- Using a backward elimination procedure, one first
determines which of the two product terms HT
AGE and HT SEX is the least significant in a
model containing these terms and all main effect
terms. If this least significant term is significant,
then both interaction terms are retained in the
model. If the least significant term is nonsignificant,
it is then dropped from the model. The model is then
refitted with the remaining product term and all main
effects. In the refitted model, the remaining interac-
tion term is tested for significance. If significant, it is
retained; if not significant, it is dropped. - Interaction assessment would be carried out first
using a “chunk” test for overall interaction as
described in Exercise 1. If this test is not significant,
one could drop both interaction terms from the model
as being not significant overall. If the chunk test is
significant, then backward elimination, as described
in Exercise 2, can be carried out to decide if both
interaction terms need to be retained or whether one
of the terms can be dropped. Also, even if the chunk
test is not significant, backward elimination may be
carried out to determine whether a significant inter-
action term can still be found despite the chunk test
results. - The odds ratio formula is given by exp(b), wherebis
the coefficient of the HT variable. AllV variables
remain in the model at the end of the interaction
assessment stage. These are HS, CT, AGE, and SEX.
To evaluate which of these terms are confounders, one
has to consider whether the odds ratio given by exp(b)
changes as one or more of theVvariables are dropped
from the model. If, for example, HS and CT are
dropped and exp(b) does not change from the (gold
standard) model containing allVs, then HS and CT do
not need to be controlled as confounders. Ideally, one
should consider as candidates for control any subset
of the fourVvariables that will give the same odds
ratio as the gold standard. - If CT and AGE do not need to be controlled for con-
founding, then, to assess precision, we must look at
the confidence intervals around the odds ratio for a
model which contains neither CT nor AGE. If this
confidence interval is meaningfully narrower than
the corresponding confidence interval around the
gold standard odds ratio, then precision is gained by
dropping CT and AGE. Otherwise, even though these
variables need not be controlled for confounding, they
238 7. Modeling Strategy for Assessing Interaction and Confounding