An Empirical Comparison of Statistical Methods for Estimating EQ-5D Health State Utilities in Rheumatoid Arthritis Clinical Trials for Economic Modelling

Technical Summary: An Empirical Comparison of Statistical Methods for Estimating EQ-5D Health State Utilities in Rheumatoid Arthritis Clinical Trials

Problem Statement
In health technology assessment (HTA), Markov models are widely used to evaluate the cost-effectiveness of interventions for chronic diseases like rheumatoid arthritis (RA). A critical input for these models is the health state utility (HSU), which quantifies patient preferences for specific health states. While clinical trials provide high-quality longitudinal data for deriving HSUs, the statistical approach used to estimate these utilities from repeated measures can vary. The ISPOR Task Force guidelines recommend specific modeling strategies, such as modeling utility decrements rather than raw utilities, and suggest generalized linear models, generalized estimating equations (GEE), and two-part models (TPMM) for handling longitudinal data and excess zeros (ceiling effects). However, there is limited empirical evidence comparing how these specific recommended models perform when applied to RA trial data and how their resulting utility estimates propagate through to economic evaluation outcomes, specifically the incremental cost-effectiveness ratio (ICER).

Methodology
The study conducted an empirical comparison of three statistical models—Linear Mixed-Effects Models (LMM), Generalized Estimating Equations (GEE), and Two-Part Mixed Models (TPMM)—using individual patient data from three randomized, double-blind RA clinical trials (NCT01721044, NCT01721057, and NCT01711359) accessed via the Vivli platform.

• Data: The analysis utilized longitudinal EQ-5D-5L and Disease Activity Score-28 (DAS28) data collected over 24 weeks. The dependent variable was the utility decrement ($1 - \text{utility}$).
• Health States: HSUs were estimated for four DAS-defined health states: remission, low disease activity, moderate disease activity, and high disease activity.
• Statistical Models:
  • LMM: Included fixed and random effects to account for within-subject correlation and between-subject variability, assuming normally distributed residuals and missing at random (MAR).
  • GEE: Specified a covariance structure to account for longitudinal correlation without random effects, assuming missing completely at random (MCAR) or MCAR-X.
  • TPMM: A two-part approach where the first part modeled the probability of a boundary value (utility decrement = 0, i.e., full health) using logistic regression, and the second part modeled the non-boundary distribution using linear regression.
• Economic Modeling: The estimated HSUs from each statistical model were applied as inputs to a published Markov model comparing treatment strategies for early RA. The model simulated patient transitions over a 5-year horizon. The study focused on comparing Strategy #2 (starting with MTX + LEF) against Strategy #1 (starting with MTX monotherapy) from a payer perspective.
• Analysis: The study compared incremental Quality-Adjusted Life Years (QALYs), Incremental Cost-Effectiveness Ratios (ICERs), and Probabilistic Sensitivity Analysis (PSA) results (including Incremental Net Benefits and Cost-Effectiveness Acceptability Curves) across the three modeling approaches.

Key Results

• Utility Estimates:
  • LMM vs. GEE: These two models produced nearly identical HSU estimates. The differences in point estimates were less than 0.002 across all health states and trials.
  • TPMM: This model consistently generated smaller HSU estimates compared to LMM and GEE. The magnitude of the difference correlated with the "ceiling effect" (the proportion of patients reporting full health). The largest discrepancies occurred in the remission state (where ceiling effects were highest, e.g., >25%), with differences ranging from 0.019 to 0.042 in point estimates depending on the trial. Differences were smallest in the high disease activity state where ceiling effects were minimal.
• Economic Impact:
  • Despite the differences in HSU estimates, the impact on the economic model was minimal. The differences in incremental QALYs between LMM/GEE and TPMM ranged from 0.0004 to 0.0007.
  • Consequently, the ICERs varied slightly but remained consistently high (ranging from ~€650,000 to ~€985,000 per QALY) across all models, far exceeding common willingness-to-pay thresholds.
  • Probabilistic Sensitivity Analysis (PSA) showed that the probability of the intervention being cost-effective was 0% across all models at standard thresholds (€50,000, €100,000, €150,000). The Incremental Net Benefits (INB) were negative in all scenarios.

Significance and Claims
The paper claims that while the choice of statistical model affects the estimated magnitude of health state utilities—particularly when ceiling effects are present due to the structural differences in how TPMM handles boundary values versus LMM/GEE—this variation had a negligible impact on the final cost-effectiveness conclusions in the specific context of this study.

The authors emphasize that the minimal impact on economic outcomes may be specific to the selected Markov model structure, which produced very similar health-state occupancy distributions between treatment arms, thereby dampening the effect of utility estimation differences. They caution that the generalizability of these findings is limited to the disease (RA) and the specific model type used. The study concludes that for the selected Markov model, LMM and GEE are interchangeable, and while TPMM yields lower utility values, it did not alter the decision-making outcome in this instance. However, the authors note that in settings with different model structures or populations with higher proportions of patients in full health, the choice of model could yield more substantial differences in economic conclusions.