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

(vip2019) #1

Model 5:Standard logistic regres-
sion (naive model)


Variable Coefficient


Model-based
Std Err

Wald
p-value

INTERCEPT 1.4362 0.6022 0.0171
BIRTHWGT 0.0005 0.0002 0.0051
GENDER 0.0453 0.2757 0.8694
DIARRHEA 0.7764 0.4538 0.0871


^b 3 for DIARRHEA samebuts^
band
WaldP-values differ.


Model 4 vs. Model 5


 Parameter estimates same


 s^bModel 4 >s^bModel 5


Other data: possible that
s^b(empirical)<s^b(model based)


Summary. Comparison of model
results for DIARRHEA
Correlation
structure


Odds
ratio 95% CI
1 AR(1) 1.25 (0.23, 6.68)
2 Exchangeable 1.91 (0.44, 8.37)
3 Fixed (user defined) 1.29 (0.26, 6.46)
4 Independent 2.17 (0.69, 6.85)
5 Independent (SLR) 2.17 (0.89, 5.29)


In particular, the coefficient estimate for
DIARRHEA is 0.7764 in both Model 4 and
Model 5; however, the standard error for DIAR-
RHEA is larger in Model 4 at 0.5857 compared
with 0.4538 for Model 5. Consequently, theP-
values for the Wald test also differ: 0.1849 for
Model 4 and 0.0871 for Model 5.

The other parameters in both models exhibit
the same pattern, in that the coefficient esti-
mates are the same, but the standard errors are
larger for Model 4. In this example, the empiri-
cal standard errors are larger than their model-
based counterparts, but this does not always
occur. With other data, the reverse can occur.

A summary of the results for each model for
the variable DIARRHEA is presented on the
left. Note that the choice of correlation struc-
ture affects both the odds ratio estimates and
the standard errors, which in turn affects the
width of the confidence intervals. The largest
odds ratio estimates are 2.17 from Model 4 and
Model 5, which use an independent correlation
structure. The 95% confidence intervals for all
of the models are quite wide, with the tightest
confidence interval (0.89, 5.29) occurring in
Model 5, which is a standard logistic regres-
sion. The confidence intervals for the odds
ratio for DIARRHEA include the null value of
1.0 for all five models.

Presentation: II. Example 1: Infant Care Study 549
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