Actual and Actuarial Probabilities of Competing Risks: Apples and Lemons

Recent editorials in two cardiac journals have promoted the use of the KM method (actuarial estimate) for competing risk events (specifically for heart valve performance) and criticized the use of the cumulative incidence (actual) estimates. This report has two aims: to explain the difference between these two estimates and to show why the KM is generally not appropriate. In the process we will rely on alternative representations of the KM estimator (using redistribution to the right and inverse probability weighting) to explain the difference between the two estimates and to show how it may be possible to adjust KM to overcome the informative censoring.