The Stochastic EM Algorithm for Censored Mixed Models

Ian C. Marschner

doi:10.1007/978-3-642-41095-6_28

The Stochastic EM Algorithm for Censored Mixed Models

Ian C. Marschner

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

1 Citation (Scopus)

Abstract

The Stochastic EM algorithm is a Monte Carlo method for approximating the regular EM algorithm in missing data situations where the E step is intractable. It produces a stationary Markov chain iterative sequence where each iteration is the result of applying complete data maximum likelihood estimation to a single simulation of the complete data conditional on the observed data. Analogously to other Markov chain Monte Carlo methods, the final estimate is the mean of the iterative sequence after a burn-in period. We consider a case study of the application of the Stochastic EM algorithm for censored mixed models, a computationally challenging context. The Stochastic EM algorithm is particularly simple to apply to either linear or non-linear mixed models with censoring. All that is required is a routine to simulate censored multivariate normal observations, and a routine to fit the desired uncensored mixed model. An application is presented involving repeated measures of HIV viral load subject to censoring caused by a lower detection limit of the assay. It is found that crude methods ignoring the censoring are biased compared to results from the Stochastic EM algorithm.

Original language	English
Title of host publication	Monte Carlo and Quasi-Monte Carlo Methods 2012
Editors	Josef Dick, Frances Y. Kuo, Gareth W. Peters, Ian H. Sloan
Place of Publication	Heidelberg
Publisher	Springer, Springer Nature
Pages	553-567
Number of pages	15
Volume	65
ISBN (Electronic)	9783642410956
ISBN (Print)	9783642410949
DOIs	https://doi.org/10.1007/978-3-642-41095-6_28
Publication status	Published - 2013
Event	10th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2012 - Sydney, NSW, Australia Duration: 13 Feb 2012 → 17 Feb 2012

Other

Other	10th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2012
Country/Territory	Australia
City	Sydney, NSW
Period	13/02/12 → 17/02/12

Access to Document

10.1007/978-3-642-41095-6_28

Cite this

@inproceedings{0bb4e598735041319778fdb92baada9a,

title = "The Stochastic EM Algorithm for Censored Mixed Models",

abstract = "The Stochastic EM algorithm is a Monte Carlo method for approximating the regular EM algorithm in missing data situations where the E step is intractable. It produces a stationary Markov chain iterative sequence where each iteration is the result of applying complete data maximum likelihood estimation to a single simulation of the complete data conditional on the observed data. Analogously to other Markov chain Monte Carlo methods, the final estimate is the mean of the iterative sequence after a burn-in period. We consider a case study of the application of the Stochastic EM algorithm for censored mixed models, a computationally challenging context. The Stochastic EM algorithm is particularly simple to apply to either linear or non-linear mixed models with censoring. All that is required is a routine to simulate censored multivariate normal observations, and a routine to fit the desired uncensored mixed model. An application is presented involving repeated measures of HIV viral load subject to censoring caused by a lower detection limit of the assay. It is found that crude methods ignoring the censoring are biased compared to results from the Stochastic EM algorithm.",

author = "Marschner, {Ian C.}",

year = "2013",

doi = "10.1007/978-3-642-41095-6_28",

language = "English",

isbn = "9783642410949",

volume = "65",

pages = "553--567",

editor = "Josef Dick and Kuo, {Frances Y.} and Peters, {Gareth W.} and Sloan, {Ian H.}",

booktitle = "Monte Carlo and Quasi-Monte Carlo Methods 2012",

publisher = "Springer, Springer Nature",

address = "United States",

note = "10th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2012 ; Conference date: 13-02-2012 Through 17-02-2012",

}

Marschner, IC 2013, The Stochastic EM Algorithm for Censored Mixed Models. in J Dick, FY Kuo, GW Peters & IH Sloan (eds), Monte Carlo and Quasi-Monte Carlo Methods 2012. vol. 65, Springer, Springer Nature, Heidelberg, pp. 553-567, 10th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2012, Sydney, NSW, Australia, 13/02/12. https://doi.org/10.1007/978-3-642-41095-6_28

TY - GEN

T1 - The Stochastic EM Algorithm for Censored Mixed Models

AU - Marschner, Ian C.

PY - 2013

Y1 - 2013

N2 - The Stochastic EM algorithm is a Monte Carlo method for approximating the regular EM algorithm in missing data situations where the E step is intractable. It produces a stationary Markov chain iterative sequence where each iteration is the result of applying complete data maximum likelihood estimation to a single simulation of the complete data conditional on the observed data. Analogously to other Markov chain Monte Carlo methods, the final estimate is the mean of the iterative sequence after a burn-in period. We consider a case study of the application of the Stochastic EM algorithm for censored mixed models, a computationally challenging context. The Stochastic EM algorithm is particularly simple to apply to either linear or non-linear mixed models with censoring. All that is required is a routine to simulate censored multivariate normal observations, and a routine to fit the desired uncensored mixed model. An application is presented involving repeated measures of HIV viral load subject to censoring caused by a lower detection limit of the assay. It is found that crude methods ignoring the censoring are biased compared to results from the Stochastic EM algorithm.

AB - The Stochastic EM algorithm is a Monte Carlo method for approximating the regular EM algorithm in missing data situations where the E step is intractable. It produces a stationary Markov chain iterative sequence where each iteration is the result of applying complete data maximum likelihood estimation to a single simulation of the complete data conditional on the observed data. Analogously to other Markov chain Monte Carlo methods, the final estimate is the mean of the iterative sequence after a burn-in period. We consider a case study of the application of the Stochastic EM algorithm for censored mixed models, a computationally challenging context. The Stochastic EM algorithm is particularly simple to apply to either linear or non-linear mixed models with censoring. All that is required is a routine to simulate censored multivariate normal observations, and a routine to fit the desired uncensored mixed model. An application is presented involving repeated measures of HIV viral load subject to censoring caused by a lower detection limit of the assay. It is found that crude methods ignoring the censoring are biased compared to results from the Stochastic EM algorithm.

UR - http://www.scopus.com/inward/record.url?scp=84893463243&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-41095-6_28

DO - 10.1007/978-3-642-41095-6_28

M3 - Conference proceeding contribution

AN - SCOPUS:84893463243

SN - 9783642410949

VL - 65

SP - 553

EP - 567

BT - Monte Carlo and Quasi-Monte Carlo Methods 2012

A2 - Dick, Josef

A2 - Kuo, Frances Y.

A2 - Peters, Gareth W.

A2 - Sloan, Ian H.

PB - Springer, Springer Nature

CY - Heidelberg

T2 - 10th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2012

Y2 - 13 February 2012 through 17 February 2012

ER -

The Stochastic EM Algorithm for Censored Mixed Models

Abstract

Other

Access to Document

Other files and links

Fingerprint

Cite this