Semi-Markov models for interval censored transient cognitive states with back transitions and a competing risk

Shaoceng Wei, Richard J. Kryscio

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Continuous-time multi-state stochastic processes are useful for modeling the flow of subjects from intact cognition to dementia with mild cognitive impairment and global impairment as intervening transient cognitive states and death as a competing risk. Each subject's cognition is assessed periodically resulting in interval censoring for the cognitive states while death without dementia is not interval censored. Since back transitions among the transient states are possible, Markov chains are often applied to this type of panel data. In this manuscript, we apply a semi-Markov process in which we assume that the waiting times are Weibull distributed except for transitions from the baseline state, which are exponentially distributed and in which we assume no additional changes in cognition occur between two assessments. We implement a quasi-Monte Carlo (QMC) method to calculate the higher order integration needed for likelihood estimation. We apply our model to a real dataset, the Nun Study, a cohort of 461 participants.

Original languageEnglish
Pages (from-to)2909-2924
Number of pages16
JournalStatistical Methods in Medical Research
Issue number6
StatePublished - Dec 1 2016

Bibliographical note

Funding Information:
This work was partially funded by the following grants to the University of Kentucky's Center on Aging (grant numbers R01 AG038651 and P30 AG028383) from the National Institute on Aging and a grant to the University of Kentucky's Center for Clinical and Translational Science (grant number U54 RR031263) from the National Center for Advancing Translational Science.

Publisher Copyright:
© SAGE Publications.


  • Weibull
  • back transitions
  • interval censoring
  • panel data
  • semi-Markov

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability
  • Health Information Management


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