Time-to-Event Estimation with Unreliably Reported Events in Medicare Health Plan Payment

Time-to-event estimation (i.e., survival analysis) is common in health research, most often using methods that assume proportional hazards and no competing risks. Because both assumptions are frequently invalid, estimators more aligned with real-world settings have been proposed. An effect can be estimated as the difference in areas below the cumulative incidence functions of two groups up to a pre-specified time point. This approach, restricted mean time lost (RMTL), can be used in settings with competing risks as well. We extend RMTL estimation for use in an understudied health policy application in Medicare. Medicare currently supports healthcare payment for over 69 million beneficiaries, most of whom are enrolled in Medicare Advantage plans and receive insurance from private insurers. These insurers are prospectively paid by the federal government for each of their beneficiaries’ anticipated health needs using an ordinary least squares linear regression algorithm. As all coefficients are positive and predictor variables are largely insurer-submitted health conditions, insurers are incentivized to upcode, or report more diagnoses than may be accurate. Such gaming is projected to cost the federal government $40 billion in 2025 alone without clear benefit to beneficiaries. We propose several novel estimators of coding intensity and possible upcoding in Medicare Advantage, including accounting for unreliable reporting. We demonstrate estimator performance in simulated data leveraging the National Institutes of Health’s All of Us study and also develop an open source R package to simulate realistic labeled upcoding data, which were not previously available.

💡 Research Summary

This paper tackles the pervasive problem of diagnostic up‑coding in Medicare Advantage (MA) plans by developing a novel statistical framework that integrates unreliable reporting (under‑coding) and possible up‑coding into time‑to‑event (TTE) analysis. Traditional TTE methods rely on proportional hazards and ignore competing risks, assumptions that are often violated in health‑policy data. The authors therefore adopt the restricted mean time lost (RMTL) metric, which quantifies the area under cumulative incidence curves up to a pre‑specified horizon, thereby capturing both the frequency and timing of events without requiring proportional hazards.

In the MA context, the CMS risk‑adjustment formula uses 115 hierarchical condition categories (HCCs) in an ordinary least squares regression with all positive coefficients. This structure creates a financial incentive for insurers to report as many diagnoses as possible, leading to two forms of up‑coding: (1) severity‑based up‑coding, where a lower‑severity HCC is replaced by a higher‑severity counterpart, and (2) availability‑based up‑coding, where previously unreported HCCs are added. The usual comparison group, Traditional Medicare (TM), suffers from under‑coding, which would inflate apparent differences if left unadjusted.

To correct for under‑coding, the authors introduce a set of reference HCCs that are not subject to competing risks. By estimating the persistence of each reference HCC across consecutive monitoring periods, they compute an under‑coding proportion ε (one minus the average persistence). This ε is then used to shift the cumulative incidence curve of the TM group, yielding an adjusted mean time without event μ* and an adjusted group difference ψ* = μ_MA – μ*TM. The framework also accommodates sequential monitoring periods, defining ψ_M = ψ_m – ψ{m‑1} and its adjusted counterpart ψ*_M when ε is known for both periods.

The methodological core is formalized with notation for true event times T, censoring times C, observed times Y = min(T, C), and event indicators Δ. Multiple mutually exclusive HCC subtypes are encoded as a competing‑risk variable S, with subtype‑specific hazards λ_s(t) and overall hazard λ(t). From these, subtype‑specific cumulative incidence functions F_s(t) and restricted mean times μ_s(τ) are derived. Group‑specific differences are expressed as ψ, while severity‑based up‑coding is captured by ω = (μ_{most severe} – μ_{least severe})MA – (μ{most severe} – μ_{least severe})_TM.

Performance is evaluated through simulation using the NIH All of Us cohort, which provides realistic self‑reported health conditions for older adults. The authors generate labeled datasets by deliberately introducing under‑coding in the TM arm and various up‑coding patterns in the MA arm. Across numerous scenarios, the RMTL‑based estimators (ψ, ψ*, ψ_M, ψ*_M, ω) demonstrate lower bias, smaller mean‑squared error, and appropriate confidence‑interval coverage compared with conventional hazard‑ratio approaches. Notably, the adjusted estimators successfully recover the true effect even when TM under‑coding is substantial.

A key contribution is the release of an open‑source R package that (i) simulates baseline HCC diagnoses based on nationally representative survey data, (ii) allows users to impose user‑specified under‑coding rates to mimic TM, and (iii) adds severity‑ or availability‑based up‑coding to create fully labeled datasets. This tool fills a gap in the field, providing researchers with realistic data for method development and policy evaluation.

In summary, the paper offers (1) an extension of RMTL methodology to a health‑policy setting with competing risks, (2) a principled adjustment for unreliable reporting in the comparison group, (3) novel estimators for detecting severity‑based up‑coding, and (4) a publicly available simulation package. These advances enable more accurate, interpretable, and policy‑relevant assessments of Medicare Advantage coding practices, potentially guiding regulatory actions to curb billions of dollars in unnecessary spending.