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

Variable Specification Summary

Flow Diagram

Choose D, E, C 1 ,... , Cp

Choose Vs from Cs

Choose Ws

from Cs as

Vi or ViVj, i.e.,

interactions

of from EVi

or EViVj

V. Causal Diagrams

Approach for variable selection:

 Not just quantitative

 Consider causal structure

 Depends on the goal

Including covariate in model could

lead to bias:

 If caused by exposure

 If caused by outcome

Lung cancer causes an abnormal

X-ray, i.e.,

Lung cancerðDÞ Chest X-rayðCÞ

We claim:

E,Dassociation controlling forCis

biased

Model:

logit PðD¼ 1 jXÞ¼b 0 þb 1 SMOKE

þb 2 XRY

WhereDcoded 1 for lung cancer

0 for no lung cancer

SMOKE coded 1 for smokers,

0 for nonsmokers

XRY coded 1 for abnormal X-ray

0 for normal X-ray

expðb 1 Þ¼ORðSMOKE¼ 1 vs: 0 Þ

holding X-ray status

constant

In summary, at the variable specification stage,

the investigator defines the largest possible

model initially to be considered. The flow dia-

gram at the left shows first the choice ofD, E,

and theCs, then the choice of theVs from the

Cs and, finally, the choice of theWs in terms of

theCs.

The decision of specifying which variables are

potential confounders should not just be based

on quantitative methods; we must also con-

sider the possible causal relationships between

the exposure, outcome, potential confounders,

and other relevant variables. Moreover, we

must be clear about the goal of our analysis.

Including a variable in the model that is asso-

ciated with the outcome could lead to bias of

the exposure–disease relationship if the level of

that variablewas causedby the exposure and/

or by the outcome.

Finding an abnormal X-ray could be a conse-

quence of lung cancer (we have indicated this

graphically by the one-sided arrow on the left – a

simple example of acausal diagram). If we were

interested in estimating the causal association

between cigarette smoking and lung cancer (as

opposed to developing our best predictive model

of lung cancer), it would bias our results to

include chest X-ray status as a covariate.

More specifically, consider a logistic model

with lung cancer as the outcome and smoking

status and chest X-ray status as covariates

(model stated on the left).

Now consider the interpretation of the odds

ratio for SMOKE derived from this model,

exp(b 1 ); i.e., the odds of lung cancer among the

smokers divided by the odds of lung cancer

among the nonsmokers, holding X-ray status

constant(i.e., adjusting for X-ray status).

Presentation: V. Causal Diagrams 175