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Figure 32. Decision tree results for ordinal target
PredIctIve modelIng to rank tHe qualIty of ProvIders
Ultimately, the definition of a patient severity index is used in a model to rank the quality of healthcare
providers. Unlike the standard logistic regression investigation of mortality, what we want to do to predict
the quality of providers is to look not at the similarity between actual and predicted values, but to look
at the difference between them. Quality rankings assume that if a provider does better than predicted,
then it must be because the provider is delivering better care compared to a provider who does worse
than predicted. This approach assumes that the predicted value is the established norm for a patient with
a certain level of severity and demographics, and any deviation from that norm is a result of the quality
of care. This assumption has not yet been validated.
We first look at the logistic regression model defined in Chapter 3. We reproduce Table 15 from Chap-
ter 3 (here as Table 7) that gives the threshold values when we consider just the three patient conditions
of pneumonia, septicemia, and immune disorder. Any choice of a threshold value will have a high false
negative rate. It we use a threshold value of 0.720 or less, then the predicted value of mortality is equal
to 4907/(782 x 10 4 ). This is approximately 0.06% of the time overall. If we choose a threshold value
above 0.760, the predicted mortality level becomes 0.034%. The only change in determining quality
rankings when changing the threshold value will be to change the predicted value but not the order of
the ranking of the providers. This is because the predicted mortality level is not really determined by
the patient's actual severity; rather, it is defined uniformly for all patients.
This table together with a defined threshold value will determine the rankings of providers. Then,
the worse the model is in predicting a provider's true mortality, the better that provider will appear in
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