GOODNESS-OF-FIT Tests for Logistic Regression Models

When continuous predictors are present, classical
Pearson and deviance goodness-of-fit tests to assess
logistic model fit break down. We propose a new
method for goodness-of-fit testing which uses a very
general partitioning strategy (clustering) in the
covariate space and is based on either a Pearson
statistic or a score statistic. Properties of the
proposed statistics are discussed. Simulation
studies on many commonly encountered model scenarios
are presented to compare the proposed tests to the
existing tests. Applications of these different
methods on a real clinical trial study are also
performed to demonstrate the usefulness of the new
method in practice and certain advantages over the
widely used Hosmer-Lemeshow test. Discussions on
extending this new method to other data situations,
such as ordinal response regression models and
marginal models for correlated binary data are also
included. This method can also be extended to models
for multinomial outcomes where generalized logit
models are often used.

Autorentext

Dr. Xian-Jin Xie is an Assistant Professor and Director of Biostatistics Core at the Simmons Comprehensive Cancer Center, University of Texas Southwestern Medical Center. His research interests focus on biostatistics and bioinformatics methodologies and their application to collaborative biomedical and clinical research.

Klappentext
When continuous predictors are present, classical Pearson and deviance goodness-of-fit tests to assess logistic model fit break down. We propose a new method for goodness-of-fit testing which uses a very general partitioning strategy (clustering) in the covariate space and is based on either a Pearson statistic or a score statistic. Properties of the proposed statistics are discussed. Simulation studies on many commonly encountered model scenarios are presented to compare the proposed tests to the existing tests. Applications of these different methods on a real clinical trial study are also performed to demonstrate the usefulness of the new method in practice and certain advantages over the widely used Hosmer-Lemeshow test. Discussions on extending this new method to other data situations, such as ordinal response regression models and marginal models for correlated binary data are also included. This method can also be extended to models for multinomial outcomes where generalized logit models are often used.