Studies of radiation therapy and/or surgery in the treatment of cancer frequently use actuarial methods to estimate curves of time to local failure and compare two such curves with statistical methods originally developed for survival data. In such analyses, patients who fail first in distant sites or die before local failure are considered censored for time to local failure. While the arithmetic of these calculations is usually correct, the interpretation of the results is almost universally incorrect. For example, an actuarial Kaplan-Meier curve of time to breast recurrence after breast conservating treatment consistently overestimates the percentage of patients who would benefit from a subsequent mastectomy. Actuarial methods require the assumption that time to local failure and time to distant failure are statistically independent. For most human malignancies this is not a reasonable assumption, since there are always some patient subgroups at high risk of both local and distant failure and some patient subgroups at low risk for either type of failure. Without the assumption of independence, the time to local failure distribution is not well defined. The basic problem is that estimating time to local failure falls into the category of analyzing 'competing risks', since the various causes of failure are competing for the same patient. For this reason, the effects of a particular treatment on local failure cannot be assessed separately from its effects on distant failure. This report explains the concepts of statistical independence, nonidentifiability, and competing risks and illustrates the pitfalls of using actuarial methods to assess local tumor control. We propose a solution to the problem of analyzing local failure, which uses a two-step procedure: first analyzing time to first failure (in any site) and then analyzing the distribution of sites of first failure.
