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

EXAMPLE (continued)

Options A and B(continued)

Cannot drop PREVHOSP or

PAMU

Using Options A or B:

No -Interaction Model A is best model

Logit P(X) = a + b 1 E 1 + b 2 E 2 + g 1 V 1 + g 2 V 2

fl

X*¼ðE 1 *¼ 1 ;

yes

E 2 *¼ 1 Þ

yes

vs:X¼ðE 1 ¼ 0 ;

no

E 2 ¼no 0 Þ

ORmodel A¼exp½b 1 ð 1  0 Þ

þb 2 ð 1  0 ފ

¼exp½b 1 þb 2 Š

OR = exp[b 1 + b 2 ]

= exp[1.4855 + 1.7819] = 26.2415

95% CI: (11.5512, 59.6146)

Conclusion fromOptions AandB:

Very strong (but highly variable)

combined effect of PREVHOSP and

PAMU

ORE 1 E 2 ,V 1 ,V 2 =exp[b 1 ] =exp[1.4855]

95% CIE 1 E 2 ,V 1 ,V 2 = [2.2004, 9.734]

=4.417

ORE 2 E 1 ,V 1 ,V 2 =exp[b 2 ] =exp[1.7819]

95% CIE 2 E 1 ,V 1 ,V 2 =[2.873, 12.285]

=5.941

Options A or B: Additional

conclusions

Both PREVHOSP and PAMU

have moderately strong and

significant individual effects.

Thus, based on these Wald statistics, we cannot

drop either variable from the model (and simi-

lar conclusions from LR tests).

Consequently, usingOptionsAorB,ourbest

modelis the (reduced) no-interaction model A,

which we have called the Gold Standard

model.

For this model, then, the OR that compares a

subjectX*who is positive (i.e., yes) for bothEs

with a subjectXwho is negative (i.e., no) for

bothEs simplifies to the exponential formula

shown at the left.

Below this formula, at the left, we show the

estimated OR and a 95% confidence interval

around this odds ratio.

These results show that there is a very strong

and significant (but highly variable) effect

when comparing MRSA models withX*andX.

Alternatively, we might wish to compute the

odds ratios for the effects of eachEvariable,

separately, controlling for the otherEand the

twoVvariables. The results are shown at the

left and can also be obtained using the output

for reduced modelAshown earlier.

From these results, we can conclude from

usingOptionsAorBthat both PREVHOSP

and PAMU have moderately strong and signifi-

cant individual effects (ORs of 4.417 and 5.941,

respectively) when controlling for the other

three variables in the final model, i.e., no-inter-

action modelA.

252 8. Additional Modeling Strategy Issues