Integrated likelihoods in parametric survival models for highly clustered censored data

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Modeling

Background:

• Stratification is common in time-to-event data analysis due to sampling or model adjustments.
• Standard likelihood methods can be biased when dealing with nuisance parameters in clustered data, especially with many clusters.
• The impact of censoring on these inference issues in clustered data remains unclear.

Purpose of the Study:

• To propose a frequentist inference method for clustered time-to-event data with independent censoring.
• To evaluate the performance of this new method, particularly in the presence of stratification and nuisance parameters.
• To compare the proposed method with existing approaches like the frailty model.

Main Methods:

• Development of a frequentist inference framework based on integrated likelihood.
• Application of the method to a stratified Weibull model.
• Conducting simulation studies to assess accuracy under various conditions (e.g., high clustering, heavy censoring).

Main Results:

• Integrated likelihood provides accurate inferential results across diverse settings, including extreme cases where standard methods fail.
• The proposed method is robust to high clustering and heavy censoring.
• It performs comparably to the frailty model and is superior when the frailty distribution is misspecified.

Conclusions:

• The integrated likelihood approach offers a reliable and accurate method for statistical inference in stratified, clustered time-to-event data with censoring.
• This method addresses limitations of standard likelihood procedures and offers advantages over frailty models in specific situations.
• The approach is validated through simulations and a real-world application in HIV research.