IDEAS home Printed from https://ideas.repec.org/a/tsj/stataj/v13y2013i1p165-184.html
   My bibliography  Save this article

Joint modeling of longitudinal and survival data

Author

Listed:
  • Michael J. Crowther

    (University of Leicester)

  • Keith R. Abrams

    (University of Leicester)

  • Paul C. Lambert

    (University of Leicester)

Abstract

The joint modeling of longitudinal and survival data has received remarkable attention in the methodological literature over the past decade; however, the availability of software to implement the methods lags behind. The most common form of joint model assumes that the association between the survival and the longitudinal processes is underlined by shared random effects. As a result, computationally intensive numerical integration techniques such as adaptive Gauss–Hermite quadrature are required to evaluate the likelihood. We describe a new user-written command, stjm, that allows the user to jointly model a continuous longitudinal response and the time to an event of interest. We assume a linear mixed-effects model for the longitudinal submodel, allowing flexibility through the use of fixed or random fractional polynomials of time. Four choices are available for the survival submodel: the exponential, Weibull or Gompertz proportional hazard models, and the flexible parametric model (stpm2). Flexible parametric models are fit on the log cumulative-hazard scale, which has direct computational benefits because it avoids the use of numerical integration to evaluate the cumulative hazard. We describe the features of stjm through application to a dataset investigating the effect of serum bilirubin level on time to death from any cause in 312 patients with primary biliary cirrhosis. Copyright 2013 by StataCorp LP.

Suggested Citation

  • Michael J. Crowther & Keith R. Abrams & Paul C. Lambert, 2013. "Joint modeling of longitudinal and survival data," Stata Journal, StataCorp LP, vol. 13(1), pages 165-184, March.
    • Handle: RePEc:tsj:stataj:v:13:y:2013:i:1:p:165-184
    Note: to access software from within Stata, net describe http://www.stata-journal.com/software/sj13-1/st0289/
    as

    Download full text from publisher

    File URL: http://www.stata-journal.com/article.html?article=st0289
    File Function: link to article purchase
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. William W. Gould & Jeffrey Pitblado & Brian Poi, 2010. "Maximum Likelihood Estimation with Stata," Stata Press books, StataCorp LP, edition 4, number ml4, March.
    2. Patrick Royston & Douglas G. Altman, 1994. "Regression Using Fractional Polynomials of Continuous Covariates: Parsimonious Parametric Modelling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(3), pages 429-453, September.
    3. Paul C. Lambert & Patrick Royston, 2009. "Further development of flexible parametric models for survival analysis," Stata Journal, StataCorp LP, vol. 9(2), pages 265-290, June.
    4. Dimitris Rizopoulos, 2011. "Dynamic Predictions and Prospective Accuracy in Joint Models for Longitudinal and Time-to-Event Data," Biometrics, The International Biometric Society, vol. 67(3), pages 819-829, September.
    5. Dimitris Rizopoulos & Geert Verbeke & Geert Molenberghs, 2010. "Multiple-Imputation-Based Residuals and Diagnostic Plots for Joint Models of Longitudinal and Survival Outcomes," Biometrics, The International Biometric Society, vol. 66(1), pages 20-29, March.
    6. Sophia Rabe-Hesketh & Anders Skrondal & Andrew Pickles, 2002. "Reliable estimation of generalized linear mixed models using adaptive quadrature," Stata Journal, StataCorp LP, vol. 2(1), pages 1-21, February.
    7. Guo X. & Carlin B.P., 2004. "Separate and Joint Modeling of Longitudinal and Event Time Data Using Standard Computer Packages," The American Statistician, American Statistical Association, vol. 58, pages 16-24, February.
    8. Nikos Pantazis & Giota Touloumi, 2010. "Analyzing longitudinal data in the presence of informative drop-out: The jmre1 command," Stata Journal, StataCorp LP, vol. 10(2), pages 226-251, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Thi Thu Pham Huong & Pham Hoa & Nur Darfiana, 2020. "A Bayesian inference for the penalized spline joint models of longitudinal and time-to-event data: A prior sensitivity analysis," Monte Carlo Methods and Applications, De Gruyter, vol. 26(1), pages 49-68, March.
    2. Philipson, Pete & Hickey, Graeme L. & Crowther, Michael J. & Kolamunnage-Dona, Ruwanthi, 2020. "Faster Monte Carlo estimation of joint models for time-to-event and multivariate longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    3. Murray, James & Philipson, Pete, 2023. "Fast estimation for generalised multivariate joint models using an approximate EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    4. Ram Thapa & Harold E. Burkhart & Jie Li & Yili Hong, 2016. "Modeling Clustered Survival Times of Loblolly Pine with Time-dependent Covariates and Shared Frailties," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(1), pages 92-110, March.
    5. Syden Mishi & Weliswa Matekenya & Leward Jeke & Ronney M. Ncwadi & Roseline T. Karambakuwa, 2021. "Firm and product survival analysis: Evidence from South African tax administrative and products data," WIDER Working Paper Series wp-2021-107, World Institute for Development Economic Research (UNU-WIDER).
    6. Wang, Shikun & Li, Zhao & Lan, Lan & Zhao, Jieyi & Zheng, W. Jim & Li, Liang, 2022. "GPU accelerated estimation of a shared random effect joint model for dynamic prediction," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    7. Nuzhat B. Ashra & Michael Crowther, 2019. "Developing a postestimation command for joint models in merlin," London Stata Conference 2019 02, Stata Users Group.
    8. Jiawei Xu & Matthew A. Psioda & Joseph G. Ibrahim, 2023. "Bayesian Design of Clinical Trials Using Joint Cure Rate Models for Longitudinal and Time-to-Event Data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(1), pages 213-233, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhang, Zili & Charalambous, Christiana & Foster, Peter, 2023. "A Gaussian copula joint model for longitudinal and time-to-event data with random effects," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).
    2. Peter Haan & Arne Uhlendorff, 2006. "Estimation of multinomial logit models with unobserved heterogeneity using maximum simulated likelihood," Stata Journal, StataCorp LP, vol. 6(2), pages 229-245, June.
    3. van Geloven, N. & He, Y. & Zwinderman, A.H. & Putter, H., 2021. "Estimation of incident dynamic AUC in practice," Computational Statistics & Data Analysis, Elsevier, vol. 154(C).
    4. Liu, Yue & Liu, Lei & Zhou, Jianhui, 2015. "Joint latent class model of survival and longitudinal data: An application to CPCRA study," Computational Statistics & Data Analysis, Elsevier, vol. 91(C), pages 40-50.
    5. Crowther, Michael J. & Lambert, Paul C., 2013. "stgenreg: A Stata Package for General Parametric Survival Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 53(i12).
    6. Noori Akhtar-Danesh, 2015. "A Comparison of Modeling Scales in Flexible Parametric Models," 2015 Stata Conference 15, Stata Users Group.
    7. Rizopoulos, Dimitris, 2016. "The R Package JMbayes for Fitting Joint Models for Longitudinal and Time-to-Event Data Using MCMC," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 72(i07).
    8. repec:jss:jstsof:35:i09 is not listed on IDEAS
    9. Michael J. Crowther & Keith R. Abrams & Paul C. Lambert, 2011. "Flexible joint modeling of longitudinal and time-to-event data," United Kingdom Stata Users' Group Meetings 2011 07, Stata Users Group.
    10. Kerri Brick & Martine Visser & Justine Burns, 2012. "Risk Aversion: Experimental Evidence from South African Fishing Communities," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 94(1), pages 133-152.
    11. Jan Brenner, 2007. "Parental Impact on Attitude Formation - A Siblings Study on Worries about Immigration," Ruhr Economic Papers 0022, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    12. Hünermund, Paul & Czarnitzki, Dirk, 2019. "Estimating the causal effect of R&D subsidies in a pan-European program," Research Policy, Elsevier, vol. 48(1), pages 115-124.
    13. Malloy, Elizabeth J. & Spiegelman, Donna & Eisen, Ellen A., 2009. "Comparing measures of model selection for penalized splines in Cox models," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2605-2616, May.
    14. Proto, Eugenio & Rustichini, Aldo, 2015. "Life satisfaction, income and personality," Journal of Economic Psychology, Elsevier, vol. 48(C), pages 17-32.
    15. Peter Sivey, 2012. "The effect of waiting time and distance on hospital choice for English cataract patients," Health Economics, John Wiley & Sons, Ltd., vol. 21(4), pages 444-456, April.
    16. Marino, Maria Francesca & Alfó, Marco, 2016. "Gaussian quadrature approximations in mixed hidden Markov models for longitudinal data: A simulation study," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 193-209.
    17. Marcelo Cajias & Philipp Freudenreich & Anna Heller & Wolfgang Schaefers, 2018. "Censored Quantile Regressions and the Determinants of Real Estate Liquidity," ERES eres2018_203, European Real Estate Society (ERES).
    18. Bambio, Yiriyibin & Bouayad Agha, Salima, 2018. "Land tenure security and investment: Does strength of land right really matter in rural Burkina Faso?," World Development, Elsevier, vol. 111(C), pages 130-147.
    19. Erin E. Gabriel & Michael C. Sachs & Dean A. Follmann & Therese M‐L. Andersson, 2020. "A unified evaluation of differential vaccine efficacy," Biometrics, The International Biometric Society, vol. 76(4), pages 1053-1063, December.
    20. Björn Andersson & Tao Xin, 2021. "Estimation of Latent Regression Item Response Theory Models Using a Second-Order Laplace Approximation," Journal of Educational and Behavioral Statistics, , vol. 46(2), pages 244-265, April.
    21. Pregaldini, Damiano & Backes-Gellner, Uschi & Eisenkopf, Gerald, 2020. "Girls’ preferences for STEM and the effects of classroom gender composition: New evidence from a natural experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 178(C), pages 102-123.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tsj:stataj:v:13:y:2013:i:1:p:165-184. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Christopher F. Baum or Lisa Gilmore (email available below). General contact details of provider: http://www.stata-journal.com/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.