The Enrollment Model Is Working Exactly as Built, and That Is the Problem.
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Capstone 41 · Care Management
Plain-language Brief

The Enrollment Model Is Working Exactly as Built, and That Is the Problem.

It predicts next year's cost with an AUC of 0.92 and enrolls group B at a third of group A's rate. They are not healthier. At the same risk score they carry 16 percent more chronic conditions, because the same illness costs our system less when the patient has more trouble reaching us.

To  Chief Medical Officer
From  Analytics
Re  One-year review of care-management enrollment
Where this comes from
Chapter Chapter 204 · A Fairness Audit
Part Part XXXIII · Capstone Projects: Specialized Methods
Dataset capstone-fairness-audit.xlsx
Notebook View the analysis

Recommendation

Bottom line

Change what the model predicts, from next year's cost to next year's chronic-condition count. It is a one-line change to the training target, the data is already in the record, and it puts more genuinely high-need patients into the program than the current model does. Whether to go further and equalize enrollment rates outright is a policy decision for the executive, not a technical one for us.

What we found

The program has room for about 3 percent of the panel. The model ranks everyone by predicted cost and the top slice is enrolled.

Group AGroup B
Share of our patients70.6%29.4%
Share of program places86.8%13.2%
Enrollment rate3.72%1.36%
The ratio is 0.36. The federal four-fifths guideline treats anything below 0.80 as requiring justification.

We checked the obvious explanation first. If group B genuinely costs less, a cost model is right to rank them lower and there is nothing to answer for.

They are not less sick. They are less served.

Two lines showing mean chronic conditions against decile of the model's predicted risk. Group B's line sits above group A's across the upper deciles, with the gap between them shaded, indicating that at the same predicted risk group B patients carry more chronic conditions.
Figure 1. Patients the model scores as equally risky do not carry equal illness.

At the same predicted risk, group B patients carry 16 percent more chronic conditions, and in the eighth decile the gap reaches 38 percent. They also have fewer primary-care visits and more emergency visits at every level of illness, which is the pattern you see when routine care is hard to reach until it cannot be postponed.

Why cost is the wrong yardstick

At the same number of chronic conditions, a group B patient generates 59 to 72 percent of the spending a group A patient does. Cost measures illness and access together, and we have been reading the combined number as though it were illness alone.

Why our fairness checks did not catch this

The model is close to calibrated within both groups. When it predicts fourteen thousand dollars for a group A patient they cost 14.3; when it predicts twelve thousand for a group B patient they cost 10.7, so if anything we over-estimate group B's spending.

Every check we run compares the model's predictions against cost, and cost is where the problem is. A review of this kind will return clean on this model every time it is run. That is worth stating plainly, because the reviews were not done badly.

What the options actually buy

A bar chart of group B's share of program places: 13.2 percent as deployed on the cost label, 29.9 percent with group-specific thresholds on the cost model, 19.7 percent with the need label, and 29.9 percent with both, against a dashed line marking the 29.4 percent panel share.
Figure 2. Group B's share of program places under four approaches, against their 29.4 percent share of the panel.
ApproachGroup B shareEnrollees who are genuinely high-need
As deployed13.2%84.7%
Adjust thresholds by group29.9%85.4%
Predict health need instead of cost19.7%86.6%
Both together29.9%84.7%
Changing the target improves who gets in. Adjusting thresholds evens out who gets in. They are different things.

Changing the target is the change we recommend, because it improves the measurement itself. It does not reach proportional representation, and we should be honest about why: the other things the model looks at, visits and past spending, carry the same access gap the cost label did.

Adjusting thresholds by group would close the remaining gap immediately. It also reorders nobody, and it is a decision about how to allocate a scarce program rather than a way of measuring need better. It belongs with the executive and it should appear in the minutes.

What we are asking for

Three things

One. Approve retraining the enrollment model on next year's chronic-condition count. No new data collection is required.
Two. Add an audit against clinical need, not just cost, to the quarterly model review, since the current review cannot detect this class of problem.
Three. Take the threshold question to the executive as a policy decision, with this brief attached.

From Statistics, Data Science and AI: A Visual Handbook by John Fisher. Every statistic, table, and figure in this report is reproduced by the companion notebook.