International Journal of Epidemiology
© International Epktemiotogical Association 1994
Vol. 23, No. 1
Printed in Great Britain
Letters to the Editor
Odds Ratio or Relative Risk for Cross-Sectional Data?
From JAMES LEE
Sir—The cross-sectional study is widely used in many
areas of research. Although this study design is appro-
priate mainly for descriptive investigations, it is used
also in some aetiological enquiries.1'2 Two effect
measures—the prevalence rate ratio (PRR) and
prevalence odds ratio (POR)—can be ascertained from
cross-sectional data with a dichotomous outcome
variable (presence or absence of a condition).
A cursory look at the epidemiology journals will
attest that the POR is much more frequently reported
than is the PRR. This practice is apparently attributed
to the routine use of logistic regression for the analysis
of cross-sectional data. Logistic regression is a
valuable statistical tool in that it allows statistical ad-
justment of several confounders as well as assessment
of effect modification based on modest study size. The
problem is that it gives POR as an effect measure but
the PRR appears to be a more meaningful statistic for
First, the odds ratio is incomprehensible.1'2 As em-
phasized by Savitz3 an epidemiological measure must
not only convey the most germane information, but it
must also be easy to communicate and to comprehend.
As such, the odds ratio has no direct usefulness except
as a numerical mimic to other effect measures such as
the relative risk (rate ratio) or incidence density ratio.
In contrast, the PRR is easy to interpret. If the PRR
were 5, then at any given point in time the 'exposed'
subjects in the population are 5 times more likely to
have the condition in question as are the 'unexposed'
subjects. If the condition is of low prevalence, then
POR would be numerically similar to PRR so it would
not matter which effect measure was used. Because the
cross-sectional study is not appropriate for a rare
exposure or condition, the POR will generally be
markedly discrepant from PRR.
The odds ratio is the effect measure in a case-control
study only because the rate ratio cannot be deter-
mined. Fortunately the case-control study is most
Division of Biostatistics and Health Informatics, Department of Com-
munity, Occupational and Family Medicine, National University of
Singapore, NUH, Lower Kent Ridge, Singapore 0511.
suitable for diseases of low incidence, in which case
the odds ratio numerically resembles the rate ratio.
This is one of Cornfield's4 great contributions to
epidemiology and it made the case-control study im-
mensely popular. It has also been shown that the case-
control odds ratio is a direct estimate of the incidence
density ratio without imposing the 'rare disease'
assumption.5'6 Thus the splendour of the case-control
odds ratio is simply that it need not be interpreted in
terms of the odds ratio.
Greenland7 has demonstrated persuasively that as an
effect measure, the odds ratio is more defective for
cohort studies than is generally realized. The appro-
priate effect measure for the closed cohort is the
cumulative incidence ratio and that for the dynamic
cohort is the incidence density ratio. What this means
is that logistic regression, which is sometimes
employed for the analysis of closed and dynamic
cohort data, is not appropriate. Another serious pitfall
of logistic regression is that it does not consider the
time interval between exposure and disease occurrence
in the dynamic cohort.
The choice of effect measure for the cross-sectional
study (POR versus PRR) appears to be more equivocal
and, expectedly, textbooks are not explicit and may
even be contradictory. Thus, Checkoway8 prefers
POR whereas Elwood9 seems to favour PRR. Klein-
baum et al.6 noted that for a cross-sectional study in
which the disease has a protracted risk period (long
and ill-defined interval between exposure and disease
occurrence), the logical effect measure for aetiological
inference is the incidence density ratio (IDR). (If such
a condition were studied longitudinally, the study
design of choice would be the dynamic cohort, which
gives IDR). These authors6 also showed that the cross-
sectional POR is a better numerical approximation of
the IDR than is the cross-sectional PRR (the PRR
tends to underestimate IDR). However, the apparent
advantage of POR over PRR has little practical use
since a disease with a protracted risk period, especially
if the aetiological agent is changeable oveT time,
should not be investigated by a cross-sectional
design.2-10 Indeed, the cross-sectional study should