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

Practice
Exercises

Suppose we are interested in assessing the association

between tuberculosis and degree of viral suppression in

HIV-infected individuals on antiretroviral therapy, who

have been followed for 3 years in a hypothetical cohort

study. The outcome, tuberculosis, is coded as none

(D¼0), latent (D¼1), or active (D¼2). Degree of viral

suppression (VIRUS) is coded as undetectable (VIRUS¼0)

or detectable (VIRUS¼1). Previous literature has shown

that it is important to consider whether the individual has

progressed to AIDS (no¼0, yes¼1) and is compliant

with therapy (COMPLIANCE: no¼1, yes¼0). In addi-

tion, AGE (continuous) and GENDER (female¼0, male

¼1) are potential confounders. Also there may be interac-

tion between progression to AIDS and COMPLIANCE with

therapy (AIDSCOMP¼AIDSCOMPLIANCE).

We decide to run a proportional odds logistic regression to

analyze these data. Output from the ordinal regression is

shown below. (The results are hypothetical.) The descend-

ing option was used, so Intercept 1 pertains to the compar-

ison D 2toD<2 and Intercept 2 pertains to the

comparisonD1toD<1.

Variable Coefficient S.E.

Intercept 1 (a 2 ) 2.98 0.20

Intercept 2 (a 1 ) 1.65 0.18

VIRUS 1.13 0.09

AIDS 0.82 0.08

COMPLIANCE 0.38 0.14

AGE 0.04 0.03

GENDER 0.35 0.19

AIDSCOMP 0.31 0.14

Practice Exercises 485