Sage Journals: Discover world-class research

Abstract

Atrial fibrillation is an arrhythmic disorder where the electrical signals of the heart become irregular. The probability of atrial fibrillation (binary response) is often time varying in a structured fashion, as is the influence of associated risk factors. A generalized nonlinear mixed effects model is presented to estimate the time-related probability of atrial fibrillation using a temporal decomposition approach to reveal the pattern of the probability of atrial fibrillation and their determinants. This methodology generalizes to patient-specific analysis of longitudinal binary data with possibly time-varying effects of covariates and with different patient-specific random effects influencing different temporal phases. The motivation and application of this model is illustrated using longitudinally measured atrial fibrillation data obtained through weekly trans-telephonic monitoring from an NIH sponsored clinical trial being conducted by the Cardiothoracic Surgery Clinical Trials Network.

Keywords

Binary longitudinal response nonlinear model mixed effects model temporal decomposition multiphase model time varying coefficient

Get full access to this article

View all access options for this article.

References

Lloyd-Jones

Adams

Brown

et al.

Heart disease and stroke statistics–2010 update. A report from the american heart association. Circulation 2010; 121: e1–e170.

Gillinov

. Choice of surgical lesion set: Answers from the data. Ann Thoracic Surgery 2007; 84: 1786–1792.

Laird

Ware

. Random-effects models for longitudinal data. Biometrics 1982; 38: 963–974.

Muller

Rosner

. A Bayesian population model with hierarchical mixture prior applied to blood count data. J Am Statis Assoc 1997; 92: 1279–1292.

Mikulich

Zerbe

Jones

et al.

Comparing Linear and Nonlinear mixed model approaches to Cosinor analysis. Statis Med 2003; 22: 3195–3211.

Ding

. Population HIV-1 dynamics in vivo: Applicable models and inferential tools for virological data from AIDS clinical trials. Biometrics 1999; 55: 410–418.

Davidian

Giltinan

. Nonlinear models for repeated measurement data, New York: Chapman and Hall, 1995.

Vonesh

Chinchilli

. Linear and nonlinear models for the analysis of repeated measurements, London: Chapman and Hall, 1997.

Molenberghs

Verbeke

. Models for discrete longitudinal data, New York: Springer, 2005.

10.

Vonesh

. Generalized linear and nonlinear models for correlated data: Theory and applications using SAS, Cary, NC: SAS Institute Inc, 2012.

11.

Guo

. Functional data analysis in longitudinal setting using smoothing splines. Statis Meth Med Res 2004; 13: 49–62.

12.

Pinheiro

Bates

. Approximations to the log-likelihood function in the non-linear mixed-effects model. J Computat Graphic Stat 1995; 4: 12–35.

13.

Vonesh

. Non-linear models for the analysis of longitudinal data. Stat Med 1992; 11: 1929–1954.

14.

. A joint model for nonlinear mixed-effects models with censoring and covariates measured with error, with application to AIDS studies. J Am Stat Assoc 2002; 97: 955–964.

15.

Rajeswaran

Blackstone

. A multiphase non-linear mixed effects model: An application to Spirometry after lung transplantation. Stat Meth Med Res 2017; 26: 21–42.

16.

Faes

Aerts

Geys

et al.

Bayesian testing for trend in a power model for clustered binary data. Environ Ecol Stat 2004; 11: 305–322.

17.

. Nonparametric varying-coefficient models for the analyses of longitudinal data. Int Stat Rev 2000; 3: 373–393.

18.

Zhang

. Nonparametric regression methods for longitudinal data analysis: Mixed-effects modeling approaches, New York: John Wiley & Sons Inc, 2006.

19.

Senturk

Muller

. Generalized varying coefficient models for longitudinal data. Biometrika 2008; 95: 653–666.

20.

Gillinov

Argenziano

Blackstone

et al.

Designing comparative effectiveness trials of surgical ablation for atrial fibrillation: Experience of the Cardiothoracic Surgical Trials Network. J Thorac Cardiovasc Surg 2011; 142: 257–264.

21.

Martinussen

Scheike

. Dynamic regression models for survival data, New York: Springer, 2005.

22.

Blackstone

Naftel

Turner

Jr . The decomposition of time-varying hazard into phases, each incorporating a separate stream of concomitant information. J Am Stat Assoc 1986; 81: 615–624.

23.

Hazelrig

Turner

Jr. Blackstone

. Parametric survival analysis combining longitudinal and cross-sectional censored and interval-censored data with concomitant information. Biometrics 1982; 38: 1–15.

24.

Turner

Hazelrig

Blackstone

. Bounded survival. Math Biosci 1982; 59: 33–46.

25.

Banga

Gildea

Rajeswaran

et al.

The natural history of lung function after lung transplantation for a1-antitrypsin deficiency. Am J Respiratory Crit Care Med 2014; 190: 274–281.

26.

Beach

Mihaljevic

Rajeswaran

et al.

Ventricular hypertrophy and left atrial dilatation persist and are associated with reduced survival after valve replacement for aortic stenosis. J Thorac Cardiovasc Surg 2014; 147: 362–369.

27.

Mason

Rajeswaran

et al.

Effect of changes in postoperative spirometry on survival after lung transplantation. J Thorac Cardiovasc Surg 2012; 144: 197–203.

28.

Mason

Rajeswaran

Murthy

et al.

Spirometry after transplantation: How much better are two lungs than one?

Ann Thorac Surg 2008; 85: 1193–1201.

29.

Gillinov

Bhavani

Blackstone

et al.

Surgery for permanent atrial fibrillation: Impact of patient factors and lesion set. Ann Thoracic Surg 2006; 82: 502–514.

30.

Diggle

Heagerty

Liang

K-Y

et al.

Analysis of longitudinal data, (2nd version). New York: Oxford, 2002.

31.

Kleinman

. Proportions with extraneous variance: Single and independent samples. J Am Stat Assoc 1973; 68: 46–54.

32.

McCulloch

. Maximum likelihood algorithm for generalized linear mixed models. J Am Stat Assoc 1997; 92: 162–170.

33.

Joe

. Accuracy of Laplace approximation for discrete response mixed models. Computat Data Analysis 2008; 52: 5066–5074.

34.

Breslow

Clayton

. Approximate inference in generalized linear mixed models. J Am Statis Assoc 1993; 88: 9–25.

35.

. Mixed effects models for complex data, New York: Chapman and Hall, 2010.

36.

Lee

Nelder

Pawitan

. Generalized linear models with random effects: Unified analysis via H-likelihood, New York: Chapman and Hall, 2006.

37.

Fitzmaurice

Laird

Ware

. Applied longitudinal analysis, New Jersey: John Wiley & Sons, 2002.

Supplementary Material

Please find the following supplemental material available below.

For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.

For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.

0.00 MB

0.33 MB

Probability of atrial fibrillation after ablation: Using a parametric nonlinear temporal decomposition mixed effects model

Abstract

Keywords

Get full access to this article

References

Supplementary Material