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169 – SPEED: Statistical Computing and Sports

Estimating Dynamic Characteristics of Longitudinal and Survival Data in Stochastic Process Models: Insights from Simulation Studies

at Duke University

The stochastic process model (SPM) provides a general framework for modeling the dynamics of repeatedly measured variables (represented by a stochastic process) in relation to time-to-event outcomes (modeled as the quadratic function of such stochastic covariates). Until recently, there were no publically available software tools implementing the SPM methodology. Recently we developed an R package stpm implementing different specifications of the SPM including discrete- and continuous-time multidimensional versions and a one-dimensional model with time-dependent components. In this work, we present simulation studies focusing on two aspects of applications of SPM currently underexplored in the literature: 1) behavior of estimation procedures in cases of small numbers of longitudinal observations per individual and 2) sensitivity to violations of assumption on independence of individuals. We consider here the one-dimensional model taking the recently developed measure of physiological dysregulation based on the statistical (Mahalanobis) distance of biomarker profiles as an example of a variable repeatedly measured in a longitudinal study. Simulations illustrated that the estimation algorithms produce reasonable estimates in case of small numbers of observations per individual. Simulations investigating the sensitivity of the estimation procedure to violations of independence assumption showed that only parameters of baseline hazard are affected in case of dependence in hazards induced by a gamma-distributed random variable. Development of SPM modifications that take into account dependence between individuals (both in hazard rates as well as in the dynamics of longitudinal variables) is necessary to accommodate such dependencies in analyses.