Invited Commentary: Simple Models for a Complicated Reality
Enrique F. Schisterman
and Sonia Herna
Epidemiology Branch, National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, MD.
Department of Epidemiology, Harvard School of Public Health, Boston, MA.
Slone Epidemiology Center, Boston University, Boston, MA.
Received for publication February 27, 2006; accepted for publication March 6, 2006.
The renowned statistician George P. Box famously said
that all models are wrong, but some are useful. Far from an
indictment of statistical models, Box’s statement can be
taken to mean that even when complex realities are not
exactly represented by simple ﬁtted models, much can be
learned. The paper by Basso et al. (1) in this issue of the
Journal provides an opportunity to consider the costs and
beneﬁts that arise from the simpliﬁcation necessary for gen-
erating statistical models of complex biologic processes.
Considering the relation among birth weight, mortality,
and third factors, Basso et al. postulate that birth weight is
not itself on the causal path to mortality; rather, the relation
between birth weight and mortality might be explained by
a confounding factor. The authors conclude that, to produce
the observed inverse J shape of the birth-weight-speciﬁc
mortality curve, the putative confounding factors (matrix
X ¼ (X
)) must be very rare and have very large
In reducing complex situations to simple models, assump-
tions are made, especially when modeling a biologic process.
For example, parametric models make assumptions regard-
ing distributions. The ﬂexibility of the models is limited by
that of the assumptions on which it depends. Basso et al.’s
model makes the following assumptions: 1) birth weight
follows a Gaussian distribution, 2) there is a uniform effect
of the confounding factors X
on mortality, 3) birth
weight does not cause neonatal mortality, and 4) there is no
interaction between factors X
and birth weight.
Notably, some of these assumptions are interrelated, and a
change in one might affect the others.
As previously stated, consideration of the potential limi-
tations of this model requires further attention to the assump-
tions on which it is based. Let us review each of these
assumptions regarding their substance, the possible impact
on the ﬁndings if they are violated, and whether they seem
Gaussian distribution for birth weight
This assumption requires that birth weight follow a Nor-
mal distribution at all strata of the confounding factor. The
hypothetical birth weights in the left tail of this distribution
may be regarded with some skepticism because of their
questionable compatibility with viability. If the left tail is
indeed truncated, the Gaussian birth-weight assumption will
be violated. Moreover, a confounding factor might increase
the proportion of low-birth-weight babies without shifting
the whole birth-weight distribution, resulting in a skewed
distribution within that stratum. However, given the rela-
tively low prevalence of fetal-growth-restricted babies, ma-
jor deviations from a Gaussian distribution are unusual in
real life. Additionally, a small violation of this assumption
will have little impact on the shape of the overall association
between birth weight and neonatal mortality.
Uniform effect of risk factors
This assumption states that all babies exposed to the pu-
tative confounding factor X are assumed to have identical
shifts in birth weight and identical elevation of their mor-
tality risk. In their paper, Basso et al. acknowledge that this
assumption is unlikely to be true. However, a modiﬁcation
of this assumption seems to entail minor changes on the
noncausal link between birth weight and neonatal mortality.
The authors reﬁned the model by substituting distributions
for the constant effects and obtained similar results.
Correspondence to Dr. Enrique F. Schisterman, Division of Epidemiology, Statistics and Prevention Research, NICHD, NIH, 6100 Executive
Boulevard, 7B03, Rockville, MD 20852 (e-mail: email@example.com).
312 Am J Epidemiol 2006;164:312–314
American Journal of Epidemiology
ª 2006 by the Johns Hopkins Bloomberg School of Public Health
All rights reserved; printed in U.S.A.
Vol. 164, No. 4
Advance Access publication July 17, 2006
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