Joint analysis of stochastic processes with application to smoking patterns and insomnia
This article proposes a joint modeling framework for longitudinal insomnia measurements and a stochastic smoking cessation process in the presence of a latent permanent quitting state (i.e., ‘cure’). We use a generalized linear mixed‐effects model and a stochastic mixed‐effects model for the longitu...
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| Published in | Statistics in medicine Vol. 32; no. 29; pp. 5133 - 5144 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
England
Blackwell Publishing Ltd
20.12.2013
Wiley Subscription Services, Inc |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0277-6715 1097-0258 1097-0258 |
| DOI | 10.1002/sim.5906 |
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| Abstract | This article proposes a joint modeling framework for longitudinal insomnia measurements and a stochastic smoking cessation process in the presence of a latent permanent quitting state (i.e., ‘cure’). We use a generalized linear mixed‐effects model and a stochastic mixed‐effects model for the longitudinal measurements of insomnia symptom and for the smoking cessation process, respectively. We link these two models together via the latent random effects. We develop a Bayesian framework and Markov Chain Monte Carlo algorithm to obtain the parameter estimates. We formulate and compute the likelihood functions involving time‐dependent covariates. We explore the within‐subject correlation between insomnia and smoking processes. We apply the proposed methodology to simulation studies and the motivating dataset, that is, the Alpha‐Tocopherol, Beta‐Carotene Lung Cancer Prevention study, a large longitudinal cohort study of smokers from Finland. Copyright © 2013 John Wiley & Sons, Ltd. |
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| AbstractList | This article proposes a joint modeling framework for longitudinal insomnia measurements and a stochastic smoking cessation process in the presence of a latent permanent quitting state (i.e., 'cure'). We use a generalized linear mixed-effects model and a stochastic mixed-effects model for the longitudinal measurements of insomnia symptom and for the smoking cessation process, respectively. We link these two models together via the latent random effects. We develop a Bayesian framework and Markov Chain Monte Carlo algorithm to obtain the parameter estimates. We formulate and compute the likelihood functions involving time-dependent covariates. We explore the within-subject correlation between insomnia and smoking processes. We apply the proposed methodology to simulation studies and the motivating dataset, that is, the Alpha-Tocopherol, Beta-Carotene Lung Cancer Prevention study, a large longitudinal cohort study of smokers from Finland. This article proposes a joint modeling framework for longitudinal insomnia measurements and a stochastic smoking cessation process in the presence of a latent permanent quitting state (i.e., ‘cure’). We use a generalized linear mixed‐effects model and a stochastic mixed‐effects model for the longitudinal measurements of insomnia symptom and for the smoking cessation process, respectively. We link these two models together via the latent random effects. We develop a Bayesian framework and Markov Chain Monte Carlo algorithm to obtain the parameter estimates. We formulate and compute the likelihood functions involving time‐dependent covariates. We explore the within‐subject correlation between insomnia and smoking processes. We apply the proposed methodology to simulation studies and the motivating dataset, that is, the Alpha‐Tocopherol, Beta‐Carotene Lung Cancer Prevention study, a large longitudinal cohort study of smokers from Finland. Copyright © 2013 John Wiley & Sons, Ltd. This article proposes a joint modeling framework for longitudinal insomnia measurements and a stochastic smoking cessation process in the presence of a latent permanent quitting state (i.e., 'cure'). We use a generalized linear mixed-effects model and a stochastic mixed-effects model for the longitudinal measurements of insomnia symptom and for the smoking cessation process, respectively. We link these two models together via the latent random effects. We develop a Bayesian framework and Markov Chain Monte Carlo algorithm to obtain the parameter estimates. We formulate and compute the likelihood functions involving time-dependent covariates. We explore the within-subject correlation between insomnia and smoking processes. We apply the proposed methodology to simulation studies and the motivating dataset, that is, the Alpha-Tocopherol, Beta-Carotene Lung Cancer Prevention study, a large longitudinal cohort study of smokers from Finland.This article proposes a joint modeling framework for longitudinal insomnia measurements and a stochastic smoking cessation process in the presence of a latent permanent quitting state (i.e., 'cure'). We use a generalized linear mixed-effects model and a stochastic mixed-effects model for the longitudinal measurements of insomnia symptom and for the smoking cessation process, respectively. We link these two models together via the latent random effects. We develop a Bayesian framework and Markov Chain Monte Carlo algorithm to obtain the parameter estimates. We formulate and compute the likelihood functions involving time-dependent covariates. We explore the within-subject correlation between insomnia and smoking processes. We apply the proposed methodology to simulation studies and the motivating dataset, that is, the Alpha-Tocopherol, Beta-Carotene Lung Cancer Prevention study, a large longitudinal cohort study of smokers from Finland. This article proposes a joint modeling framework for longitudinal insomnia measurements and a stochastic smoking cessation process in the presence of a latent permanent quitting state (i.e., “cure”). A generalized linear mixed-effects model is used for the longitudinal measurements of insomnia symptom and a stochastic mixed-effects model is used for the smoking cessation process. These two models are linked together via the latent random effects. A Bayesian framework and Markov Chain Monte Carlo algorithm are developed to obtain the parameter estimates. The likelihood functions involving time-dependent covariates are formulated and computed. The within-subject correlation between insomnia and smoking processes is explored. The proposed methodology is applied to simulation studies and the motivating dataset, i.e., the Alpha-Tocopherol, Beta-Carotene (ATBC) Lung Cancer Prevention study, a large longitudinal cohort study of smokers from Finland. This article proposes a joint modeling framework for longitudinal insomnia measurements and a stochastic smoking cessation process in the presence of a latent permanent quitting state (i.e., 'cure'). We use a generalized linear mixed-effects model and a stochastic mixed-effects model for the longitudinal measurements of insomnia symptom and for the smoking cessation process, respectively. We link these two models together via the latent random effects. We develop a Bayesian framework and Markov Chain Monte Carlo algorithm to obtain the parameter estimates. We formulate and compute the likelihood functions involving time-dependent covariates. We explore the within-subject correlation between insomnia and smoking processes. We apply the proposed methodology to simulation studies and the motivating dataset, that is, the Alpha-Tocopherol, Beta-Carotene Lung Cancer Prevention study, a large longitudinal cohort study of smokers from Finland. [PUBLICATION ABSTRACT] |
| Author | Luo, Sheng |
| Author_xml | – sequence: 1 givenname: Sheng surname: Luo fullname: Luo, Sheng email: Correspondence to: Sheng Luo, Division of Biostatistics University of Texas School of Public Health 1200 Pressler St Houston Texas 77030 U.S.A., sheng.t.luo@uth.tmc.edu organization: Division of Biostatistics, University of Texas School of Public Health, 1200 Pressler St, Texas 77030, Houston, U.S.A |
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| References | Li Y, Wileyto EP, Heitjan DF. Modeling smoking cessation data with alternating states and a cure fraction using frailty models. Statistics in Medicine 2010; 29(6):627-638. Bixler EO, Kales A, Soldatos CR, Kales JD, Healey S. Prevalence of sleep disorders in the Los Angeles metropolitan area. The American Journal of Psychiatry 1979; 136:1257-1262. Phillips B, Mannino DM. Do insomnia complaints cause hypertension or cardiovascular disease?. Journal of Clinical Sleep Medicine 2007; 3:489-94. Hughes JR. Effects of abstinence from tobacco: valid symptoms and time course. Nicotine & Tobacco Research 2007; 9:315-327. Group AS. Incidence of cancer and mortality following α-tocopherol and β-carotene supplementation. Journal of American Medical Association 2003; 290(4):476-485. Diggle PJ, Heagerty P, Liang KY, Zeger SL. Analysis of Longitudinal Data. Oxford University Press, 2002. Prochaska JO, DiClemente CC. Stages and processes of self-change of smoking: toward an integrative model of change. Journal of Consulting and Clinical Psychology 1983; 31:390-395. Kalbfleisch JD, Prentice RL. The Statistical Analysis of Failure Time Data. John Wiley & Sons, 2002. Daniels MJ, Zhao YD. Modelling the random effects covariance matrix in longitudinal data. Statistics in Medicine 2003; 22(10):1631-1647. Gelman A, Carlin J, Stern H, Rubin D. Bayesian Data Analysis. CRC press, 2004. Luo S, Crainiceanu CM, Louis TA, Chatterjee N. Analysis of smoking cessation patterns using a stochastic mixed-effects model with a latent cured state. Journal of the American Statistical Association 2008; 103:1002-13. Wetter DW, Young TB. The relation between cigarette smoking and sleep disturbance. Preventive Medicine 1994; 23:328-334. Zeng D, Cai J. Asymptotic results for maximum likelihood estimators in joint analysis of repeated measurements and survival time. The Annals of Statistics 2005; 33(5):2132-2163. Mellinger GD, Balter MB, Uhlenhuth EH. Insomnia and its treatment. Prevalence and correlates. Archives of General Psychiatry 1985; 42:225-232. Zeger SL, Liang KY. Feedback models for discrete and continuous time series. Statistica Sinica 1991; 1:51-64. Heagerty PJ, Kurland BF. Misspecified maximum likelihood estimates and generalised linear mixed models. Biometrika 2001; 88(4):973. Ford DE, Kamerow DB. Epidemiologic study of sleep disturbances and psychiatric disorders. An opportunity for prevention?. The Journal of American Medical Association 1989; 262:1479-1484. Anderson T. An Introduction to Multivariate Statistical Analysis, 3rd edn. John Wiley & Sons, 2003. Song X, Davidian M, Tsiatis AA. A semiparametric likelihood approach to joint modeling of longitudinal and time-to-event data. Biometrics 2002; 58(4):742-753. Molenberghs G, Verbeke G. Models for Discrete Longitudinal Data. Springer Verlag, 2005. Li Y, Wileyto EP, Heitjan DF. Prediction of individual long-term outcomes in smoking cessation trials using frailty models. Biometrics 2011; 67:1321-1329. Luo S, Crainiceanu CM, Louis TA, Chatterjee N. Bayesian inference for smoking cessation with a latent cure state. Biometrics 2009; 65:970-978. 1979; 136 2002; 58 1991; 1 2009; 65 2010; 29 1989; 262 1983; 31 1994; 23 2007; 9 2003; 290 2005 2004 2011; 67 2008; 103 2003 2007; 3 2002 2001; 88 1985; 42 2005; 33 2003; 22 e_1_2_8_18_1 e_1_2_8_19_1 e_1_2_8_13_1 Anderson T (e_1_2_8_16_1) 2003 Prochaska JO (e_1_2_8_5_1) 1983; 31 Phillips B (e_1_2_8_7_1) 2007; 3 Molenberghs G (e_1_2_8_15_1) 2005 Zeger SL (e_1_2_8_9_1) 1991; 1 e_1_2_8_3_1 Gelman A (e_1_2_8_17_1) 2004 e_1_2_8_2_1 e_1_2_8_4_1 e_1_2_8_6_1 e_1_2_8_8_1 e_1_2_8_20_1 e_1_2_8_10_1 e_1_2_8_21_1 e_1_2_8_11_1 e_1_2_8_22_1 e_1_2_8_12_1 e_1_2_8_23_1 Diggle PJ (e_1_2_8_14_1) 2002 2858188 - Arch Gen Psychiatry. 1985 Mar;42(3):225-32 2769898 - JAMA. 1989 Sep 15;262(11):1479-84 8078854 - Prev Med. 1994 May;23(3):328-34 314756 - Am J Psychiatry. 1979 Oct;136(10):1257-62 17803012 - J Clin Sleep Med. 2007 Aug 15;3(5):489-94 12876090 - JAMA. 2003 Jul 23;290(4):476-85 19305513 - J Am Stat Assoc. 2008 Sep 1;103(483):1002-1013 20077505 - Stat Med. 2010 Mar 15;29(6):627-38 19173701 - Biometrics. 2009 Sep;65(3):970-8 12495128 - Biometrics. 2002 Dec;58(4):742-53 6863699 - J Consult Clin Psychol. 1983 Jun;51(3):390-5 17365764 - Nicotine Tob Res. 2007 Mar;9(3):315-27 21401566 - Biometrics. 2011 Dec;67(4):1321-9 12720301 - Stat Med. 2003 May 30;22(10):1631-47 |
| References_xml | – reference: Mellinger GD, Balter MB, Uhlenhuth EH. Insomnia and its treatment. Prevalence and correlates. Archives of General Psychiatry 1985; 42:225-232. – reference: Wetter DW, Young TB. The relation between cigarette smoking and sleep disturbance. Preventive Medicine 1994; 23:328-334. – reference: Diggle PJ, Heagerty P, Liang KY, Zeger SL. Analysis of Longitudinal Data. Oxford University Press, 2002. – reference: Song X, Davidian M, Tsiatis AA. A semiparametric likelihood approach to joint modeling of longitudinal and time-to-event data. Biometrics 2002; 58(4):742-753. – reference: Ford DE, Kamerow DB. Epidemiologic study of sleep disturbances and psychiatric disorders. An opportunity for prevention?. The Journal of American Medical Association 1989; 262:1479-1484. – reference: Luo S, Crainiceanu CM, Louis TA, Chatterjee N. Bayesian inference for smoking cessation with a latent cure state. Biometrics 2009; 65:970-978. – reference: Hughes JR. Effects of abstinence from tobacco: valid symptoms and time course. Nicotine & Tobacco Research 2007; 9:315-327. – reference: Group AS. Incidence of cancer and mortality following α-tocopherol and β-carotene supplementation. Journal of American Medical Association 2003; 290(4):476-485. – reference: Kalbfleisch JD, Prentice RL. The Statistical Analysis of Failure Time Data. John Wiley & Sons, 2002. – reference: Zeng D, Cai J. Asymptotic results for maximum likelihood estimators in joint analysis of repeated measurements and survival time. The Annals of Statistics 2005; 33(5):2132-2163. – reference: Luo S, Crainiceanu CM, Louis TA, Chatterjee N. Analysis of smoking cessation patterns using a stochastic mixed-effects model with a latent cured state. Journal of the American Statistical Association 2008; 103:1002-13. – reference: Bixler EO, Kales A, Soldatos CR, Kales JD, Healey S. Prevalence of sleep disorders in the Los Angeles metropolitan area. The American Journal of Psychiatry 1979; 136:1257-1262. – reference: Prochaska JO, DiClemente CC. Stages and processes of self-change of smoking: toward an integrative model of change. Journal of Consulting and Clinical Psychology 1983; 31:390-395. – reference: Anderson T. An Introduction to Multivariate Statistical Analysis, 3rd edn. John Wiley & Sons, 2003. – reference: Heagerty PJ, Kurland BF. Misspecified maximum likelihood estimates and generalised linear mixed models. Biometrika 2001; 88(4):973. – reference: Li Y, Wileyto EP, Heitjan DF. Prediction of individual long-term outcomes in smoking cessation trials using frailty models. Biometrics 2011; 67:1321-1329. – reference: Zeger SL, Liang KY. Feedback models for discrete and continuous time series. Statistica Sinica 1991; 1:51-64. – reference: Gelman A, Carlin J, Stern H, Rubin D. Bayesian Data Analysis. CRC press, 2004. – reference: Li Y, Wileyto EP, Heitjan DF. Modeling smoking cessation data with alternating states and a cure fraction using frailty models. Statistics in Medicine 2010; 29(6):627-638. – reference: Phillips B, Mannino DM. Do insomnia complaints cause hypertension or cardiovascular disease?. Journal of Clinical Sleep Medicine 2007; 3:489-94. – reference: Daniels MJ, Zhao YD. Modelling the random effects covariance matrix in longitudinal data. Statistics in Medicine 2003; 22(10):1631-1647. – reference: Molenberghs G, Verbeke G. Models for Discrete Longitudinal Data. 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| SubjectTerms | Bayes Bayes Theorem Bayesian analysis Cohort Studies Computer Simulation cure model Finland Humans Insomnia joint modeling Longitudinal Studies Markov analysis MCMC mixed-effects model Models, Statistical Monte Carlo simulation Parameter estimation recurrent events Sleep Initiation and Maintenance Disorders - psychology Smoking cessation Smoking Cessation - psychology Stochastic Processes |
| Title | Joint analysis of stochastic processes with application to smoking patterns and insomnia |
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