Methodology

The question

For each Medicare provider: are their cost and volume metrics within the range of normal variation for providers of the same specialty practicing in the same state? If not — by how much, and on which metrics? The output is a per-provider triage signal, not a deterministic judgment.

The peer group

Switching from CMS specialty text to NPPES taxonomy split "Internal Medicine" into 28 subspecialties and dropped its MAD-flag rate from 45% → ~32% — Cardiology ($416k median Part D cost) and Hematology/Oncology ($1.1M) are clearly different populations from general IM ($97k). The n ≥ 30 floor keeps MAD/σ stable on small samples; 9,490 peer groups survive, covering 7.06M of 7.21M providers.

Six metrics

Part D: total_drug_cost, part_d_total_claims, brand_cost_share, avg_cost_per_claim. Part B: total_medicare_payment, part_b_total_services.

A provider flags if any metric fires. Each flag is gated on that metric's own peer coverage being ≥ 30, so no one is flagged against a median computed from a handful of observations.

Classical z-score vs. modified z-score (MAD)

• Classical z: (x − mean) / stddev, threshold |z| ≥ 2.0. The mean and σ are themselves dragged toward the right tail we're hunting, so it under-flags — 2.01% of providers.
• Modified z (MAD): 0.6745 × (x − median) / MAD, threshold |z̃| ≥ 3.5 (Iglewicz & Hoaglin). The median doesn't budge and MAD stays a stable measure of typical deviation, so it flags 5.23% — the correct answer for a right-skewed population.

A z-score is a unitless number of (robust) standard deviations, not a percentage; it can be negative and very large (the top outlier's modified-z is ~134,510).

What a flag does not mean

"Outlier" is a statistical descriptor, not an allegation. A flagged provider is one whose published 2023 metric sits > 3.5 modified-z from their peer-group median. That is not a claim of fraud, abuse, medically inappropriate practice, or a recommendation to audit.

Many legitimate patterns produce extreme scores:

• A single attending NPI absorbing facility-level prescribing for billing (the dominant pattern in top Emergency-Medicine outliers).
• Sub-specialists sitting in a generic taxonomy code.
• Providers serving unusually sick panels (oncology, transplant, advanced HIV care).

Every name comes from the public NPPES registry; every dollar from the public CMS Provider Data Catalog. No PHI, no claims-level data. If you cite a specific finding, quote the statistical descriptor — not a value judgment.

Full math and code: github.com/kristenmartino/medicare-provider-outliers.