Statistical Methods - Text Mining Techniques for Healthcare Provider Quality Determination - page 106

Table 21. Coefficients for race and income quartile

Coefficient Normal Gamma Negative Binomial

Quartile 1 -0.0710 -0.2836 -0.2836

Quartile 2 -0.2026 -0.2560 -0.2560

Quartile 3 -0.2506 -0.1382 -0.1382

Caucasian -0.2337 -0.1095 -0.1095

African American -0.0298 0.0585 0.0585

Hispanic 0.0485 0.2563 0.2563

Asian -0.1652 0.2103 0.2103

Native American -0.5059 -0.1585 -0.1585

and the heavy tail of the distribution inflates the value of the standard error.
We also consider the example for cardiovascular surgery. For a rare occurrence, a Poisson approximation
is better than a normal approximation. If we modify the model and assume a Poisson link function, the
result is a probability, and we need to find an optimal threshold value. The SAS code for this model is

PROC GENMOD DATA=nis.nischarlson
;

CLASS FEMALE ami chf pvd cva pd ctd pu ld diabetes dc paraplegia rd cancer mc sld

hiv
;
MODEL DIED= AGE FEMALE ami chf pvd cva pd ctd pu ld diabetes dc paraplegia rd cancer
mc sld hiv
/
DIST=POISSON
;
OUTPUT OUT=SASUSER.predicted
PREDICTED=_predicted1
RESDEV=_resdev1
RESCHI=_reschi1
UPPER=_upper1
LOWER=_lower1
HESSWGT=_hesswgt1
XBETA=_xbeta1;
RUN ; QUIT ;

We need to use the predicted value to compute the threshold value. We use kernel density estimation
to model the predictions (Figure 23).
If we let 0.05 be the threshold value for prediction, we can compare mortality to predicted mortality.
This threshold successfully predicts 50% of the deaths but with 132 (9%) false positives. If we let 0.03
be the threshold value, it predicts 57% of deaths with 213 or 15% false positives. For a threshold value
of 0.08, the model successfully predicts 25% of the deaths, but reduces the false positive rate to 5%.