On the issue of 'multiple' first failures in competing risks analysis

In the classical competing risks framework, a subject may only fail from one of several distinct causes. However, in the context of cancer clinical trials where information on first relapse is usually of interest, there could be occasions when 'multiple' first recurrences are identified at a particular follow-up. In this instance, the competing risks methodology cannot be implemented without first tackling the issue of 'tied' first failure. When the tied events were substantial, Arriagada et al. regarded each competing failure separately, and combined the 'simultaneous' failures into a single category for analysis. This paper describes two other methods of accounting for 'multiple' failures. First, the ties were dealt with by applying a weighting factor which was equal to the reciprocal of the number of ties. We also considered 'jittering' which randomly adds or subtracts a small number to each 'tied' event time to randomly break the tie. As illustrated using the data obtained from a randomized trial of patients with operable osteosarcoma, the estimates based on Arriagada's approach have larger standard errors. Estimates from the other alternative methods were similar. Multiple jittering has the advantage of wide applicability in any situation of tied survival times. However, it takes a longer computer running time, especially when the number of replicates is large. The weighted Cox approach is the method of choice where statistical software allows its implementation without extra programming effort.