Penalized spline joint models for longitudinal and time-to-event data

Huong Pham, Darfiana Nur, Alan Branford

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)


    The joint models for longitudinal data and time-to-event data have recently received numerous attention in clinical and epidemiologic studies. Our interest is in modeling the relationship between event time outcomes and internal time-dependent covariates. In practice, the longitudinal responses often show non linear and fluctuated curves. Therefore, the main aim of this paper is to use penalized splines with a truncated polynomial basis to parameterize the non linear longitudinal process. Then, the linear mixed-effects model is applied to subject-specific curves and to control the smoothing. The association between the dropout process and longitudinal outcomes is modeled through a proportional hazard model. Two types of baseline risk functions are considered, namely a Gompertz distribution and a piecewise constant model. The resulting models are referred to as penalized spline joint models; an extension of the standard joint models. The expectation conditional maximization (ECM) algorithm is applied to estimate the parameters in the proposed models. To validate the proposed algorithm, extensive simulation studies were implemented followed by a case study. In summary, the penalized spline joint models provide a new approach for joint models that have improved the existing standard joint models.

    Original languageEnglish
    Pages (from-to)10294-10314
    Number of pages21
    Issue number20
    Early online date2017
    Publication statusPublished - 2017


    • Joint models
    • longitudinal data
    • random effects
    • survival data
    • time-dependent covariates


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