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An Empirical Method for Analyzing Count Data

Jiren Sun, Linda Amoafo, Yongming Qu

TL;DR

This paper addresses analyzing count outcomes in clinical trials, where standard NB regression can fail under sparse data or model misspecification. It introduces an empirical method that targets the marginal rate ratio by transforming counts to subject-level rates and applying ANCOVA/ANHECOVA with robust variance, avoiding full likelihood-based modeling. Through simulations, the method demonstrates controlled Type I error and competitive power, with consistent efficiency gains from covariate adjustment and superior numerical stability in sparse settings. A real-data example from the QWINT-5 trial shows the empirical method yielding stable marginal rate estimates closely aligned with observed data, highlighting its practical value for safety endpoints and regulatory reporting when event counts are low.

Abstract

Count endpoints are common in clinical trials, particularly for recurrent events such as hypoglycemia. When interest centers on comparing overall event rates between treatment groups, negative binomial (NB) regression is widely used because it accommodates overdispersion and requires only event counts and exposure times. However, NB regression can be numerically unstable when events are sparse, and the efficiency gains from baseline covariate adjustment may be sensitive to model misspecification. We propose an empirical method that targets the same marginal estimand as NB regression -- the ratio of marginal event rates -- while avoiding distributional assumptions on the count outcome. Simulation studies show that the empirical method maintains appropriate Type I error control across diverse scenarios, including extreme overdispersion and zero inflation, achieves power comparable to NB regression, and yields consistent efficiency gains from baseline covariate adjustment. We illustrate the approach using severe hypoglycemia data from the QWINT-5 trial comparing insulin efsitora alfa with insulin degludec in adults with type 1 diabetes. In this sparse-event setting, the empirical method produced stable marginal rate estimates and rate ratios closely aligned with observed rates, while NB regression exhibited greater sensitivity and larger deviations from the observed rates in the sparsest intervals. The proposed empirical method provides a robust and numerically stable alternative to NB regression, particularly when the number of events is low or when numerical stability is a concern.

An Empirical Method for Analyzing Count Data

TL;DR

This paper addresses analyzing count outcomes in clinical trials, where standard NB regression can fail under sparse data or model misspecification. It introduces an empirical method that targets the marginal rate ratio by transforming counts to subject-level rates and applying ANCOVA/ANHECOVA with robust variance, avoiding full likelihood-based modeling. Through simulations, the method demonstrates controlled Type I error and competitive power, with consistent efficiency gains from covariate adjustment and superior numerical stability in sparse settings. A real-data example from the QWINT-5 trial shows the empirical method yielding stable marginal rate estimates closely aligned with observed data, highlighting its practical value for safety endpoints and regulatory reporting when event counts are low.

Abstract

Count endpoints are common in clinical trials, particularly for recurrent events such as hypoglycemia. When interest centers on comparing overall event rates between treatment groups, negative binomial (NB) regression is widely used because it accommodates overdispersion and requires only event counts and exposure times. However, NB regression can be numerically unstable when events are sparse, and the efficiency gains from baseline covariate adjustment may be sensitive to model misspecification. We propose an empirical method that targets the same marginal estimand as NB regression -- the ratio of marginal event rates -- while avoiding distributional assumptions on the count outcome. Simulation studies show that the empirical method maintains appropriate Type I error control across diverse scenarios, including extreme overdispersion and zero inflation, achieves power comparable to NB regression, and yields consistent efficiency gains from baseline covariate adjustment. We illustrate the approach using severe hypoglycemia data from the QWINT-5 trial comparing insulin efsitora alfa with insulin degludec in adults with type 1 diabetes. In this sparse-event setting, the empirical method produced stable marginal rate estimates and rate ratios closely aligned with observed rates, while NB regression exhibited greater sensitivity and larger deviations from the observed rates in the sparsest intervals. The proposed empirical method provides a robust and numerically stable alternative to NB regression, particularly when the number of events is low or when numerical stability is a concern.
Paper Structure (20 sections, 10 equations, 4 figures, 3 tables)

This paper contains 20 sections, 10 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. The Empirical Method
  3. Estimand
  4. Inferences
  5. Simulation Studies
  6. Simulation Study 1: Correlated Negative Binomial Counts
  7. Data Generation
  8. Simulation Scenarios
  9. Methods Compared
  10. Results
  11. Simulation Study 2: Zero-Inflated Negative Binomial Counts
  12. Data Generation
  13. Simulation Scenarios
  14. Results
  15. Summary of Simulation Findings
  16. ...and 5 more sections

Figures (4)

  • Figure 1: Type I error rates for the null scenarios (Cases A, B, D, E) across different correlations and sample sizes.
  • Figure 2: Power for Cases C and F across different correlations and sample sizes.
  • Figure 3: Type I error rates for the null scenarios (Cases G and H) across different correlations and sample sizes.
  • Figure 4: Power for Cases I and J across different correlations and sample sizes.