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

VI. Risk Ratios vs. Odds
Ratios

OR

vs.

?

follow-up study

RR

However, according to mathematical theory,

the value provided for the constant does not

really estimatea. In fact, this value estimates

some other parameter of no real interest. There-

fore, an investigator should be forewarned that,

even though the computer will print out a num-

ber corresponding to the constanta, the num-

ber will not be an appropriate estimate ofain

case-control or cross-sectional studies.

The use of an odds ratio estimate may still be of

some concern, particularly when the study is a

follow-up study. In follow-up studies, it is com-

monly preferred to estimate a risk ratio rather

than an odds ratio.

We previously illustrated that a risk ratio can

be estimated for follow-up data provided all the

independent variables in the fitted model are

specified. In the example, we showed that we

could estimate the risk ratio for CHD by com-

paring high catecholamine persons (that is,

those with CAT¼1) to low catecholamine per-

sons (those with CAT¼0), given that both per-

sons were 40 years old and had no previous

ECG abnormality. Here, we have specified

values for all the independent variables in our

model, namely, CAT, AGE, and ECG, for the

two types of persons we are comparing.

EXAMPLE (repeated)

Case-control Printout

Variable Coefficient

Constant  4 : 50 ¼^a

X 1 0 : 70 ¼^b 1

X 2 0 : 05 ¼^b 2

X 3 0 : 42 ¼^b 3

^anot a valid estimate ofa

SUMMARY

Logistic

Model ^PðXÞOR

Follow-up üüü

Case-control ü X ü

Cross-sectional ü X ü

We have described that the logistic model can

be applied to case-control and cross-sectional

data, even though it is intended for a follow-

up design. When using case-control or cross-

sectional data, however, a key limitation is

that you cannot estimate risks like^PðXÞ, even

though you can still obtain odds ratios. This

limitation is not extremely severe if the goal of

the study is to obtain a valid estimate of an

exposure–disease association in terms of an

odds ratio.

EXAMPLE

RRc¼^PðCHD¼^1 jCAT¼^1 ;AGE¼^40 ;ECG¼^0 Þ

^PðCHD¼ 1 jCAT¼ 0 ;AGE¼ 40 ;ECG¼ 0 Þ

Model:

PðXÞ¼

1

1 þeðaþb^1 CATþb^2 AGEþb^3 ECGÞ

Presentation: VI. Risk Ratios vs. Odds Ratios 15