Distribution-free estimation of local growth rates around interval censored anchoring events

Chenghao Chu, Ying Zhang, Wanzhu Tu

Research output: Contribution to journalArticlepeer-review


Biological processes are usually defined on timelines that are anchored by specific events. For example, cancer growth is typically measured by the change in tumor size from the time of oncogenesis. In the absence of such anchoring events, longitudinal assessments of the outcome lose their temporal reference. In this paper, we considered the estimation of local change rates in the outcomes when the anchoring events are interval-censored. Viewing the subject-specific anchoring event times as random variables from an unspecified distribution, we proposed a distribution-free estimation method for the local growth rates around the unobserved anchoring events. We expressed the rate parameters as stochastic functionals of the anchoring time distribution and showed that under mild regularity conditions, consistent and asymptotically normal estimates of the rate parameters could be achieved, with a √n convergence rate. We conducted a carefully designed simulation study to evaluate the finite sample performance of the method. To motivate and illustrate the use of the proposed method, we estimated the skeletal growth rates of male and female adolescents, before and after the unobserved pubertal growth spurt (PGS) times.

Original languageEnglish (US)
Pages (from-to)463-474
Number of pages12
Issue number2
StatePublished - 2019
Externally publishedYes


  • Interval censoring
  • empirical process
  • nonparametric maximum likelihood
  • pubertal growth

ASJC Scopus subject areas

  • Statistics and Probability
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics


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