×

Estimating equation for additive hazards model with censored length-biased data. (English) Zbl 1485.62140

Summary: Aalen’s additive hazards model plays a very important role in survival analysis. In this paper we are interested in the problem of estimating regression coefficients in the additive hazards model with censored length-biased data. Through both of the parametric invariance of the proportional likelihood ratio model and the unique structure of length-biased data, we propose a pairwise pseudo-likelihood estimating equation, which only relies on the complete residual lifetimes in censored length-biased data. In addition, two combined estimating equations are also considered to estimate covariate coefficients. These estimators are proved to be consistent and asymptotically normal. In order to evaluate the performance of the proposed estimators in a finite sample, some simulations are conducted. Finally, a real data example is also provided.

MSC:

62N02 Estimation in survival analysis and censored data
62G05 Nonparametric estimation
62G08 Nonparametric regression and quantile regression
62P10 Applications of statistics to biology and medical sciences; meta analysis
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Aalen, O.; Klonecki, W.; Kozek, A.; Rosiński, J., A model for nonparametric regression analysis of counting processes, Mathematical Statistics and Probability Theory. Lecture Notes in Statistics (1980), New York, NY: Springer, New York, NY · Zbl 0445.62095
[2] Blumenthal, S., Proportional sampling in life length studies, Technometrics, 9, 205-218 (1967) · doi:10.1080/00401706.1967.10490456
[3] Chan, KCG; Chen, YQ; Di, C-Z, Proportional mean residual life model for right-censored length-biased data, Biometrika (2012) · Zbl 1452.62798 · doi:10.1093/biomet/ass049
[4] Chan, KCG, Nuisance parameter elimination for proportional likelihood ratio models with nonignorable missingness and random truncation, Biometrika, 100, 1, 1-8 (2013) · Zbl 1452.62570 · doi:10.1093/biomet/ass056
[5] Chen, X.; Cai, J., Reweighting estimators for additive hazard model with censoring indicators missing at random, Lifetime Data Analysis, 24, 2, 224-249 (2018) · Zbl 1468.62360 · doi:10.1007/s10985-017-9398-z
[6] Chen, W.; Chen, A.; Xia, Y.; Ling, L., The effect of sample size and censoring proportion on the power and bias of survival analysis models, Chinese Journal of Health Statistics, 30, 1, 5-8 (2013)
[7] Chen, C-M; Shen, P-S, Conditional maximum likelihood estimation in semiparametric transformation model with LTRC data, Lifetime Data Analysis, 24, 2, 250-272 (2018) · Zbl 1468.62374 · doi:10.1007/s10985-016-9385-9
[8] Chen, X.; Zhou, Y., Quantile regression for right-censored and length-biased data, Acta Mathematicae Applicatae Sinica, English Series, 28, 443-462 (2012) · Zbl 1252.62044 · doi:10.1007/s10255-012-0157-3
[9] Cox, DR; Johnson, NL; Smith, H., Some sampling problems in technology, New Developments in Survey Sampling (1969), New York: wiley, New York
[10] Cox, DR, Regression model and life table, Journal of the Royal Statistical Society: Series B, 34, 2, 187-220 (1972) · Zbl 0243.62041
[11] Crouch, LA; May, S.; Chen, YQ, On estimation of Covariate-Specific Residual Time Quantiles under the proportional Hazards Model, Lifetime Data Analysis, 22, 2, 299-319 (2016) · Zbl 1356.62181 · doi:10.1007/s10985-015-9332-1
[12] Ghosh, D., Goodness-of-fit methods for additive risk models in tumorigenicity experiments, Biometrics, 59, 721-726 (2003) · Zbl 1210.62160 · doi:10.1111/1541-0420.00083
[13] Guo, L.; Hu, XJ; Liu, Y., Estimation under Cox proportional hazards model with covariates missing not at random, Communications in Statistics-Theory and Methods, 46, 18, 8952-8972 (2017) · Zbl 1378.62108 · doi:10.1080/03610926.2016.1197252
[14] Hoeffding, W., A class of Statistics with Asymptotically Normal Distribution, Annals of Mathematical Statistics, 19, 293-325 (1948) · Zbl 0032.04101 · doi:10.1214/aoms/1177730196
[15] Huang, C-Y; Qin, J., Nonparametric estimation for length-biased and right-censored data, Biometrika, 98, 177-186 (2011) · Zbl 1215.62032 · doi:10.1093/biomet/asq069
[16] Huang, C-Y; Qin, J., Composite partial likelihood estimation under length-biased sampling, with application to a prevalent cohort study of Dementia, Journal of the American Statistical Association, 107, 946-957 (2012) · Zbl 1299.62123 · doi:10.1080/01621459.2012.682544
[17] Huang, C-Y; Qin, J., Semiparametric estimation for the additive hazards model with left-truncated and right-censored data, Biometrika, 100, 4, 877-888 (2013) · Zbl 1452.62713 · doi:10.1093/biomet/ast039
[18] Kim, J.; Song, MS; Lee, S., Goodness-of-fit tests for the additive risk model with \((p>2)\)-dimensional time-invariant covariates, Lifetime Data Analysis, 4, 405-416 (1998) · Zbl 0917.62041 · doi:10.1023/A:1009638204063
[19] Lancaster, T., The Econometric analysis of transition data (1990), Cambridge: Cambridge University Press, Cambridge · Zbl 0717.62106 · doi:10.1017/CCOL0521265967
[20] Lin, Y.; Wang, S.; Chappell, RJ, Lasso tree for cancer staging with survival data, Biostatistics, 14, 2, 327-339 (2013) · doi:10.1093/biostatistics/kxs044
[21] Lin, DY; Ying, Z., Semiparametric analysis of the additive risk model, Biometrika, 81, 1, 61-71 (1994) · Zbl 0796.62099 · doi:10.1093/biomet/81.1.61
[22] Luo, X.; Tsai, WY, A proportional likelihood ratio model, Biometrika, 99, 211-222 (2012) · Zbl 1437.62545 · doi:10.1093/biomet/asr060
[23] Ma, H.; Zhang, F.; Zhou, Y., Composite estimating equation approach for additive risk model with length-biased and right-censored data, Statistics and Probability Letters, 96, 45-53 (2015) · Zbl 1314.62220 · doi:10.1016/j.spl.2014.08.021
[24] McFadden, JA, On the lengths of intervals in a stationary point process, Journal of the Royal Statistical Society: Series B, 24, 364-382 (1962) · Zbl 0201.50002
[25] Chen, M.; Bai, J.; Wei, Y.; Huang, L.; Zhao, Y.; Yu, H., Effect of difference censored rates between groups in clinical trails, Chinese Journal of Clinical Pharmacology and Therapeutics, 22, 4, 434-438 (2017)
[26] Qi, Lihong; Zhang, Xu; Sun, Yanqing; Wang, Lu; Zhao, Yichuan, Weighted estimating equations for additive hazards models with missing covariates, Annals of the Institute of Statistical Mathematics, 71, 2, 365-387 (2018) · Zbl 1417.62092 · doi:10.1007/s10463-018-0648-y
[27] Sen, PK, On some convergence properties of U-statistics, Calcutta Statistical Association Bulletin, 10, 1-18 (1960) · Zbl 0109.12504 · doi:10.1177/0008068319600101
[28] Shi, J.; Ma, H.; Zhou, Y., The nonparametric quantile estimation for length-biased and right-censored data, Statistics and Probability Letters, 134, 150-158 (2018) · Zbl 1463.62098 · doi:10.1016/j.spl.2017.10.020
[29] Shen, P-S, Semiparametric analysis of survival data with left truncation and right censoring, Computational Statistics and Data Analysis, 53, 4417-4432 (2009) · Zbl 1453.62196 · doi:10.1016/j.csda.2009.06.013
[30] Wang, M-S, Nonparametric Estimation from Cross-Sectional Survival Data, Journal of the American Statistical Association, 86, 413, 130-143 (1991) · Zbl 0739.62026 · doi:10.1080/01621459.1991.10475011
[31] Wang, Y.; Zhou, Z.; Zhou, X.; Zhou, Y., Nonparametric and Semiparametric estimation of quantile residual lifetime for length-biased and right-censored data, Canadian Journal of Statistics, 45, 2, 220-250 (2017) · Zbl 1474.62343 · doi:10.1002/cjs.11319
[32] Wicksell, SD, The corpuscle problem: A mathematical study of a biometric problem, Biometrika, 17, 1-2, 84-99 (1925) · JFM 51.0392.02 · doi:10.2307/2332027
[33] Wu, H., & Shan, A. (2019). Nonparametric inference on mean residual life function with length-biased right-censored data. Communications in Statistics-Theory and Methods, doi:10.1080/03610926.2019.1568483. · Zbl 1511.62251
[34] Xu, J.; Ma, J.; Connors, MH; Brodaty, H., Proportional hazard model estimation under dependent censoring using copulas and penalized likelihood, Statistics in Medicine, 37, 14, 2238-2251 (2018) · doi:10.1002/sim.7651
[35] Yin, G., Model checking for additive hazards model with multivariate survival data, Journal of Multivariate Analysis, 98, 1018-1032 (2007) · Zbl 1113.62123 · doi:10.1016/j.jmva.2006.02.005
[36] Zhu, H., Likelihood approaches for proportional likelihood ratio model with right-censored data, Statistics in Medicine, 33, 14, 2467-2479 (2014) · doi:10.1002/sim.6105
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.