Bayesian bent-cable growth mixture tobit models for longitudinal data with skewness and detection limit: application to AIDS studies
This paper presents a new Bayesian methodology for identifying a transition period for the development of drug resistance to antiretroviral drug or therapy in HIV/AIDS studies or other related fields. Estimation of such a transition period requires an availability of longitudinal data where growth t...
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| Published in | Statistics in medicine Vol. 35; no. 28; pp. 5302 - 5314 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
England
Blackwell Publishing Ltd
10.12.2016
Wiley Subscription Services, Inc |
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| Online Access | Get full text |
| ISSN | 0277-6715 1097-0258 1097-0258 |
| DOI | 10.1002/sim.7061 |
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| Abstract | This paper presents a new Bayesian methodology for identifying a transition period for the development of drug resistance to antiretroviral drug or therapy in HIV/AIDS studies or other related fields. Estimation of such a transition period requires an availability of longitudinal data where growth trajectories of a response variable tend to exhibit a gradual change from a declining trend to an increasing trend rather than an abrupt change. We assess this clinically important feature of the longitudinal HIV/AIDS data using the bent‐cable framework within a growth mixture Tobit model. To account for heterogeneity of drug resistance among subjects, the parameters of the bent‐cable growth mixture Tobit model are also allowed to differ by subgroups (subpopulations) of patients classified into latent classes on the basis of trajectories of observed viral load data with skewness and left‐censoring. The proposed methods are illustrated using real data from an AIDS clinical study. Copyright © 2016 John Wiley & Sons, Ltd. |
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| AbstractList | This paper presents a new Bayesian methodology for identifying a transition period for the development of drug resistance to antiretroviral drug or therapy in HIV/AIDS studies or other related fields. Estimation of such a transition period requires an availability of longitudinal data where growth trajectories of a response variable tend to exhibit a gradual change from a declining trend to an increasing trend rather than an abrupt change. We assess this clinically important feature of the longitudinal HIV/AIDS data using the bent-cable framework within a growth mixture Tobit model. To account for heterogeneity of drug resistance among subjects, the parameters of the bent-cable growth mixture Tobit model are also allowed to differ by subgroups (subpopulations) of patients classified into latent classes on the basis of trajectories of observed viral load data with skewness and left-censoring. The proposed methods are illustrated using real data from an AIDS clinical study. Copyright © 2016 John Wiley & Sons, Ltd. This paper presents a new Bayesian methodology for identifying a transition period for the development of drug resistance to antiretroviral drug or therapy in HIV/AIDS studies or other related fields. Estimation of such a transition period requires an availability of longitudinal data where growth trajectories of a response variable tend to exhibit a gradual change from a declining trend to an increasing trend rather than an abrupt change. We assess this clinically important feature of the longitudinal HIV/AIDS data using the bent-cable framework within a growth mixture Tobit model. To account for heterogeneity of drug resistance among subjects, the parameters of the bent-cable growth mixture Tobit model are also allowed to differ by subgroups (subpopulations) of patients classified into latent classes on the basis of trajectories of observed viral load data with skewness and left-censoring. The proposed methods are illustrated using real data from an AIDS clinical study. This paper presents a new Bayesian methodology for identifying a transition period for the development of drug resistance to antiretroviral drug or therapy in HIV/AIDS studies or other related fields. Estimation of such a transition period requires an availability of longitudinal data where growth trajectories of a response variable tend to exhibit a gradual change from a declining trend to an increasing trend rather than an abrupt change. We assess this clinically important feature of the longitudinal HIV/AIDS data using the bent-cable framework within a growth mixture Tobit model. To account for heterogeneity of drug resistance among subjects, the parameters of the bent-cable growth mixture Tobit model are also allowed to differ by subgroups (subpopulations) of patients classified into latent classes on the basis of trajectories of observed viral load data with skewness and left-censoring. The proposed methods are illustrated using real data from an AIDS clinical study. Copyright © 2016 John Wiley & Sons, Ltd.This paper presents a new Bayesian methodology for identifying a transition period for the development of drug resistance to antiretroviral drug or therapy in HIV/AIDS studies or other related fields. Estimation of such a transition period requires an availability of longitudinal data where growth trajectories of a response variable tend to exhibit a gradual change from a declining trend to an increasing trend rather than an abrupt change. We assess this clinically important feature of the longitudinal HIV/AIDS data using the bent-cable framework within a growth mixture Tobit model. To account for heterogeneity of drug resistance among subjects, the parameters of the bent-cable growth mixture Tobit model are also allowed to differ by subgroups (subpopulations) of patients classified into latent classes on the basis of trajectories of observed viral load data with skewness and left-censoring. The proposed methods are illustrated using real data from an AIDS clinical study. Copyright © 2016 John Wiley & Sons, Ltd. |
| Author | Dagne, Getachew A. |
| Author_xml | – sequence: 1 givenname: Getachew A. surname: Dagne fullname: Dagne, Getachew A. email: gdagne@health.usf.edu, Correspondence to: Getachew Dagne, Department of Epidemiology & Biostatistics, College of Public Health, MDC 56, University of South Florida, Tampa, FL33612, U.S.A., gdagne@health.usf.edu organization: Department of Epidemiology & Biostatistics, College of Public Health, MDC 56, University of South Florida, FL, 33612, Tampa, U.S.A |
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| Cites_doi | 10.1111/j.1467-985X.2007.00514.x 10.1016/j.jmva.2004.10.002 10.1111/1467-9868.00194 10.4324/9780203879962 10.1038/373123a0 10.1080/01621459.1996.10476679 10.1002/(SICI)1097-0258(20000229)19:4<617::AID-SIM360>3.0.CO;2-R 10.1002/sim.6445 10.1016/S0167-9473(02)00148-2 10.1002/0471721182 10.1002/9780470434567 10.1128/JVI.02413-06 10.7326/0003-4819-133-1-200007040-00004 10.4135/9781412986311.n19 10.2307/1907382 10.1086/515591 10.2307/1912776 10.2307/3316064 10.1080/09332480.2009.10722965 10.1002/icd.483 10.1002/sim.6388 10.1016/j.ijfoodmicro.2007.02.001 10.2307/2533329 10.1111/j.1751-9004.2007.00054.x 10.1080/01621459.1981.10477752 10.1002/sim.5799 10.1201/9780203492000 10.1198/016214505000001177 10.1023/A:1008929526011 |
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| Keywords | change-points mixture distribution skew distribution Bayesian inference mixed-effects models |
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| References | Paterson DL, Swindells S, Mohr J, Brester M, Vergis EN, Squier C, Wagener MM, Singh N. Adherence to protease inhibitor therapy and outcomes in patients with HIV infection. Annals of Internal Medicine 2000; 133:21-30. Ray N, Harrison JE, Blackburn LA, Martin JN, Deeks SG, Doms RW. Clinical resistance to enfuvirtide does not affect susceptibility of human immunodeficiency virus type 1 to other classes of entry inhibitors. Journal of Virology 2007; 81:3240-3250. Duncan TE, Duncan SC, Strycker LA. An Introduction to Latent Variable Growth Curve Modeling: Concepts, Issues, 2nd Ed.Routledge: New York, 2013. Khan SA, Chiu G, Dubin JA. Atmospheric concentration of chloroflurocarbons: Addressing the global concern with the longitudinal bent-cable model. Chance 2009; 22:8-17. Hall CB, Ying J, Kuo L, Lipton RB. Bayesian and profile likelihood change point methods for modeling cognitive function over time. Computational Statistics & Data Analysis 2003; 42:91-109. Hoeksma JB, Kelderman H. On growth curves and mixture models. Infant and Child Development 2006; 15:627-634. Azzalini A, Capitanio A.. Statistical applications of the multivariate skew normal distributions. Journal of Royal Statistical Society, Series B 1999; 61:579-602. Zhao L, Feng D, Neelon B, Buyse M. Evaluation of treatment efficacy using a Bayesian mixture piecewise linear model of longitudinal biomarkers. Statistics in Medicine 2015; 34(10):1733-1746. Muthén B, Asparouhov T. Growth mixture modeling with non-normal distributions. Statistics in Medicine 2014; 34(6):1041-1058. Lorimer MF, Kiermeier A. Analysing microbiologicaldata: Tobit or not Tobit?International Journal of Food Microbilogy 2007; 116:313-318. Lederman MM, Connick E, Landay A, Kuritzkes DR, Spritzler J, Clair SM, Kotzin BL, Fox L, Chiozzi MH, Leonard JM, Rousseau F, Wade M, Roe JD, Martinez A, Kessler H. 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A Joint latent class C changepoint model to improve the prediction of time to graft failure. Journal of the Royal Statistical Society. Series A (Statistics in Society) 2008; 171:299-308. Slate EH, Turnbull BW. (2000). Statistical models for longitudinal biomarkers of disease onset. Statistics in Medicine 2000; 19(4):617-37. Ho DD, Neumann AU, Perelson AS, Chen W, Leonard JM, Markowitz M. Rapid turnover of plasma virions and CD4 lymphocytes in HIV-1 infection. Nature 1995; 373:123-126. Kiuchi AS, Hartigan JA, Holford TR, Rubinstein P, Stevens CE. Change points in the series of T4 counts prior to aids. Biometrics 1995; 51:236-248. Tishler A, Zang I. A new maximum likelihood algorithm for piecewise regression. Journal of the American Statistical Association 1981; 76:980-987. Arellano-Valle RB, Genton MG. On fundamental skew distributions. Journal of Multivariate Analysis 2005; 96:93-116. Dagne GA, Huang Y. 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| References_xml | – reference: Lederman MM, Connick E, Landay A, Kuritzkes DR, Spritzler J, Clair SM, Kotzin BL, Fox L, Chiozzi MH, Leonard JM, Rousseau F, Wade M, Roe JD, Martinez A, Kessler H. Immunologic responses associated with 12 weeks of combination antiretroviral therapy consisting of zidovudine, lamivudine, and ritonavir: results of AIDS Clinical Trials Group Protocol 315. Journal of Infectious Diseases 1998; 178:70-79. – reference: Ray N, Harrison JE, Blackburn LA, Martin JN, Deeks SG, Doms RW. Clinical resistance to enfuvirtide does not affect susceptibility of human immunodeficiency virus type 1 to other classes of entry inhibitors. Journal of Virology 2007; 81:3240-3250. – reference: Lunn DJ, Thomas A, Best N, Spiegelhalter D. WinBUGS - a Bayesian modelling framework: concepts, structure, an extensibility. Statistics and Computing 2000; 10:325-337. – reference: Hedeker D, Gibbons RD. Longitudinal Data Analysis. Wiley: New York, 2006. – reference: Chiua G, Lockharta R, Routledgea R. Bent-cable regression theory and applications. Journal of the American Statistical Association 2006; 101:542-553. – reference: Lorimer MF, Kiermeier A. Analysing microbiologicaldata: Tobit or not Tobit?International Journal of Food Microbilogy 2007; 116:313-318. – reference: Kiuchi AS, Hartigan JA, Holford TR, Rubinstein P, Stevens CE. Change points in the series of T4 counts prior to aids. Biometrics 1995; 51:236-248. – reference: Ho DD, Neumann AU, Perelson AS, Chen W, Leonard JM, Markowitz M. Rapid turnover of plasma virions and CD4 lymphocytes in HIV-1 infection. Nature 1995; 373:123-126. – reference: Muthén B, Asparouhov T. Growth mixture modeling with non-normal distributions. Statistics in Medicine 2014; 34(6):1041-1058. – reference: Tishler A, Zang I. A new maximum likelihood algorithm for piecewise regression. Journal of the American Statistical Association 1981; 76:980-987. – reference: Gelman A, John B, Carlin JB, Stern HS, Rubin DB. Bayesian Data Analysis. Chaoman and Hall/CRC: New York, 2004. – reference: Khan SA, Chiu G, Dubin JA. Atmospheric concentration of chloroflurocarbons: Addressing the global concern with the longitudinal bent-cable model. Chance 2009; 22:8-17. – reference: Dagne GA, Huang Y. Bayesian semiparametric mixture Tobit models with left-censoring, skewness and covariate measurement error. Statistics in Medicine 2013; 32:3881-3898. – reference: Zhao L, Feng D, Neelon B, Buyse M. Evaluation of treatment efficacy using a Bayesian mixture piecewise linear model of longitudinal biomarkers. Statistics in Medicine 2015; 34(10):1733-1746. – reference: Arabmazar A, Schmidt P. An Investigation of the robustness of the Tobit estimator to non-Normality. Econometrica 1982; 50:1055-1064. – reference: Ntzoufras I. Bayesian Modeling using WinBUGS. John Wiley: New Jersey, 2009. – reference: Jung T, Wickrama KAS. An introduction to latent class growth analysis and growth mixture modeling. Social and Personality Psychology Compass 2008; 2:302-317. – reference: Arellano-Valle RB, Genton MG. On fundamental skew distributions. Journal of Multivariate Analysis 2005; 96:93-116. – reference: Hoeksma JB, Kelderman H. On growth curves and mixture models. Infant and Child Development 2006; 15:627-634. – reference: Garre FG, Zwinderman AH, Geskus RB, Sijpkens YWJ. A Joint latent class C changepoint model to improve the prediction of time to graft failure. Journal of the Royal Statistical Society. Series A (Statistics in Society) 2008; 171:299-308. – reference: Genton MG. Skew-Elliptical Distributions and Their Applications: A Journey Beyond Normality. Chapman & Hall / CRC: Boca Raton, FL, 2004. – reference: Duncan TE, Duncan SC, Strycker LA. An Introduction to Latent Variable Growth Curve Modeling: Concepts, Issues, 2nd Ed.Routledge: New York, 2013. – reference: Verbeke G, Lesaffre E. A linear mixed-effects model with heterogeneity in random-effects population. Journal of the American Statistical Association 1996; 91:736-743. – reference: Slate EH, Turnbull BW. (2000). Statistical models for longitudinal biomarkers of disease onset. Statistics in Medicine 2000; 19(4):617-37. – reference: Pauler DK, Laird NM. A mixture model for longitudinal data with application to assessment of noncompliance. Journal of the Royal Statistical Society: Series A 2000; 56:464-472. – reference: Tobin J. Estimation of relationships for limited dependent variables. Econometrica 1958; 26:24-36. – reference: Azzalini A, Capitanio A.. Statistical applications of the multivariate skew normal distributions. Journal of Royal Statistical Society, Series B 1999; 61:579-602. – reference: McLachlan GJ, Peel D. Finite Mixture Models. 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| SubjectTerms | Acquired immune deficiency syndrome Acquired Immunodeficiency Syndrome - virology AIDS Antiretroviral drugs Bayes Theorem Bayesian analysis Bayesian inference change-points Drug resistance HIV Infections Humans Lentivirus Limit of Detection Longitudinal Studies Medical statistics mixed-effects models mixture distribution Models, Statistical Retroviridae skew distribution Viral Load |
| Title | Bayesian bent-cable growth mixture tobit models for longitudinal data with skewness and detection limit: application to AIDS studies |
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