A Bayesian Nonlinear Mixed-Effects Disease Progression Model

Abstract

A nonlinear mixed-effects approach is developed for disease progression models that incorporate variation in age in a Bayesian framework. We further generalize the probability model for sensitivity to depend on age at diagnosis, time spent in the preclinical state and sojourn time. The developed models are then applied to the Johns Hopkins Lung Project data and the Health Insurance Plan for Greater New York data using Bayesian Markov chain Monte Carlo and are compared with the estimation method that does not consider random-effects from age. Using the developed models, we obtain not only age-specific individual-level distributions, but also population-level distributions of sensitivity, sojourn time and transition probability.

Quantifying the duration of the preclinical detectable phase in cancer screening: a systematic review

“…From 689 publications identified in the search, 33 were included in this review, describing 34 methods ( Supplementary Material 2 ). From these, 5 distinct mathematical approaches to estimate the PCDP duration were identified: prevalence-to-incidence ratio [ 6 , 13 - 19 ], maximum likelihood estimation [ 7 , 12 , 18 , 20 - 32 ], expectation-maximization algorithm [ 33 ], regression of observed on expected [ 8 , 11 , 34 - 37 ], and Bayesian Markov-chain Monte Carlo estimation ( Table 2 ) [ 18 , 30 , 38 - 40 ]. Fourteen methods required data on a screened and an unscreened population [ 6 , 7 , 13 - 17 , 20 , 21 , 23 , 33 - 35 , 39 ], whereas 19 obtained estimates using only information from a screened population [ 8 , 11 , 12 , 18 , 19 , 22 , 24 - 32 , 36 - 38 , 40 ].…”

“…From these, 5 distinct mathematical approaches to estimate the PCDP duration were identified: prevalence-to-incidence ratio [ 6 , 13 - 19 ], maximum likelihood estimation [ 7 , 12 , 18 , 20 - 32 ], expectation-maximization algorithm [ 33 ], regression of observed on expected [ 8 , 11 , 34 - 37 ], and Bayesian Markov-chain Monte Carlo estimation ( Table 2 ) [ 18 , 30 , 38 - 40 ]. Fourteen methods required data on a screened and an unscreened population [ 6 , 7 , 13 - 17 , 20 , 21 , 23 , 33 - 35 , 39 ], whereas 19 obtained estimates using only information from a screened population [ 8 , 11 , 12 , 18 , 19 , 22 , 24 - 32 , 36 - 38 , 40 ]. The 5 mathematical estimation approaches are described below; details concerning the model assumptions in the individual studies per type of mathematical approach are reported in Table 3 and Supplementary Material 3 .…”

“…Bayesian Markov-cChain Monte Carlo simulation methods for estimating the parameters of the preclinical detectable phase duration were applied in five 5 included studies [18,30,[38][39][40]. The posterior joint distribution (usually composed of three 3 parameters, : the preclinical incidence rate, the average preclinical detectable phase duration, and test sensitivity) is formed by the prior distributions of the parameters and the likelihood function based on the observed data [42].…”