iii. The coefficientbirepresents the change
in the log odds that would result from
a one unit change in the variableXiwhen
all the otherXs are fixed.
iv. Example given for model involving CAT,
AGE, and ECG:b 1 is the change in log
odds corresponding to one unit change
in CAT, when AGE and ECG are fixed.VIII. Derivation of OR formula(pages 22–25)
A. Specifying two groups to be compared by an
odds ratio:X 1 andX 0 denote the collection
ofXs for groups 1 and 0.
B. Example involving CAT, AGE, and ECG
variables:X 1 ¼(CAT¼1, AGE¼40,
ECG¼0),X 0 ¼(CAT¼0, AGE¼40,
ECG¼0).
C. Expressing the risk odds ratio (ROR) in terms
of P(X):ROR¼ðÞodds forX 1
ðÞodds forX 0¼PðX 1 Þ= 1 PðX 1 Þ
PðX 0 Þ= 1 PðÞX 0:
D. Substitution of the model form for P(X) in the
above ROR formula to obtain general ROR
formula:
ROR¼exp½~biðX 1 iX 0 iÞ¼Pfexp½biðX 1 iX 0 iÞg
E. Interpretation from the product (P) formula:
The contribution of eachXivariable to the odds
ratio ismultiplicative.
IX. Example of OR computation(pages 25–26)
A. Example of ROR formula for CAT, AGE, and
ECG example usingX 1 andX 0 specified in VIII
B above: ROR¼exp(b 1 ), whereb 1 is the
coefficient of CAT.
B. Interpretation of exp(b 1 ): an adjusted ROR for
effect of CAT, controlling for AGE and ECG.
X. Special case for (0, 1) variables(pages 27–28)
A. General rule for (0, 1) variables: If variable is
Xi, then ROR for effect ofXicontrolling for
otherXs in model is given by the formula
ROR¼exp(bi), wherebiis the coefficient ofXi.
B. Example of formula in A for ECG, controlling
for CAT and AGE.
C. Limitation of formula in A: Model can contain
only main effect variables forXs, and variable
of focus must be (0, 1).Detailed Outline 31