Skip to main content

Survival Analysis II

  • Reference work entry
  • First Online:
Principles and Practice of Clinical Trials
  • 280 Accesses

Abstract

Survival analysis modeling is integral to clinical trial analysis, as even in well-designed randomized trials where the primary inference is to be based on fundamental quantities such as estimated survival distributions and nonparametric tests, survival models offer additional insights and succinct treatment effect summaries. The ubiquitous Cox proportional hazards model has numerous variations and extensions to fit specific analytic needs and has become a mainstay of biomedical and clinical trial data analysis. However, other models and treatment effect metrics are increasingly available and should be adopted in cases where model assumptions are not met.

A natural extension of survival analysis pertains to the case where multiple potential causes of failure may be in effect. When these causes of failure are mutually exclusive, then competing risks observations are encountered, while in other cases, there may be multiple failures per individual. Methods that address these extensions of time to event data are needed to (a) assess of value of treatment in the presence of events that may preclude observation of the disease process of interest, (b) evaluate risks and benefits of treatment in a way that reflects patient experience, and (c) provide tools for study of factors related to different failure types and model more complex multi-event failure processes.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 499.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 599.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  • Aalen O (1978a) Nonparametric estimation of partial transition probabilities in multiple decrement models. Ann Stat 6:534–545

    MathSciNet  MATH  Google Scholar 

  • Aalen O (1978b) Nonparametric inference for a family of counting processes. Ann Stat 6:701–726

    MathSciNet  MATH  Google Scholar 

  • Andersen PK, Borgan O, Gill R, Keiding N (1993) Statistical methods based on counting processes. Springer, Berlin

    Book  MATH  Google Scholar 

  • Benichou J, Gail MH (1990) Estimates of absolute cause-specific risk in cohort studies. Biometrics 46:813–826

    Article  Google Scholar 

  • Bryant J, Dignam JJ (2004) Semiparametric models for cumulative incidence functions. Biometrics 60:182–190

    Article  MathSciNet  MATH  Google Scholar 

  • Buckner J, Shaw EG, Pugh S et al (2016) Radiation plus procarbazine, CCNU, and vincristine in low-grade glioma. N Engl J Med 374:1344–1355

    Article  Google Scholar 

  • Byar D, Huse R, Bailar JC et al (1974) An exponential model relating censored survival data and concomitant information for prostatic cancer patients. J Natl Cancer Inst 52:321–326

    Article  Google Scholar 

  • Chang IM, Gelman R, Pagano M (1982) Corrected group prognostic curves and summary statistics. J Chronic Dis 35:669–674

    Article  Google Scholar 

  • Cheng SC, Fine JP, Wei LJ (1998) Prediction of cumulative incidence function under the proportional hazards model. Biometrics 54:219–228

    Article  MathSciNet  MATH  Google Scholar 

  • Cox DR (1959) The analysis of exponentially distributed life-times with two types of failure. J Roy Stat Soc B 21:411–421

    MathSciNet  MATH  Google Scholar 

  • Cox DR (1972) Regression models and life tables. J Roy Stat Soc B 34:187–220

    MathSciNet  MATH  Google Scholar 

  • Cox DR (1975) Partial likelihood. Biometrika 62:269–276

    Article  MathSciNet  MATH  Google Scholar 

  • Crowder M (1991) On the identifiability crisis in competing risks analysis. Scand J Stat 18:223–233

    MathSciNet  MATH  Google Scholar 

  • Dignam JJ, Kocherginsky MN (2008) Choice and interpretation of statistical tests used when competing risks are present. J Clin Oncol 26:4027–4034

    Article  Google Scholar 

  • Dignam JJ, Zhang Q, Kocherginsky MN (2012) The use and interpretation of competing risks regression models. Clin Cancer Res 18:2301–2308

    Article  Google Scholar 

  • Feigl P, Zelen M (1965) Estimation of exponential survival probabilities with concomitant information. Biometrics 21:826–838

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Fisher B, Dignam J, Bryant J et al (1996) Five versus more than five years of tamoxifen therapy for breast cancer patients with negative lymph nodes and estrogen-receptor positive tumors. J Natl Cancer Inst 88:1529–1542

    Article  Google Scholar 

  • Fleming TR, Harrington DP (1991) Counting processes and survival analysis. Wiley, New York

    MATH  Google Scholar 

  • Freidlin B, Korn EL (2005) Testing treatment effects in the presence of competing risks. Stat Med 24:1703–1712

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Gaynor JJ, Feuer EJ, Tan CC, Wu DH, Little CR, Straus DJ, Clarkson BD, Brennan MF (1993) On the use of cause-specific failure and conditional failure probabilities: examples from clinical oncology data. J Am Stat Assoc 88:400–409

    Article  MATH  Google Scholar 

  • Gilbert PB, Wei LJ, Kosorok MR, Clemens JD (2002) Simultaneous inferences on the contrast of two hazard functions with censored observations. Biometrics 58:773–780

    Article  MathSciNet  MATH  Google Scholar 

  • Gilbert M, Dignam JJ, Armstrong TS et al (2014) A randomized trial of bevacizumab for newly diagnosed glioblastoma. N Engl J Med 370:699–708

    Article  Google Scholar 

  • Grambsch P, Therneau T, Fleming TR (1995) Diagnostic plots to reveal functional form for covariates in multiplicative intensity models. Biometrics 51:1469–1482

    Article  MATH  Google Scholar 

  • Gray RJ (1988) A class of K-sample tests for comparing the cumulative incidence of a competing risk. Ann Stat 16:1141–1154

    Article  MathSciNet  MATH  Google Scholar 

  • Gray RJ (1994) Spline-based tests in survival analysis. Biometrics 50:640–652

    Article  MathSciNet  MATH  Google Scholar 

  • Karrison TG (1997) Use of Irwin’s restricted mean as an index for comparing survival in different treatment groups – interpretation and power considerations. Contemp Clin Trials 18:151–167

    Article  Google Scholar 

  • Klein JP, Andersen PK (2005) Regression modeling of competing risks data based on pseudovalues of the cumulative incidence function. Biometrics 61:223–229

    Article  MathSciNet  MATH  Google Scholar 

  • Korn EL, Dorey FJ (1992) Applications of crude incidence curves. Stat Med 11:813–829

    Article  Google Scholar 

  • Lawless JF (2002) Statistical models and methods for lifetime data, 2nd edn. Wiley, New York

    Book  MATH  Google Scholar 

  • Rubinstein LV, Gail MH, Santner TJ (1981) Planning the duration of a comparative clinical trial with loss to follow-up and a period of continued observation. J Chron Dis 34(9–10):469–479

    Google Scholar 

  • Lawton C, Lin X, Hanks GE et al (2017) Duration of androgen deprivation in locally advanced prostate cancer: long-term update of NRG oncology RTOG 9202. Int J Radiat Oncol Biol Phys 98:296–303

    Article  Google Scholar 

  • Le-Rademacher JG, Peterson RA, Therneau TM, Sanford BL, Stone RM, Mandrekar SJ (2018) Application of multi-state models in cancer clinical trials. Clin Trials 15:489–498

    Article  Google Scholar 

  • Lin DY (1997) Nonparametric inference for cumulative incidence functions in competing risks studies. Stat Med 85:901–910

    Article  Google Scholar 

  • Makuch RW (1982) Adjusted survival curve estimation using covariates. J Chronic Dis 35:437–443

    Article  Google Scholar 

  • Mantel N (1966) Evaluation of survival data and two rank order statistics in its consideration. Cancer Chemother Rep 50:163–170

    Google Scholar 

  • Moeschberger ML, Klein JP (1995) Statistical methods for dependent competing risks. Lifetime Data Anal 1:195–204

    Article  MATH  Google Scholar 

  • Nelson W (1972) Theory and application of hazard plotting for censored failure data. Technometrics 19:945–966

    Article  Google Scholar 

  • Pepe MS, Mori M (1993) Kaplan-Meier, marginal, or conditional probability curves in summarizing competing risks failure time data? Stat Med 12:737–751

    Article  Google Scholar 

  • Peterson AV (1976) Bounds for a joint distribution function with fixed subdistribution functions: applications to competing risks. Proc Natl Acad Sci 73:11–13

    Article  MATH  Google Scholar 

  • Peterson B, George SL (1993) Sample size requirements and length of study for testing interaction in a 2 x k factorial design when time-to-failure is the outcome [corrected]. Control Clin Trials 14:511–522. Erratum in: Control Clin Trials 1994 15:326

    Article  Google Scholar 

  • Polley MY, Freidlin B, Korn EL et al (2013) Statistical and practical considerations for clinical evaluation of predictive markers. J Natl Cancer Inst 105:1677–1683

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Royston P, Parmar MK (2002) Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modeling and estimation of treatment effects. Stat Med 21:2175–2197

    Article  Google Scholar 

  • Schoenfeld D (1983) Sample-size formula for the proportional hazards regression model. Biometrics 39:499–503

    Article  MATH  Google Scholar 

  • Therneau TM, Grambsch PM (2000) Modeling survival data: extending the Cox model. Springer, New York

    Book  MATH  Google Scholar 

  • Tsiatis AA (1975) A non-identifiability aspect of the problem of competing risks. Proc Natl Acad Sci 72:20–22

    Article  MathSciNet  MATH  Google Scholar 

  • Tsiatis AA (1981) A large sample study of Cox’s regression model. Ann Stat 9:93–108

    Article  MathSciNet  MATH  Google Scholar 

  • Zhao L, Claggett B, Tian L et al (2016) On the restricted mean survival time curve in survival analysis. Biometrics 72:215–221

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to James J. Dignam .

Editor information

Editors and Affiliations

Section Editor information

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer Nature Switzerland AG

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Dignam, J.J. (2022). Survival Analysis II. In: Piantadosi, S., Meinert, C.L. (eds) Principles and Practice of Clinical Trials. Springer, Cham. https://doi.org/10.1007/978-3-319-52636-2_120

Download citation

Publish with us

Policies and ethics