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Marginal versus conditional rate estimation for count and recurrent event data with an estimand framework.

Sarah C Conner1, Yijie Zhou1, Tu Xu2

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Summary

Model-estimated event rates in clinical research, particularly for pulmonary exacerbations (PEx) in COPD or asthma, can differ from descriptive rates due to conditional versus marginal rate distinctions. Covariate adjustment in nonlinear models impacts these estimations, aligning with recent FDA guidance.

Keywords:
CollapsibilityEstimand frameworkG-computationGeneralized linear modelMarginal/conditional rateRecurrent events

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Area of Science:

  • Clinical Trials
  • Biostatistics
  • Epidemiology

Background:

  • Count and recurrent event endpoints are crucial for assessing treatment efficacy in clinical research.
  • Pulmonary exacerbations (PEx) in conditions like COPD and asthma are common recurrent events analyzed using nonlinear models (e.g., Poisson, Negative Binomial).
  • A discrepancy is often observed where model-estimated within-group event rates are lower than descriptive rates.

Purpose of the Study:

  • To mathematically explore the relationship between model-estimated and descriptive event rates.
  • To elucidate the impact of covariate adjustment on estimating event rates and rate ratios in nonlinear models.
  • To discuss the application of the estimand framework for count and recurrent event data.

Main Methods:

  • Mathematical analysis to differentiate between conditional and population-level (marginal) event rates.
  • Closed-form derivations and simulation studies to demonstrate the effect of covariate adjustment.
  • Review and discussion of the ICH E9 addendum on the estimand framework.

Main Results:

  • The observed difference between model-estimated and descriptive rates is mathematically explained by the distinction between conditional and marginal rates.
  • Covariate adjustment in nonlinear models can lead to different estimations of event rates and rate ratios compared to unadjusted models.
  • Findings support the FDA's 2023 guidance on covariate adjustment in nonlinear models.

Conclusions:

  • Understanding the difference between conditional and marginal rates is essential for accurate interpretation of clinical trial results.
  • Covariate adjustment strategies require careful consideration in nonlinear models for recurrent events, impacting treatment effect estimation.
  • The estimand framework provides a structured approach for defining and estimating treatment effects in complex clinical trial designs.