Research Article| Volume 56, ISSUE 6, P536-545, June 2003

Improving estimates of event incidence over time in populations exposed to other events

Application to three large databases


      The Kaplan-Meier (KM) method is commonly used to estimate the incidence of an event over time. It assumes independence between the event of interest and any competing event that precludes the event of interest to occur. However, when the competing event is death without the event of interest, censoring these patients will affect the incidence of the event of interest by modifying the number of exposed patients, so that KM results will be misleading. Three prospective cohorts were studied: (1) 657 renal transplant recipients, (2) 262 children with acute leukemia who received bone marrow transplants, and (3) 8,353 intensive care patients. The main outcome measures were kidney graft loss, leukemia relapse, and ICU-acquired infection, respectively, with death before the main outcome as the competing event. The incidence of each main outcome was overestimated by the KM method. The magnitude of overestimation ranged from 3% to 30%, and varied with baseline patient characteristics and follow-up duration, with most of this variation being related to the rate of the competing event. A competing-risk approach must be used to analyze the risk of events other than death in cohort studies, particularly when mortality rates are high.


      To read this article in full you will need to make a payment

      Purchase one-time access:

      Academic & Personal: 24 hour online accessCorporate R&D Professionals: 24 hour online access
      One-time access price info
      • For academic or personal research use, select 'Academic and Personal'
      • For corporate R&D use, select 'Corporate R&D Professionals'


      Subscribe to Journal of Clinical Epidemiology
      Already a print subscriber? Claim online access
      Already an online subscriber? Sign in
      Institutional Access: Sign in to ScienceDirect


        • Hunsicker L.G.
        A survival advantage for renal transplantation.
        N Engl J Med. 1999; 341: 1762-1763
        • Landais P.
        • Jais J.P.
        • Margreiter R.
        • Tufreson G.
        • Brunner F.
        • Selwood N.
        • et al.
        Modelling long-term survival in 52,315 first cadaveric grafts: the European experience.
        Transplant Proc. 1993; 25: 1316-1317
        • Hariharan S.
        • Johnson C.P.
        • Bresnahan B.A.
        • Taranto S.E.
        • McIntosh M.J.
        • Stablein D.
        Improved graft survival after renal transplantation in the United States, 1988 to 1996.
        N Engl J Med. 2000; 342: 605-612
        • Gjertson D.W.
        Look-up survival tables for renal transplantation.
        Clin Transplant. 1997; : 337-383
        • Mange K.C.
        • Joffe M.M.
        • Feldman H.I.
        Effect of the use or nonuse of long-term dialysis on the subsequent survival of renal transplants from living donors.
        N Engl J Med. 2001; 344: 726-731
        • Kaplan E.L.
        • Meier P.
        Non-parametric estimation from incomplete observations.
        J Am Stat Assoc. 1958; 53: 457-481
        • Gooley T.A.
        • Leisenring W.
        • Crowley J.
        • Storer B.E.
        Estimation of failure probabilities in the presence of competing risks: new representations of old estimators.
        Stat Med. 1999; 18: 695-706
        • Pepe M.S.
        • Mori M.
        Kaplan-Meier, marginal or conditional probability curves in summarizing competing risks failure time data?.
        Stat Med. 1993; 12: 737-751
        • Arriagada R.
        • Kramar A.
        • Le Chevalier T.
        • De Cremoux H.
        Competing events determining relapse-free survival in limited small-cell lung carcinoma. The French Cancer Centers' Lung Group.
        J Clin Oncol. 1992; 10: 447-451
        • Gelman R.
        • Gelber R.
        • Henderson I.C.
        • Coleman C.N.
        • Harris J.R.
        Improved methodology for analyzing local and distant recurrence.
        J Clin Oncol. 1990; 8: 548-555
        • Tai B.C.
        • Machin D.
        • White I.
        • Gebski V.
        Competing risks analysis of patients with osteosarcoma: a comparison of four different approaches.
        Stat Med. 2001; 20: 661-684
        • Pepe M.S.
        • Longton G.
        • Pettinger M.
        • Mori M.
        • Fisher L.D.
        • Storb R.
        Summarizing data on survival, relapse, and chronic graft-versus-host disease after bone marrow transplantation: motivation for and description of new methods.
        Br J Haematol. 1993; 83: 602-607
        • Rocha V.
        • Cornish J.
        • Sievers E.L.
        • Filpovich A.
        • Locatelli F.
        • Peters C.
        • et al.
        Comparison of outcomes of unrelated bone marrow and umbilical cord blood transplants in children with acute leukemia.
        Blood. 2001; 97: 2962-2971
        • Kalbfleish J.D.
        • Prentice R.L.
        Multivariate failure time data and competing risks.
        in: Kalbfleish J.D. Prentice R.L. The statistical analysis of failure time data. Wiley, New York1980: 163-188
        • Benichou J.
        • Gail M.H.
        Estimates of absolute cause-specific risk in cohort studies.
        Biometrics. 1990; 46: 813-826
        • Korn E.L.
        • Dorey F.J.
        Applications of crude incidence curves.
        Stat Med. 1992; 11: 813-829
        • Gaynor J.J.
        • Feuer E.J.
        • Tan C.C.
        • Wu D.H.
        • Little C.R.
        • Strauss D.J.
        • et al.
        On the use of cause-specific failure and conditional failure probabilities: examples from clinical oncology data.
        J Am Stat Assoc. 1993; 88: 602-607
        • Peto R.
        • Peto J.
        Asymptotically efficient rank invariant test procedures(with discussion).
        J R Stat Soc. 1972; 135: 185-207
        • Gray R.J.
        A class of K-sample tests for comparing the cumulative incidence of a competing risk.
        Ann Stat. 1988; 16: 1141-1154
        • Flechner S.M.
        • Modlin C.S.
        • Serrano D.P.
        • Goldfarb D.A.
        • Papajcik D.
        • Mastroianni B.
        • et al.
        Determinants of chronic renal allograft rejection in cyclosporine-treated recipients.
        Transplantation. 1996; 62: 1235-1241
        • Hariharan S.
        • McBride M.A.
        • Bennett L.E.
        • Cohen E.P.
        Risk factors for renal allograft survival from older cadaver donors.
        Transplantation. 1997; 64: 1748-1754
        • Pirsch J.D.
        • Ploeg R.J.
        • Gange S.
        • D'Alessandro A.M.
        • Knechtle S.J.
        • Sollinger H.W.
        • et al.
        Determinants of graft survival after renal transplantation.
        Transplantation. 1996; 61: 1581-1586
        • Mange K.C.
        • Cizman B.
        • Joffe M.
        • Feldman H.I.
        Arterial hypertension and renal allograft survival.
        JAMA. 2000; 283: 633-638
        • Matas A.J.
        • Gillingham K.J.
        • Sutherland D.E.
        Half-life and risk factors for kidney transplant outcome importance of death with function.
        Transplantation. 1993; 55: 757-761
        • Le Gall J.R.
        • Lemeshow S.
        • Saulnier F.
        A new Simplified Acute Physiology Score (SAPS II) based on a European/North American multicenter study.
        JAMA. 1993; 270: 2957-2963
        • West M.
        • Sutherland D.E.
        • Matas A.J.
        Kidney transplant recipients who die with functioning grafts: serum creatinine level and cause of death.
        Transplantation. 1996; 62: 1029-1030
        • Prentice R.L.
        • Kalbfleisch J.D.
        • Peterson Jr., A.V.
        • Flourney N.
        • Farewell V.T.
        • Breslow N.E.
        The analysis of failure times in the presence of competing risks.
        Biometrics. 1978; 34: 541-554
        • Thiel G.
        • Bock A.
        • Spondlin M.
        • Brunner F.P.
        • Mihatsch M.
        • Rufli T.
        • et al.
        Long-term benefits and risks of cyclosporin A (sandimmun)—an analysis at 10 years.
        Transplant Proc. 1994; 26: 2493-2498