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Biometrika 1999 86(1):27-43; doi:10.1093/biomet/86.1.27
© 1999 by Biometrika Trust
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Maximum likelihood estimation in semiparametric selection bias models with application to AIDS vaccine trials

PB GilbertA1, SR LeleA2 and Y VardiA

A1 Department of Biostatistics, Harvard University, Boston, MA 02115, USA pgilbert@hsph.harvard.edu A2 Department of Biostatistics, Johns Hopkins University, Baltimore, Maryland 21205, USA slele@welchlink.welch.jhu.edu A Department of Statistics, Rutgers University, New Brunswick, New Jersey 08903, USA vardi@stat.rutgers.edu

The following problem is treated: given s possibly selection biased samples from an unknown distribution function, and assuming that the sampling rule weight functions for each of the samples are mathematically specified up to a common unknown finite-dimensional parameter, how can we use the data to estimate the unknown parameters? We propose a simple maximum partial likelihood method for deriving the semiparametric maximum likelihood estimator. A discussion of assumptions under which the selection bias model is identifiable and uniquely estimable is presented. We motivate the need for the methodology by discussing the generalised logistic regression model (Gilbert, Self & Ashby, 1998), a semiparametric selection bias model which is useful for assessing from vaccine trial data how the efficacy of an HIV vaccine varies with characteristics of the exposing virus. We show through simulations and an example that the maximum likelihood estimator in the generalised logistic regression model has satisfactory finite-sample properties.

Keywords:Biased sampling model; Confidence interval; Generalised logistic regression model; Human immunodeficiency virus vaccine efficacy trial; Hypothesis testing; Partial likelihood; Profile likelihood; Semiparametric model; Weighted distribution.


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