When Does the Model Pay?

Population

Cost per patient contacted Medicaid pays ≈ $44 for a home visit and ≈ $47 for a physician phone call (national means per claim line)

Readmissions prevented among those reached Base case 20%, range 10–50%; 50% is optimistic (Supplementary Table S2)

Cost of one readmission Base case $8,100 (mean hospital cost, NRD, 2024 dollars); median-based $5,200; range $5,200–11,100

Model running cost per delivery Charged to the model strategy only. Base case $3.00 (range $2.30–4.10) per delivery

Model Risks are Platt-recalibrated on training folds, then scored on the untouched test set

SIMULATION Show a hypothetical better model

Its AUC Idealised, perfectly calibrated binormal model at the same 1.7% prevalence. Not fitted to data.

Net value per 1,000 deliveriesSavings from prevented readmissions minus outreach and model costs. Zero is "contact no one".

What the model adds over the better no-model strategyShaded band: 95% bootstrap interval from the 46 test-set readmissions. Where it straddles zero, the gain is not established.

Across states: does contacting every mother pay at Medicaid's price?Post hoc. Each dot is a state: the nuMoM2b test set reweighted to that state's first births. Break-even = readmission rate × effectiveness × readmission cost. Above the diagonal, a home visit for every mother at that state's Medicaid price pays for itself; a model can only help close to the line. Hollow dots use the national price (state has too few claims). Click a dot to select the state.

Table: all states at the current settings

Table: all models at the selected cost

How a strategy is scored. Contacting one patient who would have been readmitted is worth effectiveness × readmission cost. The model contacts everyone whose recalibrated risk exceeds contact cost ÷ that value, the rational cut-off. The value of every strategy is computed from the same test-set patients.

Why the window sits where it does. When contacting is cheap, contacting everyone wins and the model can only lose readmissions it fails to flag. When it is expensive, few patients have enough risk to justify it. A model helps most near the cost where contacting everyone and no one break even, which is prevalence × value per readmission reached.

States (post hoc, exploratory). nuMoM2b recruited at eight US centres and has no state variable. For each state, test-set participants are reweighted (raking) so that their race and ethnicity, Medicaid coverage, education, BMI and age match that state's first births in 2022–24 (CDC WONDER). This assumes that readmission risk given these characteristics is the same everywhere; it captures differences in who gives birth, not in how care is delivered. To keep every published count at 11 or more, only state-level summaries are published: the curves for a state scale the test-set readmission rates to that state's reweighted rate and keep the model's ranking as in the test set, so they show how the economics shift with the state's readmission rate and prices, not with its AUC (shown separately). Intervals for a state are approximate: resampling is scaled to its effective sample size. West Virginia is omitted (fewer than 11 effective readmissions). Medicaid prices are amounts paid per claim line in 2022–23 (T-MSIS), for a home visit (CPT 99347–99350) and a physician telephone call (99441–99443); states with fewer than 1,000 claim lines use the national mean.

Data. To respect the data-use agreement, risks are grouped into four bins per model, each with at least 11 readmissions and 11 non-readmissions. Within each bin the page knows the average predicted risk of each twentieth of the bin (at least 11 people each; not who was readmitted), so it contacts the parts of a bin above the cut-off and assumes readmissions among them in proportion to predicted risk. Results therefore approximate, and differ from, the patient-level figures in the manuscript (results/revision/economic_check.json). Source: results/revision/economic_bins_public.json, produced by src/public_bins.py.