A new approach to estimation of the proportional hazards model based on interval-censored data with missing covariates.
Case II interval-censored data
EM algorithm
Missing at random
Sieve approach
Journal
Lifetime data analysis
ISSN: 1572-9249
Titre abrégé: Lifetime Data Anal
Pays: United States
ID NLM: 9516348
Informations de publication
Date de publication:
07 2022
07 2022
Historique:
received:
24
03
2021
accepted:
03
02
2022
pubmed:
31
3
2022
medline:
14
7
2022
entrez:
30
3
2022
Statut:
ppublish
Résumé
This paper discusses the fitting of the proportional hazards model to interval-censored failure time data with missing covariates. Many authors have discussed the problem when complete covariate information is available or the missing is completely at random. In contrast to this, we will focus on the situation where the missing is at random. For the problem, a sieve maximum likelihood estimation approach is proposed with the use of I-spline functions to approximate the unknown cumulative baseline hazard function in the model. For the implementation of the proposed method, we develop an EM algorithm based on a two-stage data augmentation. Furthermore, we show that the proposed estimators of regression parameters are consistent and asymptotically normal. The proposed approach is then applied to a set of the data concerning Alzheimer Disease that motivated this study.
Identifiants
pubmed: 35352270
doi: 10.1007/s10985-022-09550-y
pii: 10.1007/s10985-022-09550-y
doi:
Types de publication
Journal Article
Research Support, Non-U.S. Gov't
Langues
eng
Sous-ensembles de citation
IM
Pagination
335-355Informations de copyright
© 2022. The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Références
Chen K, Jin Z, Ying Z (2002) Semiparametric analysis of transformation models with censored data. Biometrika 89:659–668
doi: 10.1093/biomet/89.3.659
Chen HY, Little RJ (1999) Proportional hazards regression with missing covariates. J Am Stat Assoc 94(447):896–908
doi: 10.1080/01621459.1999.10474195
Chang IS, Wen CC, Wu YJ (2007) A profile likelihood theory for the correlated gamma-frailty model with current status family data. Stat Sin 17:1023–1046
Du MY, Li HQ, Sun JG (2021) Regression analysis of censored data with nonignorable missing covariates and application to Alzheimer Disease. Comput Stat Data Anal 157:1–15
doi: 10.1016/j.csda.2020.107157
Efron B (1981) Nonparametric estimates of standard error: the jackknife, the bootstrap and other methods. Biometrika 68(3):589–599
doi: 10.1093/biomet/68.3.589
Gilks WR, Wild P (1992) Adaptive rejection sampling for Gibbs sampling. J R Stat Soc Ser C (Appl Stat) 41:337–348
Herring AH, Ibrahim JG (2001) Likelihood-based methods for missing covariates in the Cox proportional hazards model. J Am Stat Assoc 96:292–302
doi: 10.1198/016214501750332866
Horton NJ, Kleinman KP (2007) Much ado about nothing: a comparison of missing data methods and software to fit incomplete data regression models. Am Stat 61(1):79–90
doi: 10.1198/000313007X172556
Hu T, Zhou Q, Sun J (2017) Regression analysis of bivariate current status data under the proportional hazards model. Can J Stat 45:410–424
doi: 10.1002/cjs.11344
Ibrahim JG, Lipsitz SR, Chen MH (1999) Missing covariates in generalized linear models when the missing data mechanism is nonignorable. J R Stat Soc Ser B (Stat Methodol) 61(1):173–190
doi: 10.1111/1467-9868.00170
Li S, Hu T, Wang P et al (2017) Regression analysis of current status data in the presence of dependent censoring with applications to tumorigenicity experiments. Comput Stat Data Anal 110:75–86
doi: 10.1016/j.csda.2016.12.011
Lipsitz SR, Ibrahim JG, Zhao LP (1994) A weighted estimating equation for missing covariate data with properties similar to maximum likelihood. J Am Stat Assoc 94:1147–1160
doi: 10.1080/01621459.1999.10473870
Little RJ, Rubin DB (2002) Statistical analysis with missing data. Wiley, New York
doi: 10.1002/9781119013563
Li S, Wu Q, Sun J (2020) Penalized estimation of semiparametric transformation models with interval-censored data and application to Alzheimer disease. Stat Methods Med Res 29(8):2151–2166
doi: 10.1177/0962280219884720
Ma L, Hu T, Sun J (2015) Sieve maximum likelihood regression analysis of dependent current status data. Biom J 102:731–738
McMahan CS, Wang L, Tebbs JM (2013) Regression analysis for current status data using the EM algorithm. Stat Med 32:4452–4466
doi: 10.1002/sim.5863
Qi L, Wang CY, Prentice RL (2005) Weighted estimators for proportional hazards regression with missing covariates. J Am Stat Assoc 100:1250–1263
doi: 10.1198/016214505000000295
Ramsay JO (1988) Monotone regression splines in action. Stat Sci 3(4):425–441
Schomaker M, Heumann C (2018) Bootstrap inference when using multiple imputations. Stat Med 37(14):2252–2266
doi: 10.1002/sim.7654
Sun J (2006) The statistical analysis of interval-censored failure time data. Springer, New York
Shen X, Wong WH (1994) Convergence rate of sieve estimates. Ann Stat 22:580–615
doi: 10.1214/aos/1176325486
Su YR, Wang JL (2016) Semiparametric efficient estimation for shared-frailty models with doubly-censored clustered data. Ann Stat 44(3):1298–1331
Van der Vaart AW (1998) Asymptotic statistic. Cambridge University Press, Cambridge
doi: 10.1017/CBO9780511802256
Van Der Vaart A, Wellner JA (1996) Weak convergence and empirical processes: with applications to statistics. Springer, New York
doi: 10.1007/978-1-4757-2545-2
Wen CC, Lin CT (2011) Analysis of current status data with missing covariates. Biometrics 67:760–769
doi: 10.1111/j.1541-0420.2010.01505.x
Wang L, McMahan CS, Hudgens MG et al (2016) A flexible, computationally efficient method for fitting the proportional hazards model to interval-censored data. Biometrics 72:222–231
doi: 10.1111/biom.12389
Zhao S, Hu T, Ma L et al (2015) Regression analysis of informative current status data with the additive hazards model. Lifetime Data Anal 21:241–258
doi: 10.1007/s10985-014-9303-y
Zeng D, Mao L, Lin DY (2016) Maximum likelihood estimation for semiparametric transformation models with interval-censored data. Biometrika 103:253–271
doi: 10.1093/biomet/asw013
Zhou H, Pepe MS (1995) Auxiliary covariate data in failure time regression. Biometrika 82(1):139–149
doi: 10.1093/biomet/82.1.139