Statistical Methods - Text Mining Techniques for Healthcare Provider Quality Determination - page 98

increases as the number of nonzero X's increases. The greater this value, the greater the likelihood that
it will cross the threshold value that predicts mortality.
However, consider for a moment that just about every patient condition has a small risk of mortality.
Once the threshold value is crossed, every patient with similar conditions are predicted to die. Therefore,
the more patients who can be defined over the threshold value, the higher the predicted mortality rate,
decreasing the difference between predicted and actual mortality. Again, there is considerable incentive
to upcode patient diagnoses.
To simplify, we start with just one input variable to the logistic regression, the occurrence of pneumo-
nia. Table 12 gives the chi-square table for the two variables. Only 7% of the patients with pneumonia
died compared to just under 2% generally. Unquestionably, patients with pneumonia are more likely to
die compared to patients who do not die. In addition, if we consider the classification table (Table 13)
for a logistic regression with pneumonia as the input and mortality as the outcome variable, the accuracy
rate is above 90% for any choice of threshold value of less than 1.0 where 100% of the values are to
predict mortality. Therefore, even though patients with pneumonia are almost four times as likely to die
compared to patients without pneumonia, pneumonia by itself is a poor predictor of mortality because
of the rare occurrence.

Table 12. Chi-square table for mortality by pneumonia

Table of pneumonia by DIED

pneumonia DIED Total

Frequency
Row Pct
Col Pct

0 1

0 7431129

98.21
94.97

135419
1.79
81.02

7566548

1 393728

92.54
5.03

31731
7.46
18.98

425459

Total 7824857 167150 7992007

Frequency Missing = 3041

Table 13. Classification table for logistic regression

Classification Table

Prob
Level

Correct Incorrect Pe rcentages

Event Event Correct

Non-
Event

Non-
Event

Sensi-
tivity

Speci-
ficity

False
POS

False
NEG

0.920 782E4 0 167E3 0 97.9 100.0 0.0 2.1 .

0.940 743E4 31731 135E3 394E3 93.4 95.0 19.0 1.8 92.5

0.960 743E4 31731 135E3 394E3 93.4 95.0 19.0 1.8 92.5

0.980 743E4 31731 135E3 394E3 93.4 95.0 19.0 1.8 92.5

1.000 0 167E3 0 782E4 2.1 0.0 100.0 . 97.9