Model selection and diagnostics for joint modeling of survival and longitudinal data with crossing hazard rate functions

Stat Med. 2014 Nov 20;33(26):4532-46. doi: 10.1002/sim.6259. Epub 2014 Jul 7.


Comparison of two hazard rate functions is important for evaluating treatment effect in studies concerning times to some important events. In practice, it may happen that the two hazard rate functions cross each other at one or more unknown time points, representing temporal changes of the treatment effect. Also, besides survival data, there could be longitudinal data available regarding some time-dependent covariates. When jointly modeling the survival and longitudinal data in such cases, model selection and model diagnostics are especially important to provide reliable statistical analysis of the data, which are lacking in the literature. In this paper, we discuss several criteria for assessing model fit that have been used for model selection and apply them to the joint modeling of survival and longitudinal data for comparing two crossing hazard rate functions. We also propose hypothesis testing and graphical methods for model diagnostics of the proposed joint modeling approach. Our proposed methods are illustrated by a simulation study and by a real-data example concerning two early breast cancer treatments.

Keywords: crossing hazard rates; joint model; longitudinal data; model diagnostics; model selection; survival data.

MeSH terms

  • Antineoplastic Combined Chemotherapy Protocols / therapeutic use
  • Breast Neoplasms / drug therapy
  • Cisplatin / therapeutic use
  • Computer Simulation
  • Cyclophosphamide / therapeutic use
  • Cytarabine / therapeutic use
  • Epirubicin / therapeutic use
  • Female
  • Fluorouracil / therapeutic use
  • Humans
  • Life Tables
  • Longitudinal Studies*
  • Methotrexate / therapeutic use
  • Models, Statistical*
  • Survival Analysis*


  • Cytarabine
  • Epirubicin
  • Cyclophosphamide
  • Cisplatin
  • Fluorouracil
  • Methotrexate

Supplementary concepts

  • CEF regimen
  • CMF protocol