Laplacian-P-splines for Bayesian inference in the mixture cure model.

Area of Science:

• Biostatistics
• Survival Analysis
• Computational Statistics

Background:

• Mixture cure models analyze survival data with a potentially 'cured' subgroup.
• Bayesian inference for cure models often relies on computationally intensive Markov chain Monte Carlo (MCMC) methods.
• MCMC methods can suffer from slow convergence and require extensive diagnostic checks.

Purpose of the Study:

• To develop a fast and flexible sampling-free Bayesian inference strategy for mixture cure models.
• To improve computational efficiency and reduce sampling times compared to traditional MCMC approaches.
• To provide accurate and smooth estimates of survival curves and related functions.

Main Methods:

• Combining Laplace approximations with penalized B-splines (P-splines) for Bayesian inference.
• Utilizing analytical gradient and Hessian formulas for Laplace approximations to accelerate posterior distribution estimation.
• Modeling cure proportion with logistic regression and susceptible survival with a Cox model featuring a P-spline baseline hazard.

Main Results:

• The proposed Laplacian-P-splines mixture cure (LPSMC) methodology significantly speeds up the approximation of posterior distributions.
• LPSMC provides smooth estimates of survival curves and credible intervals within seconds.
• Simulation studies demonstrate that LPSMC is statistically sound and computationally efficient, comparable to MCMC.

Conclusions:

• Laplacian-P-splines mixture cure (LPSMC) offers a computationally efficient and accurate alternative for Bayesian inference in mixture cure models.
• The method accelerates analysis without compromising statistical performance.
• LPSMC is a practical tool for analyzing real-world survival data with cure fractions.