[Paper Review] A kernel regression model for panel count data with time-varying coefficients

Yang Wang, Zhangsheng Yu|arXiv (Cornell University)|Mar 25, 2019

Statistical Methods and Inference25 references4 citations

TL;DR

This paper proposes a local kernel regression method for panel count data with time-varying coefficients, using kernel-weighted partial log-likelihood to estimate nonparametric coefficients. The method achieves strong uniform consistency and asymptotic normality, with simulations showing accurate coverage of confidence intervals and successful application to a childhood wheezing study.

ABSTRACT

For the conditional mean function of panel count model with time-varying coefficients, we propose to use local kernel regression method for estimation. Partial log-likelihood with local polynomial is formed for estimation. Under some regularity conditions, strong uniform consistency rates are obtained for the local estimator. At target time point, we show that the local estimator converges in distribution to normal distribution. The baseline mean function estimator is also shown to be consistent. Simulation studies show that the time-varying coefficient estimator is close to the true value, the empirical coverage probabilities of the confidence interval is close to the nominal level. We also applied the proposed method to analyze a clinical study on childhood wheezing.

Motivation & Objective

• To address the limitation of parametric models in capturing time-varying covariate effects in panel count data.
• To develop a nonparametric estimation method for time-varying coefficients in panel count models with unknown baseline mean functions.
• To establish the theoretical properties of the local kernel estimator under nonhomogeneous Poisson process assumptions.
• To provide valid inference through confidence intervals with empirical coverage close to nominal levels.
• To apply the method to real-world clinical data on childhood wheezing for practical validation.

Proposed method

• Uses local kernel regression to estimate time-varying coefficients in a panel count model with unspecified baseline mean function.
• Constructs a kernel-weighted local partial log-likelihood function based on nonhomogeneous Poisson process assumptions.
• Employs local estimating equations to solve for coefficient estimates at each target time point.
• Applies modern empirical process theory and functional central limit theorems to derive asymptotic distributions.
• Derives strong uniform consistency rates for the local estimator under regularity conditions.
• Establishes asymptotic normality of the coefficient estimator at any fixed time point.

Experimental results

Research questions

• RQ1 Can local kernel regression provide consistent and efficient estimation for time-varying coefficients in panel count data?
• RQ2 How do the proposed estimators perform in terms of bias, variance, and coverage probability under finite sample sizes?
• RQ3 Does the method maintain good performance when the true coefficient function is non-monotonic or complex?
• RQ4 Can the estimator achieve asymptotic normality and valid inference despite the non-i.i.d. nature of panel count data?
• RQ5 How does the method compare to existing parametric or spline-based approaches in terms of robustness and accuracy?

Key findings

• The local kernel estimator for time-varying coefficients achieves strong uniform consistency under regularity conditions.
• At any fixed time point, the estimator converges in distribution to a normal distribution, enabling valid inference.
• The baseline mean function estimator is consistent, supporting reliable modeling of the underlying intensity.
• Simulation studies show that the time-varying coefficient estimator is close to the true value with empirical coverage probabilities of confidence intervals near the nominal level.
• The method successfully captures complex time-varying effects, as demonstrated in the analysis of a childhood wheezing clinical dataset.
• Theoretical results confirm that the estimator remains consistent and asymptotically normal even when the coefficient function is nonparametrically estimated.