Stochastic EM Algorithm for Joint Model of Logistic Regression and Mechanistic Nonlinear Model in Longitudinal Studies
We study a joint model where logistic regression is applied to binary longitudinal data with a mismeasured time-varying covariate that is modeled using a mechanistic nonlinear model. Multiple random effects are necessary to characterize the trajectories of the covariate and the response variable, le...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/10/2317 |
| _version_ | 1797599181745946624 |
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| author | Hongbin Zhang |
| author_facet | Hongbin Zhang |
| author_sort | Hongbin Zhang |
| collection | DOAJ |
| description | We study a joint model where logistic regression is applied to binary longitudinal data with a mismeasured time-varying covariate that is modeled using a mechanistic nonlinear model. Multiple random effects are necessary to characterize the trajectories of the covariate and the response variable, leading to a high dimensional integral in the likelihood. To account for the computational challenge, we propose a stochastic expectation-maximization (StEM) algorithm with a Gibbs sampler coupled with Metropolis–Hastings sampling for the inference. In contrast with previous developments, this algorithm uses single imputation of the missing data during the Monte Carlo procedure, substantially increasing the computing speed. Through simulation, we assess the algorithm’s convergence and compare the algorithm with more classical approaches for handling measurement errors. We also conduct a real-world data analysis to gain insights into the association between CD4 count and viral load during HIV treatment. |
| first_indexed | 2024-03-11T03:31:07Z |
| format | Article |
| id | doaj.art-3d18637bc57846f08a98405b2844b033 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T03:31:07Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-3d18637bc57846f08a98405b2844b0332023-11-18T02:19:17ZengMDPI AGMathematics2227-73902023-05-011110231710.3390/math11102317Stochastic EM Algorithm for Joint Model of Logistic Regression and Mechanistic Nonlinear Model in Longitudinal StudiesHongbin Zhang0Department of Biostatistics, College of Public Health, University of Kentucky, Lexington, KY 40536, USAWe study a joint model where logistic regression is applied to binary longitudinal data with a mismeasured time-varying covariate that is modeled using a mechanistic nonlinear model. Multiple random effects are necessary to characterize the trajectories of the covariate and the response variable, leading to a high dimensional integral in the likelihood. To account for the computational challenge, we propose a stochastic expectation-maximization (StEM) algorithm with a Gibbs sampler coupled with Metropolis–Hastings sampling for the inference. In contrast with previous developments, this algorithm uses single imputation of the missing data during the Monte Carlo procedure, substantially increasing the computing speed. Through simulation, we assess the algorithm’s convergence and compare the algorithm with more classical approaches for handling measurement errors. We also conduct a real-world data analysis to gain insights into the association between CD4 count and viral load during HIV treatment.https://www.mdpi.com/2227-7390/11/10/2317logistic regressionlongitudinal binary datameasurement errortime-varying covariatemechanistc nonelinear modelstochastic EM |
| spellingShingle | Hongbin Zhang Stochastic EM Algorithm for Joint Model of Logistic Regression and Mechanistic Nonlinear Model in Longitudinal Studies Mathematics logistic regression longitudinal binary data measurement error time-varying covariate mechanistc nonelinear model stochastic EM |
| title | Stochastic EM Algorithm for Joint Model of Logistic Regression and Mechanistic Nonlinear Model in Longitudinal Studies |
| title_full | Stochastic EM Algorithm for Joint Model of Logistic Regression and Mechanistic Nonlinear Model in Longitudinal Studies |
| title_fullStr | Stochastic EM Algorithm for Joint Model of Logistic Regression and Mechanistic Nonlinear Model in Longitudinal Studies |
| title_full_unstemmed | Stochastic EM Algorithm for Joint Model of Logistic Regression and Mechanistic Nonlinear Model in Longitudinal Studies |
| title_short | Stochastic EM Algorithm for Joint Model of Logistic Regression and Mechanistic Nonlinear Model in Longitudinal Studies |
| title_sort | stochastic em algorithm for joint model of logistic regression and mechanistic nonlinear model in longitudinal studies |
| topic | logistic regression longitudinal binary data measurement error time-varying covariate mechanistc nonelinear model stochastic EM |
| url | https://www.mdpi.com/2227-7390/11/10/2317 |
| work_keys_str_mv | AT hongbinzhang stochasticemalgorithmforjointmodeloflogisticregressionandmechanisticnonlinearmodelinlongitudinalstudies |