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

The first set of results described by the printout

information considers a model – called

Model A – with no interaction terms. Thus,

Model A contains the exposure variable CAT

and the five covariables AGE, CHL, ECG,

SMK, and HPT. Using theE, V, Wformulation,

this model contains fiveVvariables, namely,

the covariables, and noWvariables.

The second set of results considers Model B,

which contains two interaction terms in addi-

tion to the variables contained in the first

model. The two interaction terms are called

CH and CC, where CH equals the product CAT

HPT and CC equals the product CATCHL.

Thus, this model contains fiveVvariables and

twoWvariables, the latter being HPT and CHL.

Both sets of results have been obtained using

unconditional ML estimation. Note that no

matching has been done and that the number

of parameters in each model is 7 and 9, respec-

tively, which is quite small compared with the

number of subjects in the data set, which is 609.

We focus for now on the set of results involving

the no interaction Model A. The information

provided consists of the log likelihood statistic 2

lnL^at the top followed by a listing of each vari-

able and its corresponding estimated coefficient,

standard error, chi-square statistic, andP-value.

For this model, because CAT is the exposure

variable and there are no interaction terms, the

estimated odds ratio is given by e to the esti-

mated coefficient of CAT, which is e to the quan-

tity 0.5978, which is 1.82. Because Model A

contains fiveVvariables, we can interpret this

odds ratio as an adjusted odds ratio for the effect

of the CAT variable, which controls for the poten-

tial confounding effects of the fiveVvariables.

We can use this information to carry out a

hypothesis test for the significance of the esti-

mated odds ratio from this model. Of the two

test procedures described, namely, the likelihood

ratio test and the Wald test, the information

provided only allows us to carry out the Wald test.

EXAMPLE (continued)

Model A results are at bottom of

previous page

Model B Output:

2lnL^¼347.23

Variable Coefficient S.E.

Chi

sq P

Intercept 4.0497 1.2550 10.41 0.0013

8 CAT 12.6894 3.1047 16.71 0.0000

>>>

>>>>

<

>>>>

>>>

:

AGE 0.0350 0.0161 4.69 0.0303

CHL 0.0055 0.0042 1.70 0.1923

Vs ECG 0.3671 0.3278 1.25 0.2627

SMK 0.7732 0.3273 5.58 0.0181

HPT 1.0466 0.3316 9.96 0.0016

CH 2.3318 0.7427 9.86 0.0017

CC 0.0692 0.3316 23.20 0.0000

interaction

Ws

CH = CAT × HPT and CC = CAT × CHL

unconditional ML estimation

n¼609, # parameters¼ 9

Model A: no interaction

2lnL^¼400.39

Variable Coefficient S.E. Chi sq P

Intercept –6.7747 1.1402 35.30 0.0000

0.0894

0.1310

CAT 0.5978 0.3520 2.88

HPT 0.4392 0.2908 2.28

OR = exp(0.5978) = 1.82

Test statistic Info. available?

LR No

Wald Yes

Presentation: VIII. Numerical Example 147