Logistic Regression: A Self-learning Text, Third Edition (Statistics in the Health Sciences)

Answers:

Q1. Yes:

 Statistical testing only

(questionable)

 Does not consider

confounding or

interaction

Assess confounding withD(0,1),
E(0,1), oneC:

Logit PðXÞ¼aþbE;

where P(X)¼Pr(D¼1|E)

Logit PðXÞ¼aþbEþgC;

where P*(X)¼Pr(D¼1|E,C)

ˆ*

|

ˆ

ORDE=eb ¹ ORDE C =eb

Confounding: meaningfully different

Assess interaction with D(0,1),
E(0,1), oneC:

Logit PðXÞ¼aþbEþgCþdEC;

where P(X)¼Pr(D¼1|E,C,EC)

H 0 :d¼ 0

Wald¼ ^d=s^d

 2

w^21 dfunderH 0

LR¼2lnLR(2lnLF)w^2 1df
underH 0

Q1. Is there anything that can be criticized

about Method 0?

Yes, Method 0 involves statistical testing only;

it does not consider confounding or effect

modification (interaction) when assessing

variables one-at-a-time.

To assess confounding involving binary dis-

easeD, binary exposureE, and a single poten-

tial confounder C, you need to fit two

regression models (shown at left), one of

which contains E and C, and the other of

which contains onlyE.

Confounding is present if we conclude that

corresponding odds ratio estimates are mean-

ingfully different for the two models.

To assess interaction involving binary disease

D, binary exposureE, and a single potential

confounderC, we need to fit the following

logistic regression model shown at the left

that contains the main effects ofEandCand

the product termEC.

Interaction is then assessed by testing the null

hypothesis that the coefficient (d) of the prod-

uct term is zero using either a Wald test or a

likelihood ratio test (preferred), where the test

statistic is chi square with 1 df underH 0.

266 8. Additional Modeling Strategy Issues