Statistics and Its Interface

Volume 1 (2008)

Number 1

A penalized likelihood approach to joint modeling of longitudinal measurements and time-to-event data

Pages: 33 – 45



Xihong Lin (Department of Biostatistics, Harvard School of Public Health, Boston, Mass., U.S.A.)

Jeremy M.G. Taylor (Department of Biostatistics, University of Michigan, Ann Arbor, Mich., U.S.A)

Wen Ye (Department of Biostatistics, University of Michigan, Ann Arbor, Mich., U.S.A.)


Recently joint models for longitudinal and time-to-event data have attracted a lot attention. A full joint likelihood approach using an EM algorithm or Bayesian methods of estimation not only eliminates the bias in naive and twostage methods, but also improves efficiency. However, both the EM algorithm and a Bayesian method are computationally intensive, limiting the utilization of these joint models. We propose to use an estimation procedure based on a penalized joint likelihood generated by Laplace approximation of a joint likelihood and by using a partial likelihood instead of the full likelihood for the event time data. The results of a simulation study show that this penalized likelihood approach performs as well as the corresponding EM algorithm under a variety of scenarios, but only requires a fraction of the computational time. An additional advantage of this approach is that it does not require estimation of the baseline hazard function. The proposed procedure is applied to a data set for evaluating the effect of the longitudinal biomarker PSA on the recurrence of prostate cancer.


penalized likelihood, survival, longitudinal, joint modeling, Laplace approximation

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