should be retained in the model if precision is not
gained by dropping them.
- The odds ratio formula is given by exp(bþd 1 AGEþ
d 2 SEX).
- Using the hierarchy principle, CT and HS are eligible
to be dropped as nonconfounders.
- Drop CT, HS, or both CT and HS from the model and
determine whether the coefficientsb,d 1 , andd 2 in the
odds ratio expression change. Alternatively, deter-
mine whether the odds ratio itself changes by compar-
ing tables of odds ratios for specified values of the
effect modifiers AGE and SEX. If there is no change
in coefficients and/or in odds ratio tables, then the
variables dropped do not need to be controlled for
confounding.
- Drop CT from the model and determine if the confi-
dence interval around the odds ratio is wider than the
corresponding confidence interval for the model that
contains CT. Because the odds ratio is defined by the
expression exp(bþd 1 AGEþd 2 SEX), a table of confi-
dence intervals for both the model without CT and
with CT will need to be obtained by specifying differ-
ent values for the effect modifiers AGE and SEX. To
assess whether CT needs to be controlled for precision
reasons, one must compare these tables of confidence
intervals. If the confidence intervals when CT is not in
the model are narrower in some overall sense than
when CT is in the model, precision is gained by
dropping CT. Otherwise, CT should be controlled as
precision is not gained when the CT variable is
removed.
- Assessing confounding and precision in Exercises
8 and 9 requires subjective comparisons of either sev-
eral regression coefficients, several odds ratios, or
several confidence intervals. Such subjective compar-
isons are likely to lead to highly debatable conclu-
sions, so that a safe course of action is to control for
allVvariables regardless of whether they are confoun-
ders or not.
Answers to Practice Exercises 239
