Weighted scores method for regression models with dependent data

Area of Science:

• Biostatistics
• Statistical Modeling
• Health Services Research

Background:

• Existing copula-based models for dependent data (e.g., clustered, longitudinal overdispersed counts) offer straightforward estimation but can be complex when dependence is not the primary interest.
• Regression analysis with dependent data often requires specialized models that account for complex correlation structures.

Purpose of the Study:

• To propose and evaluate a novel "weighted scores method" for regression analysis of dependent data.
• To provide a method that focuses on univariate regression parameters while effectively handling data dependence.
• To assess the robustness and efficiency of the proposed method compared to existing approaches.

Main Methods:

• The weighted scores method involves weighting score functions of univariate margins.
• Weight matrices are derived from fitting a discretized multivariate normal distribution to capture dependence.
• The methodology is applied to negative binomial regression models for overdispersed count data.

Main Results:

• Asymptotic and small-sample efficiency calculations demonstrate the robustness of the weighted scores method.
• The proposed method achieves efficiency comparable to maximum likelihood estimation in fully specified copula models.
• The method is effective for analyzing health care utilization data based on family characteristics.

Conclusions:

• The weighted scores method offers a practical and efficient alternative for regression with dependent data when the focus is on marginal parameters.
• This approach simplifies analysis without sacrificing significant statistical efficiency.
• The method is applicable to real-world health services research, as shown in the healthcare utilization example.