Lifetime Data Analysis

, Volume 23, Issue 2, pp 183–206 | Cite as

Jointly modeling longitudinal proportional data and survival times with an application to the quality of life data in a breast cancer trial

  • Hui Song
  • Yingwei Peng
  • Dongsheng Tu


Motivated by the joint analysis of longitudinal quality of life data and recurrence free survival times from a cancer clinical trial, we present in this paper two approaches to jointly model the longitudinal proportional measurements, which are confined in a finite interval, and survival data. Both approaches assume a proportional hazards model for the survival times. For the longitudinal component, the first approach applies the classical linear mixed model to logit transformed responses, while the second approach directly models the responses using a simplex distribution. A semiparametric method based on a penalized joint likelihood generated by the Laplace approximation is derived to fit the joint model defined by the second approach. The proposed procedures are evaluated in a simulation study and applied to the analysis of breast cancer data motivated this research.


Censoring Gauss–Hermite numerical integration Laplace approximation Logit transformation Logistic-normal distribution Random effects  Simplex distribution 



The work of Hui Song is supported by the Fundamental Research Funds for the Central Universities of China. The work of Yingwei Peng and Dongsheng Tu is supported in part by research grants from Natural Sciences and Engineering Research Council of Canada. This work was made possible by the facilities of the Shared Hierarchical Academic Research Computing Network (SHARCNET: and Compute/Calcul Canada.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.School of Mathematical SciencesDalian University of TechnologyDalianChina
  2. 2.Departments of Public Health Sciences and Mathematics and StatisticsQueen’s UniversityKingstonCanada

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