A marginal cure rate proportional hazards model for spatial survival data

Patrick Schnell, Dipankar Bandyopadhyay, Brian J. Reich, Martha Nunn

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Dental studies often produce spatially referenced multivariate time-to-event data, such as the time until tooth loss due to periodontal disease. These data are used to identify risk factors that are associated with tooth loss, and to predict outcomes for an individual patient. The rate of spatial referencing can vary with various tooth locations. In addition, these event time data are heavily censored, mostly because a certain proportion of teeth in the population are not expected to experience failure and can be considered 'cured'. We assume a proportional hazards model with a surviving fraction to model these clustered correlated data and account for dependence between nearby teeth by using spatial frailties which are modelled as linear combinations of positive stable random effects. This model permits predictions (conditioned on spatial frailties) that account for the survival status of nearby teeth and simultaneously preserves the proportional hazards relationship marginally over the random effects for the susceptible teeth, allowing for interpretable estimates of the effects of risk factors on tooth loss. We explore the potential of this model via simulation studies and application to a real data set obtained from a private periodontal practice, and we illustrate its advantages over other competing models to identify important risk factors for tooth loss and to predict the remaining lifespan of a patient's teeth.

Original languageEnglish (US)
Pages (from-to)673-691
Number of pages19
JournalJournal of the Royal Statistical Society. Series C: Applied Statistics
Issue number4
StatePublished - Aug 1 2015

Bibliographical note

Publisher Copyright:
© 2015 Royal Statistical Society.


  • Bayesian hierarchical modelling
  • Cure rate
  • Dental data
  • Extreme value analysis
  • Frailty
  • Positive stable
  • Tooth loss


Dive into the research topics of 'A marginal cure rate proportional hazards model for spatial survival data'. Together they form a unique fingerprint.

Cite this