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

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 two-stage 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.