An information matrix test for logistic regression models based on case-control data

Abstract

SUMMARY We propose an information-matrix-based goodness-of-fit statistic to test the validity of the logistic regression model based on case-control data by extending the information matrix test of White (1982) for detecting one-sample parametric model misspecification to the semiparametric profile likelihood setting under a two-sample semiparamnetric model, which is equivalent to the assumed logistic regression model. The proposed test statistic requires a high-dimensional matrix inversion, but is otherwise easily computed and has an asymptotic chi-squared distribution. This test statistic is an alternative to the Kolmogorov-Smirnov-type statistic of Qin & Zhang (1997) and the chi-squared-type statistic of Zhang (1999) and needs neither to employ a bootstrap method to evaluate its critical values nor to group the combined sample data into a finite number of mutually exclusive categories even when the underlying population distribution is continuous. We demonstrate that the proposed test statistic and its asymptotic distribution may be obtained by fitting the prospective logistic regression model to case-control data. We present some results on simulation and on the analysis of three real datasets.