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Analysis of generalized semiparametric regression models for cumulative incidence functions with missing covariates. (English) Zbl 1469.62096

Summary: The cumulative incidence function quantifies the probability of failure over time due to a specific cause for competing risks data. The generalized semiparametric regression models for the cumulative incidence functions with missing covariates are investigated. The effects of some covariates are modeled as nonparametric functions of time while others are modeled as parametric functions of time. Different link functions can be selected to add flexibility in modeling the cumulative incidence functions. The estimation procedures based on the direct binomial regression and the inverse probability weighting of complete cases are developed. This approach modifies the full data weighted least squares equations by weighting the contributions of observed members through the inverses of estimated sampling probabilities which depend on the censoring status and the event types among other subject characteristics. The asymptotic properties of the proposed estimators are established. The finite-sample performances of the proposed estimators and their relative efficiencies under different two-phase sampling designs are examined in simulations. The methods are applied to analyze data from the RV144 vaccine efficacy trial to investigate the associations of immune response biomarkers with the cumulative incidence of HIV-1 infection.

MSC:

62-08 Computational methods for problems pertaining to statistics
62P10 Applications of statistics to biology and medical sciences; meta analysis
62N02 Estimation in survival analysis and censored data

Software:

cmprsk; osDesign
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Alam, S.; Liao, H.; Tomaras, G.; Bonsignori, M.; Tsao, C.; Hwang, K., Antigenicity and immunogenicity of RV144 vaccine AIDSVAX clade E envelope immunogen is enhanced by a gp120 N-terminal deletion, J. Virol., 87, 3, 1554-1568, (2013)
[2] Breslow, N.; Lumley, T.; Ballantyne, C.; Chambless, L.; Kulich, M., Improved horvitz-Thompson estimation of model parameters from two-phase startified samples: applications in epidemiology, Stat. Biosci., 1, 32-49, (2009)
[3] Breslow, N.; Lumley, T.; Ballantyne, C.; Chambless, L.; Kulich, M., Using the whole cohort in the anlaysis of case-cohort data, Am. J. Epidemiol., 169, 1398-1405, (2009)
[4] Cheng, S.; Fine, J.; Wei, L., Prediction of cumulative incidence function under the proportional hazards model, Biometrics, 54, 219-228, (1988) · Zbl 1058.62593
[5] Cox, D., Partial likelihood, Biometrika, 62, 269-276, (1975) · Zbl 0312.62002
[6] Fine, J. P.; Gray, R. J., A proportional hazards model for the subdistribution of a competing risk, J. Amer. Statist. Assoc., 94, 496-509, (1999) · Zbl 0999.62077
[7] Fleming, T.; Harrington, D., Counting processes and survival analysis, (1991), John Wiley & Sons, Inc. New York · Zbl 0727.62096
[8] Haneuse, S.; Saegusa, T.; Lumley, T., Osdesign: an R package for the analysis, evaluation, and desgin of two-phase and case-control studies, J. Stat. Softw., 43, 11, (2011)
[9] Haynes, B.; Gilbert, P.; McElrath, M.; Zolla-Pazner, S.; Tomaras, G.; Alam, S.; Evans, D.; Montefiori, D.; Karnasuta, C.; Sutthent, R.; Liao, H.; DeVico, A.; Lewis, G.; Williams, C.; Pinter, A.; Fong, Y.; Janes, H.; deCamp, A.; Huang, Y.; Rao., M.; Billings, E.; Karasavvas, N.; Robb, M.; Ngauy, V.; de Souza, M.; Paris, R.; Ferrari, G.; Bailer, R.; Soderberg, K.; Andrews, C.; Berman, P.; Frahm, N.; De Rosa, S.; Alpert, M.; Yates, N.; Shen, X.; Koup, R.; Pitisuttithum, P.; Kaewkungwal, J.; Nitayaphan, S.; Rerks-Ngarm, S.; Michael, N.; Kim, J., Immune-correlates analysis of an HIV-1 vaccine efficacy trial, N. Engl. J. Med., 366, 1275-1286, (2012)
[10] Horvitz, D.; Thompson, D., A generalization of sampling without replacement from a finite universe, J. Amer. Statist. Assoc., 47, 663-685, (1952) · Zbl 0047.38301
[11] Kalbfleisch, J.; Prentice, R., The statistical analysis of failure time data, (1980), Wiley New York · Zbl 0504.62096
[12] Kang, S.; Cai, J., Marginal additive hazards model for case-cohort studies with multiple disease outcomes, Biometrika, 94, 887-901, (2009) · Zbl 1179.62140
[13] Kang, S.; Cai, J.; Chambless, L., Marginal additive hazards model for case-cohort studies with multiple disease outcomes: an application to the atherosclerosis risk in communities (ARIC) study, Biostatistics, 14, 28-41, (2013)
[14] Katsahian, S.; Resche-Rigon, M.; Chevret, S.; Porcher, R., Analysing multicentre competing risks data with a mxed proportinal hazards model for the subdistribution, Stat. Med., 25, 4267-4278, (2006)
[15] Klein, J. P.; Andersen, P., Regression modeling of competing risks data based on pseudovalues of the cumulative incidence function, Biometrika, 61, 1, 223-229, (2005) · Zbl 1077.62081
[16] Latouche, A.; Boisson, V.; Chevret, S.; Porcher, R., Misspecified regression model for the subdistribution hazard of a competing risk, Stat. Med., 26, 965-974, (2007)
[17] Lin, D.; Ying, Z., Semiparametric analysis of the additive risk model, Biometrika, 81, 61-71, (1994) · Zbl 0796.62099
[18] Lin, D.; Ying, Z., Semiparametric and nonparametric regression analysis of longitudinal data, J. Amer. Statist. Assoc., 96, 103-126, (2001) · Zbl 1015.62038
[19] McKeague, I.; Sasieni, P., A partly parametric additive risk model, Biometrika, 81, 501-514, (1994) · Zbl 0812.62041
[20] Nickle, D. C.; Heath, L.; Jensen, M. A.; Gilbert, P. B.; Mullins, J. I.; Kosakovsky Pond, S. L., HIV-specific probabilistic models of protein evolution, PLoS One, 2, 6, e503, (2007)
[21] Prentice, R., A case-cohort design for epidemiologic cohort studies and disease prevention trials, Biometrika, 73, 1-11, (1986) · Zbl 0595.62111
[22] Rerks-Ngarm, S.; Pitisuttithum, P.; Nitayaphan, S.; Kaewkungwal, J.; Chiu, J.; Paris, R.; Premsri, N.; Namwat, C.; de Souza, M.; Adams, E.; Benenson, M.; Gurunathan, S.; Tartaglia, J.; McNeil, J.; Francis, D.; Stablein, D.; Birx, D.; Chunsuttiwat, S.; Khamboonruang, C.; Thongcharoen, P.; Robb, M.; Michael, N.; Kunasol, P.; Kim, J., Vaccination with ALVAC and AIDSVAX to prevent HIV-1 infection in Thailand, N. Engl. J. Med., 361, 2209-2220, (2009)
[23] Rubin, D. B., Inference and missing data, Biometrika, 63, 3, 581-592, (1976) · Zbl 0344.62034
[24] Scheike, T.; Zhang, M., An additive-multiplicative Cox-aalen regression model, Scand. J. Stat., 29, 1, 75-88, (2002) · Zbl 1017.62095
[25] Scheike, T.; Zhang, M., Extensions and applications of the Cox-aalen survival model, Biometrics, 59, 1036-1045, (2003) · Zbl 1274.62678
[26] Scheike, T. H.; Zhang, M.-J.; Gerds, T., Predicting cumulative incidence probability by direct binomial regression, Biometrika, 95, 205-220, (2008) · Zbl 1437.62602
[27] Shen, Y.; Cheng, S., Confidence bands for cumulative incidence curves under the additive risk model, Biometrics, 55, 1093-1100, (1999) · Zbl 1059.62711
[28] Sun, Y., Generalized nonparametric test procedures for comparing multiple cause-specific hazard rates, J. Nonparametr. Stat., 13, 171-207, (2001) · Zbl 1028.62080
[29] Sun, Y.; Qian, X.; Shou, Q.; Gilbert, P., Analysis of two-phase sampling data with semiparametric additive hazards models, Lifetime Data Anal., 23, 377-399, (2017) · Zbl 1402.62292
[30] Sun, Y.; Tiwari, R.; Zalkikar, J., Goodness-of-fit tests for multiplicative intensity models with application to competing risks data, Scand. J. Stat., 28, 241-256, (2001)
[31] Tsiatis, A. A., An example of nonidentifiability in competing risks, Scand. Actuar. J., 1978, 235-239, (1978) · Zbl 0396.62084
[32] Van der Vaart, A. W., Asymptotic statistics, (2000), Cambridge University Press · Zbl 0910.62001
[33] Yang, G.; Sun, Y.; Qi, L.; Gilbert, P., Estimation of stratified mark-specific proportional hazards models under two-phase sampling with application to HIV vaccine efficacy trials, Stat. Biosci., 1-25, (2016)
[34] Yates, N.; Liao, H.; Fong, Y.; deCamp, A.; Vandergrift, N.; Williams, W.; Alam, S.; Ferrari, G.; Yang, Z.; Seaton, K.; Berman, P.; Alpert, M.; Evans, D.; OConnell, R.; Francis, D.; Sinangil, F.; Lee, C.; Nitayaphan, S.; Rerks-Ngarm, S.; Kaewkungwal, J.; Pitisuttithum, P.; Tartaglia, J.; Pinter, A.; Zolla-Pazner, S.; Gilbert, P.; Nabel, G.; Michael, N.; Kim, J.; Montefiori, D.; Haynes, B.; Tomaras, G., Vaccine-induced env V1-V2 igg3 correlates with lower HIV-1 infection risk and declines soon after vaccination, Sci. Transl. Med., 6, (2014), 228ra39
[35] Zolla-Pazner, S.; deCamp, A.; Gilbert, P.; Williams, C.; Yates, N.; Williams, W.; Howington, R.; Fong, Y.; Morris, D.; Soderberg, K.; Irene, C.; Reichman, C.; Pinter, A.; Parks, R.; Pitisuttithum, P.; Kaewkungwal, J.; Rerks-Ngarm, S.; Nitayaphan, S.; Andrews, C.; O Connell, R.; Yang, Z.; Nabel, G.; Kim, J.; Michael, N.; Montefiori, D.; Liao, H.; Haynes, B.; Tomaras, G., Vaccine-induced igg antibodies to V1V2 regions of multiple HIV-1 subtypes correlate with decreased risk of HIV-1 infection, PLoS One, 9, 2, e87572, (2014)
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