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The Importance of Assessing the Fit
of Logistic Regression Models: A Case Study
A B S T R A C T
David W. Hosmer, PhD, Scott Taber, MS, and Stanley Lemeshow, PhD
Background. The logistic re-
gression model is being used with in-
creasing frequency in all areas of pub-
lic health research. In the calendar
year 1989, over 30% of the articles
published in theAmericanJournalofPublic Health employed some form
of logistic regression modeling. In
spite of this increase, there has been
no commensurate increase in the use
of commonly available methods for
assessing model adequacy.
Methods. We review the current
status of the use of logistic regression
modeling in the American Journal of
Public Health. We present a brief
overview of currently available andeasily used methods for assessing the
adequacy of a fitted logistic regres-
sion model.
Results. An example is used to
demonstrate the methods as well as a
few of the adverse consequences of
failing to assess the fit of the model.
One important adverse consequence
illustrated in the example is the inclu-
sion of variables in the model as a
result of the influence of one subject.Conclusions. Failure to address
model adequacy may lead to mislead-
ing or incorrect inferences. Recom-
mendations are made for the use of
methods for assessing model ade-
quacy and for future editorial policy
in regard to the review of articles us-
ing logistic regression. (Am J Public
Health. 1991;81:1630-1635)
1630 American Journal of Public Health
Introduction
Modern public healthresearch has
become increasingly reliant on sophisti-
cated statistical modeling techniques to
assess the effect of new health programs,
the impact of risk factors on disease, the
effects of health behaviors, and a host of
other public health concerns. Many such
analyses involve an outcome, or depen-
dent, variable that is dichotomous (present/
absent, yes/no, live/die, etc.), andin these
studies the logistic regression model has
become the statistical model of choice.
The reasons for this are the ease of inter-
pretation of the estimated coefficients as
"adjusted log odds ratios," the ability to
estimate the probability that a particular
subject will develop the outcome, and the
wide availability of easily used and reliable
software to perform thecomputations. It
is now common to find, in an article using
logistic regression, a table of estimated co-
efficients, estimated odds ratios, and as-
sociated confidence limits for the odds ra-
tio.
The validity of inferences drawn from
modern statistical modeling techniques
depends on the assumptions of the statis-
tical model being satisfied. A critical step
in assessing theappropriateness of the
model is to examine its fit, or how well the
model describes the observed data. Very
few articles in subject-matter journals
make any mention of having carried out
this important step in model development.
Without such an analysis, the inferences
drawn from the model may be misleading
or even totally incorrect. Unfortunately,
in some instances the results of fitting alogistic regression model have been pub-
lished when the model contained serious
errors that would have been detected had
any attempt at goodness of fit (GOF) been
performed. The logistic regression model
is a powerful statistical tool, but it must be used with caution.
The goal of this paper is to present an
overview of a few easily employed meth-
ods for assessing the fit oflogistic regres-
sion models. An example is used to dem-
onstrate the use of the methods and the
consequences of failing to assess fit. Much
of what will be presented here is described
in detail in texts by Hosmer and Leme-
show' for logistic regression modeling and
others (e.g., Kleinbaum, Kupper, and
Muller2) for linear regression modeling.
The background provided in this paper...