Bayesian Longitudinal Plateau Model of Adult Grip Strength

Objectives: This article illustrates the use of applied Bayesian statistical methods in modeling the trajectory of adult grip strength and in evaluating potential risk factors that may influence that trajectory. Methods: The data consist of from 1 to 11 repeated grip strength measurements from each of 498 men and 533 women age 18-96 years in the Fels Longitudinal Study (Roche AF. 1992. Growth, maturation and body composition: the Fels longitudinal study 1929-1991. Cambridge: Cambridge University Press). In this analysis, the Bayesian framework was particularly useful for fitting a nonlinear mixed effects plateau model with two unknown change points and for the joint modeling of a time-varying covariate. Multiple imputation (MI) was used to handle missing values with posterior inferences appropriately adjusted to account for between-imputation variability. Results: On average, men and women attain peak grip strength at the same age (36 years), women begin to decline in grip strength sooner (age 50 years for women and 56 years for men), and men lose grip strength at a faster rate relative to their peak; there is an increasing secular trend in peak grip strength that is not attributable to concurrent secular trends in body size, and the grip strength trajectory varies with birth weight (men only), smoking (men only), alcohol consumption (men and women), and sports activity (women only). Conclusions: Longitudinal data analysis requires handling not only serial correlation but often also time-varying covariates, missing data, and unknown change points. Bayesian methods, combined with MI, are useful in handling these issues.