- a. Seven subsets of possible confounders other than
all confounders (in the gold standard model):
{AGE, GEN}, {AGE, PF}, {PF, GEN}, {AGE},
{GEN}, {PF}, {no variables}.
b.
OCC¼1 OCC¼ 0
POST¼ (^1) ORd 11 ORd 10
POST¼ (^0) ORd 01 ORd 00
ORdij¼exp½^b 1 þ^b 2 þ 3 ^d 1 þ^d 2 POSTiþ^d 9 OCCj
c. The collection of ORs in a table controlling for a
given subset of confounders would be compared to
the corresponding table of ORs for the gold
standard model. Those tables that collectively give
essentially the “same” odds ratios as found in the
gold standard table identify subsets of confounders
that control for confounding. However, to decide
whether one table of ORs is collectively the “same”
as the gold standard, you typically will need to make
a subjective decision, which makes this approach
difficult to carry out.
d. You would construct two tables of confidence
intervals, one for the gold standard model and the
other for the reduced model obtained whenPFand
GENare dropped from the model. Each table has
the same form as shown above in part9b, except
that confidence intervals would be put into each
cell of the table instead of estimated ORs. You
would then compare the two tables collectively to
determine whether precision is gained (i.e.,
confidence interval width is smaller) whenPFand
GENare dropped from the model.
- a. Just because a model runs does not mean that there
is no collinearity problem, but rather that there is
no “perfect” collinearity problem (i.e, a “perfect”
linear relationship among some predictor
variables). If a collinearity problem exists, the
estimated regression coefficients are likely to be
highly unstable and therefore may give very
misleading conclusions.
b. Focus first on the highest CNI of 97. Observe the
VDPs corresponding to this CNI. Determine which
variables are high (e.g., VDP>0.5) and whether
one of these variables (e.g., an interaction term) can
be removed from the model. Rerun the reduced
model to produce collinearity diagnostics (CNIs
and VDPs) again, and proceed similarly until no
collinearity problem is identified.
678 Test Answers