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Competing risks and multivariate outcomes in epidemiological and clinical trial research

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Abstract

Data analysis methods for the study of treatments or exposures in relation to a clinical outcome in the presence of competing risks have a long history, often with inference targets that are hypothetical, thereby requiring strong assumptions for identifiability with available data. Here data analysis methods are considered that are based on single and higher dimensional marginal hazard rates, quantities that are identifiable under standard independent censoring assumptions. These lead naturally to joint survival function estimators for outcomes of interest, including competing risk outcomes, and provide the basis for addressing a variety of data analysis questions. These methods will be illustrated using simulations and Women’s Health Initiative cohort and clinical trial data sets, and additional research needs will be described.

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References

  • Andersen PK, Gill RD (1982) Cox’s regression model for counting processes: a large sample study. Ann Stat 10(4):1100–1120

    Article  MathSciNet  Google Scholar 

  • Anderson G, Cummings S, Freedman L, Furberg C, Henderson M, Johnson S, Kuller L, Manson J, Oberman A, Prentice R (1998) Design of the Women’s Health Initiative clinical trial and observational study. Control Clin Trials 19(1):61–109

    Article  Google Scholar 

  • Cheng Y, Fine JP, Kosorok MR (2007) Nonparametric association analysis of bivariate competing-risks data. J Am Stat Assoc 102(480):1407–1415. http://www.jstor.org/stable/27639990

  • Clayton DG (1978) Model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65:141–151

    Article  MathSciNet  Google Scholar 

  • Cook RJ, Lawless JF (1997) Marginal analysis of recurrent events and a terminating event. Stat Med 16(8):911–924

    Article  Google Scholar 

  • Cook RJ, Lawless JF (2007) The statistical analysis of recurrent events. Springer, New York

    Google Scholar 

  • Cox DR (1972) Regression models and life-tables (with discussion). J R Stat Soc Ser B (Methodol) 34(2):187–220

    Article  Google Scholar 

  • Fine JP, Gray RJ (1999) A proportional hazards model for the subdistribution of a competing risk. J Am Stat Assoc 94(446):496–509

    Article  MathSciNet  Google Scholar 

  • Fine JP, Jiang H, Chappell R (2001) On semi-competing risks data. Biometrika 88(4):907–919

    Article  MathSciNet  Google Scholar 

  • Freedman AN, Graubard BI, Rao SR, McCaskill-Stevens W, Ballard-Barbash R, Gail MH (2003) Estimates of the number of US women who could benefit from tamoxifen for breast cancer chemoprevention. J Natl Cancer Inst 95(7):526–532

    Article  Google Scholar 

  • Gail M (1975) A review and critique of some models used in competing risk analysis. Biometrics 31:209–222

    Article  MathSciNet  Google Scholar 

  • Gail MH, Costantino JP (2001) Validating and improving models for projecting the absolute risk of breast cancer. J Natl Cancer Inst 93(5):334–335

    Article  Google Scholar 

  • Gail MH, Brinton LA, Byar DP, Corle DK, Green SB, Schairer C, Mulvihill JJ (1989) Projecting individualized probabilities of developing breast cancer for white females who are being examined annually. J Natl Cancer Inst 81(24):1879–1886

    Article  Google Scholar 

  • Ghosh D, Lin DY (2002) Marginal regression models for recurrent and terminal events. Stat Sin 12:663–688

    MathSciNet  Google Scholar 

  • Gill RD, van der Laan MJ, Wellner JA (1995) Inefficient estimators of the bivariate survival function for three models. Annales de l’IHP Probabilités et Statistiques 31(3):545–597

    MathSciNet  Google Scholar 

  • Kalbfleisch JD, Prentice RL (2002) The statistical analysis of failure time data, 2nd edn. Wiley and Sons, New York

    Book  Google Scholar 

  • Latouche A, Boisson V, Chevret S, Porcher R (2007) Misspecified regression model for the subdistribution hazard of a competing risk. Stat Med 26(5):965–974

    Article  MathSciNet  Google Scholar 

  • Lin D, Wei L, Yang I, Ying Z (2000) Semiparametric regression for the mean and rate functions of recurrent events. J R Stat Soc Ser B (Stat Methodol) 62(4):711–730

    Article  MathSciNet  Google Scholar 

  • Oakes D (1986) Semiparametric inference in a model for association in bivariate survival data. Biometrika 73(2):353–361

    MathSciNet  Google Scholar 

  • Pepe MS, Cai J (1993) Some graphical displays and marginal regression analyses for recurrent failure times and time dependent covariates. J Am Stat Assoc 88(423):811–820

    Article  Google Scholar 

  • Pfeiffer RM, Gail MH (2017) Absolute risk: methods and applications in clinical management and public health. CRC Press, Boca Raton

    Book  Google Scholar 

  • Prentice RL, Zhao S (2019) The statistical analysis of multivariate failure time data: a marginal modeling approach. CRC Press, Boca Raton

    Book  Google Scholar 

  • Prentice RL, Zhao S (2021) Regression models and multivariate life tables. J Am Stat Assoc 116:1330–1345

    Article  MathSciNet  Google Scholar 

  • Prentice RL, Kalbfleisch JD, Peterson Jr AV, Flournoy N, Farewell V, Breslow N (1978) The analysis of failure times in the presence of competing risks. Biometrics 34:541–554

    Article  Google Scholar 

  • Prentice RL, Aragaki AK, Chlebowski RT, Zhao S, Anderson GL, Rossouw JE, Wallace R, Banack H, Shadyab AH, Qi L et al (2020) Dual-outcome intention-to-treat analyses in the Women’s Health Initiative randomized controlled hormone therapy trials. Am J Epidemiol 189(9):972–981

    Article  Google Scholar 

  • Rossouw J, Anderson G, Prentice R, LaCroix A, Kooperberg C, Stefanick M, Jackson R, Beresford S, Howard B, Johnson K, Kotchen J, Ockene J, Writing Group for the Women’s Health Initiative Investigators (2002) Risks and benefits of estrogen plus progestin in healthy postmenopausal women: principal results from the Women’s Health Initiative randomized controlled trial. J Am Med Assoc 288:321–333

    Article  Google Scholar 

  • Spiekerman CF, Lin D (1998) Marginal regression models for multivariate failure time data. J Am Stat Assoc 93(443):1164–1175

    Article  MathSciNet  Google Scholar 

  • Tsiatis A (1975) A nonidentifiability aspect of the problem of competing risks. Proc Natl Acad Sci 72(1):20–22

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This work was partially supported by National Institute of Health grant and National Heart, Lung, and Blood Institute contract.

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Correspondence to R. L. Prentice.

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Prentice, R.L. Competing risks and multivariate outcomes in epidemiological and clinical trial research. Lifetime Data Anal (2024). https://doi.org/10.1007/s10985-024-09629-8

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