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

Chenghao Chu, Ying Zhang, Wanzhu Tu

Research output: Contribution to journalArticle

Abstract

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)
JournalBiometrics
DOIs
StatePublished - Jan 1 2019
Externally publishedYes

Fingerprint

Distribution-free
Interval
Growth
Random variables
Tumors
neoplasms
carcinogenesis
Biological Phenomena
methodology
Regularity Conditions
Convergence Rate
Tumor
Neoplasms
Cancer
Carcinogenesis
Random variable
Outcome Assessment (Health Care)
Simulation Study
Evaluate
sampling

Keywords

  • empirical process
  • Interval censoring
  • 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

Cite this

Distribution-free estimation of local growth rates around interval censored anchoring events. / Chu, Chenghao; Zhang, Ying; Tu, Wanzhu.

In: Biometrics, 01.01.2019.

Research output: Contribution to journalArticle

@article{d454dcb29e8345238f4b986762c833cf,
title = "Distribution-free estimation of local growth rates around interval censored anchoring events",
abstract = "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.",
keywords = "empirical process, Interval censoring, nonparametric maximum likelihood, pubertal growth",
author = "Chenghao Chu and Ying Zhang and Wanzhu Tu",
year = "2019",
month = "1",
day = "1",
doi = "10.1111/biom.13015",
language = "English (US)",
journal = "Biometrics",
issn = "0006-341X",
publisher = "Wiley-Blackwell",

}

TY - JOUR

T1 - Distribution-free estimation of local growth rates around interval censored anchoring events

AU - Chu, Chenghao

AU - Zhang, Ying

AU - Tu, Wanzhu

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - empirical process

KW - Interval censoring

KW - nonparametric maximum likelihood

KW - pubertal growth

UR - http://www.scopus.com/inward/record.url?scp=85063628158&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063628158&partnerID=8YFLogxK

U2 - 10.1111/biom.13015

DO - 10.1111/biom.13015

M3 - Article

JO - Biometrics

JF - Biometrics

SN - 0006-341X

ER -