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

 AGE and SEX controlled asVs
as well asWs

 RORs depend on values ofWs
(AGE and SEX)

4. Maximum Likelihood (ML)
   Techniques: An Overview


5. Statistical Inferences Using
   ML Techniques

In our previous example using this formula,

there are q equals three exposure variables

(namely, SMK, PAL, and SBP), two confoun-

ders (namely, AGE and SEX), which are in the

model asVvariables, and two effect modifiers

(also AGE and SEX), which are in the model

asWvariables. The odds ratio expression for

this example is shown here again.

This odds ratio expression does not contain

coefficients for the confounding effects of

AGE and SEX. Nevertheless, these effects are

being controlled because AGE and SEX are

contained in the model asVvariables in addi-

tion to beingWvariables.

Note that for this example, as for any model

containing interaction terms, the odds ratio

expression will yield different values for the

odds ratio depending on the values of the effect

modifiers – in this case, AGE and SEX – that

are specified.

In the next chapter (Chap. 4), we consider how

the method of maximum likelihood is used to

estimate the parameters of the logistic model.

And in Chap. 5, we describe statistical infer-

ences using ML techniques.

SUMMARY
Chapters up to this point:

1. Introduction


2. Important Special Cases

3 3. Computing the Odds Ratio

This presentation is now complete. We have

described how to compute the odds ratio for

an arbitrarily coded single exposure variable

that may be dichotomous, ordinal, or interval.

We have also described the odds ratio formula

when the exposure variable is a polytomous

nominal variable like occupational status.

And, finally, we have described the odds ratio

formula when there are several exposure vari-

ables, controlling for confounders without

interaction terms and controlling for confoun-

ders together with interaction terms.

EXAMPLE:q¼ 3

RORE*vs:E**¼exp SMK*SMK**

   

b 1

þPAL*PAL**

   

b 2

þSBP*SBP**

   

b 3

þd 11 SMK*SMK**

   

AGE

þd 12 SMK*SMK**

   

SEX

þd 21 PAL*PAL**

   

AGE

þd 22 PAL*PAL**

   

SEX

þd 31 SBP*SBP**

   

AGE

þd 32 SBP*SBP**

   

SEX

Presentation: VI. The Model and Odds Ratio for Several Exposure Variables 91