On computing standard errors for marginal structural Cox models

Lifetime Data Analysis

Volumn 20, Issue 1, 2014, Pages 106-131

  Ali, R Ayesha ^a   Ali, M Adnan ^b   Wei, Zhe ^c  

^a UNIVERSITY OF GUELPH   (Canada)

^b Social Dynamics Corp   (Canada)

^c Canada Post Corporation   (Canada)

Author keywords

Cox models; Inverse probability of treatment weights; Marginal structural models; Score bootstrap; Time dependent weights

Indexed keywords

ARTICLE; COMPUTER SIMULATION; CONFIDENCE INTERVAL; HUMAN; LONGITUDINAL STUDY; METHODOLOGY; PROPORTIONAL HAZARDS MODEL; STATISTICAL MODEL;

COMPUTER SIMULATION; CONFIDENCE INTERVALS; HUMANS; LIKELIHOOD FUNCTIONS; LONGITUDINAL STUDIES; PROPORTIONAL HAZARDS MODELS;

EID: 84891902441     PISSN: 13807870     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10985-013-9255-7     Document Type: Article

References (24)

1. Andersen PK, Gill RD (1982) Cox's regression model for counting processes: A large sample study. Ann Stat 10(4): 1100-1120.
2. Binder DA (1983) On the variances of asymptotically normal estimators from complex surveys. Int Stat Rev 51(3): 279-292. http://www. jstor. org/stable/1402588.
3. Binder DA (1992) Fitting Cox's proportional hazards models from survey data. Biometrika 79(1): 139-147.
4. Breslow N (1974) Covariance analysis of censored survival data. Biometrics 30(1): 89-99. http://www. jstor. org/stable/2529620.
5. Burr D (1994) A comparison of certain bootstrap confidence intervals in the Cox model. J Am Stat Assoc 89(428): 1290-1302.
6. Cheng G, Huang J (2010) Bootstrap consistency for general semiparametric M-estimation. Ann Stat 38(5): 2884-2915. doi: 10. 1214/10-AOS809.
7. Cook NR, Cole SR, Hennekens CH (2002) Use of a marginal structural model to determine the effect of aspirin on cardiovascular mortality in the physicians' health study. Am J Epidemiol 155(11): 1045-1053. doi: 10. 1093/aje/155. 11. 1045, http://aje. oxfordjournals. org/cgi/content/abstract/155/11/1045, http://aje. oxfordjournals. org/cgi/reprint/155/11/1045. pdf.
8. D'Agostino RB, Lee M, Belanger AJ, Cupples A (1990) Relation of pooled logistic regression to time dependent Cox regression analysis: the Framingham heart study. Stat Med 9(12): 1501-1515.
9. Hernan MA, Brumback B, Robins JM (2000) Marginal structural models to estimate the causal effect of zidovudine on the survival of hiv-positive men. Epidemiology 11(5): 561-570. http://www. jstor. org/stable/3703998.
10. Hogan J, Lee J (2004) Marginal structural quantile models for longitudinal observational studies with time-varying treatment. Stat Sin 14: 927-944.
11. Insightful (2001) S-PLUS 8: Guide to statistics, vol 2. Insightful Corporation, Seattle.
12. Kline P, Santos A (2011) A score based approach to wild bootstrap inference. Tech. Rep. NBER-TWP-16127. The National Bureau of Economic Research.
13. Lin DY, Wei LJ (1989) The robust inference for the Cox proportional hazards model. J Am Stat Assoc 84(408): 1074-1078. http://www. jstor. org/stable/2290085.
14. Petersen M, Deeks S, Martin J, van der Lann M (2007) History-adjusted marginal structural models for estimating time-varying effect modification. Am J Epidemiol 166(9): 985-993.
15. R Development Core Team (2010) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. http://www. R-project. org. ISBN 3-900051-07-0.
16. Robins J (1992) Estimation of the time-dependent accelerated failure time model in the presence of confounding factors. Biometrika 79(2): 321-334. doi: 10. 1093/biomet/79. 2. 321, http://biomet. oxfordjournals. org/cgi/reprint/79/2/321. pdf.
17. Robins J (1998) Marginal structural models. In: 1997 Proceedings of the section on Bayesian statistical science. American Statistical Association, Alexandria, pp 1-10.
18. Robins JM, Hernan MA, Brumback B (2000) Marginal structural models and causal inference in epidemiology. Epidemiology 11(5): 550-560. http://www. jstor. org/stable/3703997.
19. Robins J, Hernan M, Siebert U (2005) Effects of multiple interventions. In: Ezzati M, Lopez A, Rodgers A, Murray C (eds) Comparative quantification of health risks: Global and regional burden of diseases attributable to selected major risks, chap 28. World Health Organization, Geneva, p 2207.
20. Therneau TM, Grambsch PM (2001) Modeling survival data: extending the Cox model. Springer, New York.
21. Wu C (1986) Jackknife, bootstrap and other resampling methods in regression analysis (with discussions). Ann Stat 14: 1161-1350.
22. Xiao Y, Abrahamowicz M, Moodie E (2010) Accuracy of conventional and marginal structural Cox model estimators: A simulation study. Int J Biostat 6(2): 1-28.
23. Young J, Hernan M, Picciottol S, Robins J (2008) Simulation from structural survival models under complex time-varying data structures. In: JSM proceedings, section on statistics in epidemiology, American Statistical Association, Denver.
24. Young J, Hernan M, Picciotto S, Robins J (2009) Relation between three classes of structural models for the effect of a time-varying exposure on survival. Lifetime Data Anal 16(1): 71-84.