Modeling semi-competing risks data as a longitudinal bivariate process

Daniel Nevo, Deborah Blacker, Eric B. Larson, Sebastien Haneuse

Research output: Contribution to journalArticlepeer-review


As individuals age, death is a competing risk for Alzheimer's disease (AD) but the reverse is not the case. As such, studies of AD can be placed within the semi-competing risks framework. Central to semi-competing risks, and in contrast to standard competing risks, is that one can learn about the dependence structure between the two events. To-date, however, most methods for semi-competing risks treat dependence as a nuisance and not a potential source of new clinical knowledge. We propose a novel regression-based framework that views the two time-to-event outcomes through the lens of a longitudinal bivariate process on a partition of the time scales of the two events. A key innovation of the framework is that dependence is represented in two distinct forms, local and global dependence, both of which have intuitive clinical interpretations. Estimation and inference are performed via penalized maximum likelihood, and can accommodate right censoring, left truncation, and time-varying covariates. An important consequence of the partitioning of the time scale is that an ambiguity regarding the specific form of the likelihood contribution may arise; a strategy for sensitivity analyses regarding this issue is described. The framework is then used to investigate the role of gender and having ≥1 apolipoprotein E (APOE) ε4 allele on the joint risk of AD and death using data from the Adult Changes in Thought study.

Original languageEnglish
Pages (from-to)922-936
Number of pages15
Issue number3
StatePublished - Sep 2022
Externally publishedYes


  • alzheimer's disease
  • b-splines
  • discrete-time survival
  • longitudinal modeling
  • penalized maximum likelihood


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