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Table 18. Coefficients of independent variables using 3 link functions to estimate length of stay
Coefficient
Normal
Gamma
Negative Binomial
Pneumonia
1.7635
-0.0397
0.3387
Septicemia
7.1664
-0.1036
0.9108
Immune Disorder
1.9484
-0.0624
0.3836
Table 19. Standard error for generalized models
Coefficient
Normal
Gamma
Negative Binomial
Pneumonia
0.0555
0.0397
0.0042
Septicemia
0.0490
0.1036
0.0059
Immune Disorder
0.02209
0.0624
0.0027
of stay; clearly this is erroneous. The negative binomial indicates that septicemia increases the length of
stay by almost one day; pneumonia and immune disorder increase it by approximately one third of a day.
The normal link function indicates that septicemia increases the length of stay by 7 days; the other two
infections increase it by almost two days. However, we must also take into consideration the intercept
value of the generalized linear model. For the normal link function, the intercept is equal to -4.0656.
For the Negative Binomial, it is 0.2358; for the Gamma, it is 1.4017. The intercept increases the value
of the model to a high of 6.8 days for a patient with pneumonia, septicemia, and immune disorder with
the normal link function. For the Negative Binomial, it is equal to 4.7 days. The other thing we have to
consider is the standard error (Table 19).
Note that the standard error is much lower for the Negative Binomial link function. It suggests that
this function ignores the heavy tail when computing standard error and mean; the normal link function
does not. It also indicates that for just these three independent variables, the Gamma link function is
inadequate.
We will next examine the data reduced to COPD to investigate the patient outcomes using the normal,
negative binomial, and gamma link functions. In order to find these patients, we use the diagnosis codes.
COPD is identified as 496. The coding is fairly straightforward:
Data work.copd;
Set nis.nis;
Code=0;
If (rxmatch('496',dx1)>0) then code=1;
If (rxmatch('496',dx2)>0) then code=2;
.
.
.
If (rxmatch('496',dx15)>0) then code=15;
Run;
Data nis.copd;
Set work.copd;
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