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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
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. 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).
    2. Nuzhat B. Ashra & Michael Crowther, 2019. "Developing a postestimation command for joint models in merlin," London Stata Conference 2019 02, Stata Users Group.
    3. 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.
    4. 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).
    5. 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).
    6. 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.
    7. 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.
    8. 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).

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