Central Surgical Association| Volume 82, ISSUE 4, P443-447, October 1977

Survival distribution in breast cancer

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      It has been stated that breast cancer survival rates follow an exponential distribution. This would mean that the mortality rate is constant. Survival distribution was analyzed by the clinical life table method in one series of 10,752 patients and in another of 656 patients followed up to 8 and 18 years, respectively. Part of the larger series' table is
      Tabled 1
      Year No. Hazard Year No. Hazard
      1 10,752 0.2424 5 507 0.0502
      2 5,353 0.1114 6 251 0.0461
      3 2,940 0.1048 7 96 0.0545
      4 1,257 0.0703 8 14 0.0
      Necessarily, clinical survival data are censored progressively. These kinds of data are analyzed best by examining the hazard function, which is the instantaneous death rate, or force of mortality. If an exponential distribution described survival in breast cancer correctly, the hazard function would be constant. These data clearly are not consistent with an exponential distribution, as the hazard function decreases. The survival distribution calculated from these data shows that the chance of dying of cancer decreases the longer a patient survives. This is more optimistic and consistent with clinical experience than is the exponential distribution.
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        • Clark V.A.
        Survival distribution.
        Ann Rev Biophys Bioeng. 1975; 4
        • Mueller C.B.
        • Jeffries W.
        Cancer of the breast: Its outcome as measured by the rate of dying and causes of death.
        Ann Surg. 1975; 182: 334
        • Nelson W.
        Theory and applications of hazard plotting for censored failure data.
        Technometrics. 1972; 14