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Biometrika Advance Access published online on May 15, 2007
Biometrika, doi:10.1093/biomet/asm033
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Copyright © 2007 Biometrika Trust

Miscellanea

Testing goodness-of-fit in logistic case-control studies

Howard D. Bondell

Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695-8203, U.S.A.

bondell{at}stat.ncsu.edu

Received for publication 1 June 2006. Revision received 1 October 2006.
  Abstract

We present a goodness-of-fit test for the logistic regression model under case-control sampling. The test statistic is constructed via a discrepancy between two competing kernel density estimators of the underlying conditional distributions given case-control status. The proposed goodness-of-fit test is shown to compare very favourably with previously proposed tests for case-control sampling in terms of power. The test statistic can be easily computed as a quadratic form in the residuals from a prospective logistic regression maximum likelihood fit. In addition, the proposed test is affine invariant and has an alternative representation in terms of empirical characteristic functions.

Key Words: Biased sampling • Case-control data • Goodness-of-fit • Kernel density • Logistic regression • Retrospective sampling


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