We aim to evaluate the marginal effects of covariates on time-to-disability in the elderly under the semi-competing risks framework, as death dependently censors disability, not vice versa. It becomes particularly challenging when time-to-disability is subject to interval censoring due to intermittent assessments. A left truncation issue arises when the age time scale is applied. We develop a flexible two-parameter copula-based semiparametric transformation model for semi-competing risks data subject to interval censoring and left truncation. The two-parameter copula quantifies both upper and lower tail dependence between two margins. The semiparametric transformation models incorporate proportional hazards and proportional odds models in both margins. We propose a two-step sieve maximum likelihood estimation procedure and study the sieve estimators’ asymptotic properties. Simulations show that the proposed method corrects biases in the marginal method. We demonstrate the proposed method in a large-scale Chinese Longitudinal Healthy Longevity Study and provide new insights into preventing disability in the elderly. The proposed method could be applied to the general semi-competing risks data with intermittently assessed disease status.
SousaRMFerriCPAcostaDet al. Contribution of chronic diseases to disability in elderly people in countries with low and middle incomes: a 10/66 dementia research group population-based survey. Lancet2009; 374: 1821–1830.
2.
GriffithLRainaPWuHet al. Population attributable risk for functional disability associated with chronic conditions in Canadian older adults. Age Ageing2010; 39: 738–745.
3.
FongJH. Disability incidence and functional decline among older adults with major chronic diseases. BMC Geriatr2019; 19: 1–9.
4.
JusterFTSuzmanR. An overview of the health and retirement study. J Hum Res1995; 30: 7–56.
5.
SteptoeABreezeEBanksJet al. Cohort profile: the English longitudinal study of ageing. Int J Epidemiol2013; 42: 1640–1648.
6.
ZengY. Reliability of age reporting among the chinese oldest-old in the CLHLS datasets. In: Healthy longevity in China. Springer, 2008. pp. 61–78.
7.
MajerIMNusselderWJMackenbachJPet al. Mortality risk associated with disability: a population-based record linkage study. Am J Public Health2011; 101: 9–15.
8.
JacobMEMarronMMBoudreauRMet al. Age, race, and gender factors in incident disability. J Gerontol: Ser A2018; 73: 194–197.
9.
AustinPCLeeDSFineJP. Introduction to the analysis of survival data in the presence of competing risks. Circulation2016; 133: 601–609.
10.
FineJPJiangHChappellR. On semi-competing risks data. Biometrika2001; 88: 907–919.
11.
EmuraTSofeuCLRondeauV. Conditional copula models for correlated survival endpoints: individual patient data meta-analysis of randomized controlled trials. Stat Methods Med Res2021; 30: 2634–2650.
12.
LeeKHRondeauVHaneuseS. Accelerated failure time models for semi-competing risks data in the presence of complex censoring. Biometrics2017; 73: 1401–1412.
13.
GaoFZengDLinDY. Semiparametric regression analysis of interval-censored data with informative dropout. Biometrics2018; 74: 1213–1222.
14.
JolyPCommengesDHelmerCet al. A penalized likelihood approach for an illness-death model with interval-censored data: application to age-specific incidence of dementia. Biostatistics2002; 3: 433–443.
15.
RouanetAJolyPDartiguesJFet al. Joint latent class model for longitudinal data and interval-censored semi-competing events: application to dementia. Biometrics2016; 72: 1123–1135.
16.
ZhouJZhangJMcLainACet al. Semiparametric regression of the illness-death model with interval censored disease incidence time: an application to the ACLS data. Stat Methods Med Res2020; 29: 3707–3720.
17.
PengLFineJP. Regression modeling of semicompeting risks data. Biometrics2007; 63: 96–108.
18.
ChenYH. Maximum likelihood analysis of semicompeting risks data with semiparametric regression models. Lifetime Data Anal2012; 18: 36–57.
19.
LiDHuXJWangR. Evaluating association between two event times with observations subject to informative censoring. J Am Stat Assoc2021; 0: 1–13.
20.
XuJKalbfleischJDTaiB. Statistical analysis of illness-death processes and semicompeting risks data. Biometrics2010; 66: 716–725.
21.
LamarcaRAlonsoJGomezGet al. Left-truncated data with age as time scale: an alternative for survival analysis in the elderly population. J Gerontol Ser A: Biol Sci Med Sci1998; 53: 337–343.
22.
WangPLiDSunJ. A pairwise pseudo-likelihood approach for left-truncated and interval-censored data under the Cox model. Biometrics2021; 77: 1303–1314.
23.
BogaertsKLesaffreE. A new, fast algorithm to find the regions of possible support for bivariate interval-censored data. J Comput Graph Stat2012; 13: 330–340.
24.
SunTDingY. Copula-based semiparametric regression method for bivariate data under general interval censoring. Biostatistics2021; 22: 315–330.
25.
PettiDElettiAMarraGet al. Copula link-based additive models for bivariate time-to-event outcomes with general censoring scheme. Comput Stat Data Anal2022; 175: 107550.
26.
MaLHuTSunJ. Sieve maximum likelihood regression analysis of dependent current status data. Biometrika2015; 102: 731–738.
27.
SklarA. Fonctions de répartition à n dimensions et leurs marges. Publications de L’Institut de Statistique de L’Université de Paris1959; 8: 229–231.
28.
NelsenRB. An introduction to copulas. New York: Springer-Verlag, 2006.
SunTDingY. copulacenr: copula based regression models for bivariate censored data in R. R Journal2020; 12: 266.
31.
HuangJRossiniA. Sieve estimation for the proportional-odds failure-time regression model with interval censoring. J Am Stat Assoc1997; 92: 960–967.
32.
ZhouQHuTSunJ. A sieve semiparametric maximum likelihood approach for regression analysis of bivariate interval-censored failure time data. J Am Stat Assoc2017; 112: 664–672.
33.
LeeCYWongKYLamKet al. Analysis of clustered interval-censored data using a class of semiparametric partly linear frailty transformation models. Biometrics2022; 78: 165–178.
34.
SunTLiuYCookRJet al. Copula-based score test for bivariate time-to-event data, with application to a genetic study of AMD progression. Lifetime Data Anal2019; 25: 546–568.
35.
SunLWangLSunJ. Estimation of the association for bivariate interval-censored failure time data. Scand J Stat2006; 33: 637–649.
36.
CuiQZhaoHSunJ. A new copula model-based method for regression analysis of dependent current status data. Stat Interface2018; 11: 463–471.
37.
DingYNanB. A sieve M-theorem for bundled parameters in semiparametric models, with application to the efficient estimation in a linear model for censored data. Ann Stat2011; 39: 2795–3443.
38.
LindfieldGRPennyJET. Microcomputers in numerical analysis. New York: Halsted Press, 1989.
39.
AndersenPKPohar PermeM. Inference for outcome probabilities in multi-state models. Lifetime Data Anal2008; 14: 405–431.
40.
VaradhanRXueQLBandeen-RocheK. Semicompeting risks in aging research: methods, issues and needs. Lifetime Data Anal2014; 20: 538–562.
41.
Meira-MachadoLSesteloM. Estimation in the progressive illness-death model: a nonexhaustive review. Biom J2019; 61: 245–263.
42.
LvYBYuanJQMaoCet al. Association of body mass index with disability in activities of daily living among chinese adults 80 years of age or older. JAMA Network Open2018; 1: e181915.
43.
FongJHSherrisMYapJ. Forecasting disability: application of a frailty model. Scand Actuar J2017; 2017: 125–147.
44.
FuinoMWagnerJ. Duration of long-term care: socio-economic factors, type of care interactions and evolution. Insur: Math Econ2020; 90: 151–168.
45.
HsiehJJWangWAdam DingA. Regression analysis based on semicompeting risks data. J R Stat Soc: Ser B (Statistical Methodology)2008; 70: 3–20.
46.
HsiehJJTsaiCFet al. Dependence model selection for semi-competing risks data. Open J Stat2020; 10: 228.
47.
KimGSilvapulleMJSilvapulleP. Comparison of semiparametric and parametric methods for estimating copulas. Comput Stat Data Anal2007; 51: 2836–2850.
48.
ZengDMaoLLinD. Maximum likelihood estimation for semiparametric transformation models with interval-censored data. Biometrika2016; 103: 253–271.
49.
LiSWuQSunJ. Penalized estimation of semiparametric transformation models with interval-censored data and application to Alzheimer’s disease. Stat Methods Med Res2020; 29: 2151–2166.
50.
GoethalsKJanssenPDuchateauL. Frailty models and copulas: similarities and differences. J Appl Stat2008; 35: 1071–1079.
51.
WienkeA. Frailty models in survival analysis. New York: Chapman and Hall/CRC, 2010.
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