Semiparametric hazard function estimation in meta-analysis for time to event data.

Area of Science:

• Biostatistics
• Survival Analysis
• Meta-Analysis Methodology

Background:

• Meta-analyses commonly combine survival data using Cox models, but few methods exist for estimating survival or hazard functions directly.
• Existing approaches often rely on cumulative survival functions and generalized estimating equations.
• Study-level random effects are considered in some meta-analysis techniques, but estimating functions remains a challenge.

Purpose of the Study:

• To propose an alternative meta-analysis approach for estimating hazard and survival functions.
• To adapt Efron's discrete logistic regression using generalized linear mixed models for survival data.
• To enable smoothed estimation of hazard functions and incorporate semi-parametric structures.

Main Methods:

• Utilized generalized linear mixed models, extending Efron's discrete logistic regression.
• Employed spline functions for fitting models and obtaining smoothed hazard function estimates.
• Incorporated a Bayesian bootstrap approach for statistical inference on hazard and survival functions.

Main Results:

• Demonstrated the feasibility of using spline functions within generalized linear mixed models for hazard function estimation.
• Developed a method capable of modeling hazard functions, from which survival functions can be derived.
• Successfully applied the proposed Bayesian bootstrap approach to two meta-analysis datasets.

Conclusions:

• The proposed method offers a robust alternative for meta-analysis of survival data, particularly for estimating hazard and survival functions.
• The use of generalized linear mixed models and splines allows for flexible modeling of complex survival data structures.
• The Bayesian bootstrap provides a reliable framework for statistical inference in this context.