Kernel and Probit Estimates in Quantal Bioassay

Abstract A kernel method for the estimation of quantal dose-response curves is considered. In contrast to parametric modeling, this local smoothing method does not require any assumptions beyond smoothness of the dose-response curve and, in this sense, is nonparametric. In finite-sample situations, the kernel estimate of the dose-response curve is not necessarily monotone and, therefore, if the additional assumption of monotonicity of the dose-response curve is made, a monotonized version is discussed. Bias, variance, asymptotic normality, and uniform consistency, including rates of convergence of kernel estimates, are derived and applied to establish consistency and limiting distribution of kernel estimates of the EDα. Here, EDα is the effective dose at level α, that is, the dose where 100α% of the subjects show a response. The properties of the kernel estimated EDα are compared with the corresponding properties of the maximum likelihood estimator assuming the probit model. Practical application of the k...

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