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Biometrika 1997 84(3):609-618; doi:10.1093/biomet/84.3.609
© 1997 by Biometrika Trust
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A goodness-of-fit test for logistic regression models based on case-control data

JING QIN and BIAO ZHANG

Department of Mathematics, University of Maryland, College Park Maryland 20742, U.S.A. e-mail: jqin{at}math.umd.edu
Department of Mathematics, University of Toledo Toledo, Ohio 43606, U.S.A. e-mail: bzhang{at}math.utoledo.edu

We test the logistic regression assumption under a case-control sampling plan. After reparameterisation, the assumed logistic regression model is equivalent to a two-sample semiparametric model in which the log ratio of two density functions is linear in data. By identifying this model with a biased sampling model, we propose a Kolmogorov-Smirnov-type statistic to test the validity of the logistic link function. Moreover, we point out that this test statistic can also be used in mixture sampling. We present a bootstrap procedure along with some results on simulation and on analysis of two real datasets.

Key Words: Biased sampling problem • Bootstrap resampling • Case-control data • Goodness-of-fit test • Kolmogorov-Smirnov two-sample statistic • Logistic regression • Prospective sampling • Retrospective sampling


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