effective dose in quantal bioassay for estimators of Dette et al (2005), Müller and Schmitt (1988), Park and Park (2006). The authors consider repeated and non-repeated measurement designs, and find in both cases the comparison of the estimates yields a similar picture.…”

“…A common strategy for choosing the bandwidth is to use leave-one-out cross validation, but it is also computationally intensive. Here we apply the rule of thumb proposed by Rice (1984) (see also Dette et al (2005), Dette and Scheder (2010), Müller and Schmitt (1988)…”

Recent progress in the nonparametric estimation of monotone curves—With applications to bioassay and environmental risk assessment

“…In the next section we provide outlines of a number of recent methods which yield asymptotically optimal rates of MISE and asymptotic variances for the estimation of F and F −1 . In particular, the recent nonparametric adaptive method NAM developed by the authors (Bhattacharya and Lin (2010), (2011), and Lin (2012)) and its smoother version SNAM introduced here are compared with an interesting kernel based methodology DNP due to Dette et al (2005) and Dette and Scheder (2010), and with cubic splines. All these methods attain asymptotically optimal MISEs under appropriate conditions.…”

“… Three recent nonparametric methodologies for estimating a monotone regression function F and its inverse F −1 are (1) the inverse kernel method DNP (Dette et al (2005), Dette and Scheder (2010)), (2) the monotone spline (Kong and Eubank (2006)) and (3) the data adaptive method NAM (Bhattacharya and Lin (2010), (2011)), with roots in isotonic regression (Ayer et al (1955), Bhattacharya and Kong (2007)). All three have asymptotically optimal error rates.…”

Testing for additivity in nonparametric quantile regression

“…In particular, we prove weak convergence of a standardized version of the statistic T n defined in (2.2) with different rates corresponding to the null hypothesis and fixed alternatives. For this discussion which is deferred to Section 3 we therefore recall the definition of an additive quantile regression estimate which has recently been introduced by Dette and Scheder (2010) and will be used throughout this paper for a test of an additive quantile regression. Let F (·|x) denote the conditional distribution function of Y j , given X j = x.…”