Estimating Parameters of Growth Curve Models by Using Hamiltonian Monte Carlo Algorithm

• Activity Number: 57 - Frontiers in Bayesian Computing
• Type: Contributed
• Date/Time: Monday, August 3, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Md Tareq Ferdous Khan* and Keren Armoni-Domany and David F Smith and Raouf S. Amin and Md Monir Hossian
• Companies: Cincinnati Children's Hospital Medical Center and Dana-Dwek Children's Hospital and UC Department of Otolaryngology and Cincinnati Children’s Hospital Medical Center and Cincinnati Children's Hospital Medical Center
• Keywords: Growth curve model; Hamiltonian Monte Carlo; ambulatory blood pressure; B-spline; periodic spline

Abstract

The SuperImposition by Translation And Rotation (SITAR) model, a shape invariant model, has recently become popular as it factors the growth pattern into the vertical shift, horizontal shift, and horizontal stretch. This model can also be applied to longitudinal data such as 24-hour ambulatory blood pressure by using the periodic spline function. The key challenge of estimating the parameters of the SITAR model is the high dependency among the parameters. Two methods among others, the R package ‘sitar,’ a frequentist approach, and the ‘rjags’ package, a Bayesian approach, can be used for estimation. Recently, the Hamiltonian Monte Carlo (HMC) method within the Bayesian framework performed better in estimating the highly correlated parameters. However, this has not yet been explored with the growth curve model. Using the 24-hour blood pressure data measured in every 15/30 minutes for hypertension subjects, we compared the HMC estimates with that obtained from ‘sitar’ and ‘rjags’. We observed that HMC provides better parameter estimates and model diagnosis. Our future works will include implementing the periodic spline function within the HMC algorithm.