• ‘actual’ cumulative incidence;
  • actual cumulative survival;
  • actuarial incidence;
  • clinical trial;
  • competing risk;
  • Cox regression;
  • cumulative survival analysis;
  • Nelson–Aalen

The problem:  The conventional method for estimating survival over time following an episode of disease or treatment is the Kaplan–Meier (K-M) technique, which results in a step-down survival plot, with upper and lower bounds of 1.0 and 0, respectively. The mirror image of this plot represents the cumulative incidence of an adverse event, such as death, with lower and upper bounds of 0 and 1.0, respectively. However, if there are two competing events that can occur during follow up, such as death or relapse, the K-M technique gives a false picture of the cumulative incidence of either one of these events. This occurs because patients who have died cannot subsequently relapse.

The solution:  When there are two competing events, another technique must be used, which is known, variously, as cumulative incidence analysis, or ‘actual’ (as opposed to actuarial) incidence analysis. An example is given in which there are two competing adverse events following haemopoietic stem cell transplantation for a haematological malignancy: (i) relapse or (ii) transplant-related death. Our analysis of the example shows that the cumulative probability of relapse is progressively inflated if the traditional K-M product-limit method is used rather than actual cumulative incidence analysis. We show how K-M and actual cumulative survival or incidence analyses can be executed by a handheld calculator for small datasets or by formulae within a computer spreadsheet for large datasets.

Conclusions:  Surgical investigators should not use the K-M technique to predict cumulative survival or risk if there are two competing adverse events. They should use, instead, the technique of actual cumulative survival or incidence analysis.