Predictive Modeling — Exploratory Associations with a Derived Target
This section models the row-level log1p(NBA) target, where NBA is Agrawal-normalized billing — the billed charge rescaled by the service's national payment-to-billing ratio and the provider's own payment level. It is not a residual target and it is not the state-level NB_s statistic. The question is descriptive: how much of this target is associated with the available geography, service-family, and volume features?
The target log1p(NBA) and charge_to_payment_ratio share billing/payment inputs. Including the ratio would leak a mechanically adjacent quantity, so it is excluded. The models use state, urban/rural category, service family, and log volume. This guardrail improves the estimand but does not make the model causal.
Two models, two datasets
For both inpatient and outpatient, we fit:
- Linear regression with one-hot encoded categoricals and explicit reference levels — descriptive coefficients for the derived target
- Random forest 150 trees, max depth 10 — permutation importance ranking catches nonlinearities
Both models use five-fold GroupKFold by provider_ccn: each provider is held out as a group, so no provider appears in both sides of a fold. Reported R² is the mean of five fold-level, row-wise R² values, not a provider-weighted average and not a future-period guarantee. The inpatient target uses average total payment; the outpatient target uses average allowed amount. Current means are linear 0.31 inpatient / 0.22 outpatient and random forest 0.29 inpatient / 0.18 outpatient. These are exploratory held-out association estimates, not causal effects.
Held-out permutation importance
Provider-group-preserving permutation importance is computed on each fold's held-out provider groups and averaged across folds. State and urban/rural values are shuffled as provider blocks; service family and log volume are shuffled within provider. It describes relative predictive association among the available features; it is not evidence that geography causes the target.
Inpatient
Outpatient
Importance ranks show which available features improve held-out prediction within this design. They should not be translated into state effects, markup behavior, or a causal ordering. The model omits important clinical and facility information.
Descriptive linear coefficients
The coefficient charts are from descriptive full-data fits, not held-out estimates. Reference levels are explicit in predictors.json: Urban for urban/rural, AL for state, Other / Unclassified for inpatient service family, and Abdominal / Peritoneal / Biliary for outpatient service family. Known-invalid DRG mapping families are quarantined from the predictor frame; remaining service families are text-derived exploratory groupings, not official crosswalks. Coefficients describe conditional association with log1p(NBA), not causal or markup effects.
Inpatient — Top positive and negative coefficients
Outpatient — Top positive and negative coefficients
What the linear model tells us, summarised:
Limitations
This model examines associations with row-level log1p(NBA). It captures a modest share (—) under provider-grouped validation, but the analysis cannot determine whether a billing/payment relationship is economically or clinically appropriate:
What additional data would help
Interpretive framing
Open questions for analyst follow-up
Portable predictor audit artifacts: data/audit/predictors_validation_inpatient.parquet and predictors_validation_outpatient.parquet contain provider-disjoint fold assignments and out-of-fold predictions; matching .json files record the target, payment denominator, references, exclusions, and fold summaries.