Two-step and likelihood methods for joint models of longitudinal and survival data

ABSTRACT

We compare the commonly used two-step methods and joint likelihood method for joint models of longitudinal and survival data via extensive simulations. The longitudinal models include LME, GLMM, and NLME models, and the survival models include Cox models and AFT models. We find that the full likelihood method outperforms the two-step methods for various joint models, but it can be computationally challenging when the dimension of the random effects in the longitudinal model is not small. We thus propose an approximate joint likelihood method which is computationally efficient. We find that the proposed approximation method performs well in the joint model context, and it performs better for more “continuous” longitudinal data. Finally, a real AIDS data example shows that patients with higher initial viral load or lower initial CD4 are more likely to drop out earlier during an anti-HIV treatment.

KEYWORDS:

• Approximation method
• Em algorithm
• Likelihood method
• Mixed effects model
• Two-step methods

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62
• Secondary 92

Acknowledgments

We are grateful for the valuable comments of the editor, associate editor and referees. The research was supported by a Canada Natural Sciences and Engineering Research Council (NSERC) discovery grant RGPIN238677.