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

Detailed
Outline

I. Overview(pages 76–77)

A. Focus: computing OR forE, Drelationship

adjusting for confounding and effect

modification.

B. Review of the special case – theE, V, Wmodel:

i. The model:

logit PðÞ¼X aþbEþ~

p 1

i¼ 1

giViþE~

p 2

j¼ 1

djWj.

ii. Odds ratio formula for theE, V, Wmodel,

whereEis a (0, 1) variable:

RORE¼ 1 vs:E¼ 0 ¼exp bþ~

p 2

j¼ 1

djWj

!

:

II. Odds ratio for other codings of a dichotomous

E(pages 77–79)

A. For theE, V, Wmodel withEcoded asE¼aif

exposed and asE¼bif unexposed, the odds ratio

formula becomes

RORE¼ 1 vs:E¼ 0 ¼exp ðÞabbþðÞab ~

p 2

j¼ 1

djWj

"

B. Examples:a¼1, b¼0: ROR¼exp(b)

a¼1, b¼1: ROR¼exp(2b)

a¼100,b¼0: ROR¼exp(100b)

C. Final computed odds ratio has the same value

provided the correct formula is used for the

corresponding coding scheme, even though the

coefficients change as the coding changes.

D. Numerical example from Evans County study.

III. Odds ratio for arbitrary coding ofE(pages 79–82)

A. For theE, V, Wmodel whereE*andE**are any

two values ofEto be compared, the odds ratio

formula becomes

RORE*vs:E**¼exp E*E**



bþ E*E**



~

p 2

j¼ 1

djWj

"

B. Examples:E¼SSU¼social support status (0–5)

E¼SBP¼systolic blood pressure (interval).

C. No interaction odds ratio formula:

RORE*vs:E**¼exp E*E**



b

:

D. Interval variables, e.g., SBP: Choose values for

comparison that represent clinically meaningful

categories, e.g., quintiles.

92 3. Computing the Odds Ratio in Logistic Regression