Dataset Information

Mixed-effects state-space models for analysis of longitudinal dynamic systems.

ABSTRACT: The rapid development of new biotechnologies allows us to deeply understand biomedical dynamic systems in more detail and at a cellular level. Many of the subject-specific biomedical systems can be described by a set of differential or difference equations that are similar to engineering dynamic systems. In this article, motivated by HIV dynamic studies, we propose a class of mixed-effects state-space models based on the longitudinal feature of dynamic systems. State-space models with mixed-effects components are very flexible in modeling the serial correlation of within-subject observations and between-subject variations. The Bayesian approach and the maximum likelihood method for standard mixed-effects models and state-space models are modified and investigated for estimating unknown parameters in the proposed models. In the Bayesian approach, full conditional distributions are derived and the Gibbs sampler is constructed to explore the posterior distributions. For the maximum likelihood method, we develop a Monte Carlo EM algorithm with a Gibbs sampler step to approximate the conditional expectations in the E-step. Simulation studies are conducted to compare the two proposed methods. We apply the mixed-effects state-space model to a data set from an AIDS clinical trial to illustrate the proposed methodologies. The proposed models and methods may also have potential applications in other biomedical system analyses such as tumor dynamics in cancer research and genetic regulatory network modeling.

SUBMITTER: Liu D

PROVIDER: S-EPMC3507995 | biostudies-literature | 2011 Jun

REPOSITORIES: biostudies-literature

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Mixed-effects state-space models for analysis of longitudinal dynamic systems.

Liu Dacheng D Lu Tao T Niu Xu-Feng XF Wu Hulin H

Biometrics 20100903 2

The rapid development of new biotechnologies allows us to deeply understand biomedical dynamic systems in more detail and at a cellular level. Many of the subject-specific biomedical systems can be described by a set of differential or difference equations that are similar to engineering dynamic systems. In this article, motivated by HIV dynamic studies, we propose a class of mixed-effects state-space models based on the longitudinal feature of dynamic systems. State-space models with mixed-effe ...[more]

PMID: 20825393

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Project description:BackgroundClinical prediction models often fail to generalize in the context of clustered data, because most models fail to account for heterogeneity in outcome values and covariate effects across clusters. Furthermore, standard approaches for modeling clustered data, including generalized linear mixed-effects models, would not be expected to provide accurate predictions in novel clusters, because such predictions are typically based on the hypothetical mean cluster. We hypothesized that dynamic mixed-effects models, which incorporate data from previous predictions to refine the model for future predictions, would allow for cluster-specific predictions in novel clusters as the model is updated over time, thus improving overall model generalizability.ResultsWe quantified the potential gains in prediction accuracy from using a dynamic modeling strategy in a simulation study. Furthermore, because clinical prediction models in the context of clustered data often involve outcomes that are dependent on patient volume, we examined whether using dynamic mixed-effects models would be robust to misspecification of the volume-outcome relationship. Our results indicated that dynamic mixed-effects models led to substantial improvements in prediction accuracy in clustered populations over a broad range of conditions, and were uniformly superior to static models. In addition, dynamic mixed-effects models were particularly robust to misspecification of the volume-outcome relationship and to variation in the frequency of model updating. The extent of the improvement in prediction accuracy that was observed with dynamic mixed-effects models depended on the relative impact of fixed and random effects on the outcome as well as the degree of misspecification of model fixed effects.ConclusionsDynamic mixed-effects models led to substantial improvements in prediction model accuracy across a broad range of simulated conditions. Therefore, dynamic mixed-effects models could be a useful alternative to standard static models for improving the generalizability of clinical prediction models in the setting of clustered data, and, thus, well worth the logistical challenges that may accompany their implementation in practice.

Project description:BACKGROUND:Renal transplant patients are mandated to have continuous assessment of their kidney function over time to monitor disease progression determined by changes in blood urea nitrogen (BUN), serum creatinine (Cr), and estimated glomerular filtration rate (eGFR). Multivariate analysis of these outcomes that aims at identifying the differential factors that affect disease progression is of great clinical significance. Thus our study aims at demonstrating the application of different joint modeling approaches with random coefficients on a cohort of renal transplant patients and presenting a comparison of their performance through a pseudo-simulation study. The objective of this comparison is to identify the model with best performance and to determine whether accuracy compensates for complexity in the different multivariate joint models. METHODS AND RESULTS:We propose a novel application of multivariate Generalized Linear Mixed Models (mGLMM) to analyze multiple longitudinal kidney function outcomes collected over 3 years on a cohort of 110 renal transplantation patients. The correlated outcomes BUN, Cr, and eGFR and the effect of various covariates such patient's gender, age and race on these markers was determined holistically using different mGLMMs. The performance of the various mGLMMs that encompass shared random intercept (SHRI), shared random intercept and slope (SHRIS), separate random intercept (SPRI) and separate random intercept and slope (SPRIS) was assessed to identify the one that has the best fit and most accurate estimates. A bootstrap pseudo-simulation study was conducted to gauge the tradeoff between the complexity and accuracy of the models. Accuracy was determined using two measures; the mean of the differences between the estimates of the bootstrapped datasets and the true beta obtained from the application of each model on the renal dataset, and the mean of the square of these differences. The results showed that SPRI provided most accurate estimates and did not exhibit any computational or convergence problem. CONCLUSION:Higher accuracy was demonstrated when the level of complexity increased from shared random coefficient models to the separate random coefficient alternatives with SPRI showing to have the best fit and most accurate estimates.

Project description:Estimating the latent dynamics underlying biological processes is a central problem in computational biology. State-space models with Gaussian statistics are widely used for estimation of such latent dynamics and have been successfully utilized in the analysis of biological data. Gaussian statistics, however, fail to capture several key features of the dynamics of biological processes (e.g., brain dynamics) such as abrupt state changes and exogenous processes that affect the states in a structured fashion. Although Gaussian mixture process noise models have been considered as an alternative to capture such effects, data-driven inference of their parameters is not well-established in the literature. The objective of this paper is to develop efficient algorithms for inferring the parameters of a general class of Gaussian mixture process noise models from noisy and limited observations, and to utilize them in extracting the neural dynamics that underlie auditory processing from magnetoencephalography (MEG) data in a cocktail party setting. We develop an algorithm based on Expectation-Maximization to estimate the process noise parameters from state-space observations. We apply our algorithm to simulated and experimentally-recorded MEG data from auditory experiments in the cocktail party paradigm to estimate the underlying dynamic Temporal Response Functions (TRFs). Our simulation results show that the richer representation of the process noise as a Gaussian mixture significantly improves state estimation and capturing the heterogeneity of the TRF dynamics. Application to MEG data reveals improvements over existing TRF estimation techniques, and provides a reliable alternative to current approaches for probing neural dynamics in a cocktail party scenario, as well as attention decoding in emerging applications such as smart hearing aids. Our proposed methodology provides a framework for efficient inference of Gaussian mixture process noise models, with application to a wide range of biological data with underlying heterogeneous and latent dynamics.

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Mixed-effects state-space models for analysis of longitudinal dynamic systems.

Publications

Mixed-effects state-space models for analysis of longitudinal dynamic systems.

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