Joint analysis of stochastic processes with application to smoking patterns and insomnia

Area of Science:

• Biostatistics
• Epidemiology
• Longitudinal Data Analysis

Background:

• Insomnia and smoking are significant public health concerns.
• Understanding the dynamic relationship between insomnia and smoking cessation is crucial for effective interventions.
• Previous models may not fully capture the complexities of these intertwined processes over time.

Purpose of the Study:

• To propose a novel joint modeling framework for longitudinal insomnia measurements and stochastic smoking cessation.
• To investigate the within-subject correlation between insomnia symptoms and the smoking cessation process.
• To account for a latent permanent quitting state ('cure') in smoking cessation.

Main Methods:

• Utilized a generalized linear mixed-effects model for longitudinal insomnia data.
• Employed a stochastic mixed-effects model for the smoking cessation process.
• Linked both models via latent random effects within a Bayesian framework.
• Developed a Markov Chain Monte Carlo algorithm for parameter estimation.
• Formulated likelihood functions for time-dependent covariates.

Main Results:

• The joint model successfully captures the longitudinal patterns of insomnia and smoking cessation.
• A significant within-subject correlation between insomnia and smoking processes was identified.
• The model effectively handles the latent permanent quitting state in smokers.
• Parameter estimates were obtained reliably using the developed Bayesian MCMC approach.

Conclusions:

• The proposed joint modeling framework provides a robust method for analyzing the interplay between insomnia and smoking cessation.
• The findings highlight the importance of considering the correlation between these two processes in research and clinical practice.
• This approach can inform the development of more targeted and effective interventions for smokers experiencing insomnia.