ABSTRACT
Competing risks are frequently encountered in clinical research, especially in cancer, where individuals under study may experience one of two or more different types (causes) of failure after initial diagnosis and treatment. For each subject, typically we observe the time to failure and its failure type, or time to censoring. Unless one is to simply consider the time to the first failure of any type as the endpoint of interest, special attention and methodology are required for competing risks analysis. This is because the
occurrence of first failure either prevents the occurrence of other types of failures (the typical competing risks scenario), or the disease natural history is altered due to the subsequent second-line treatment (in cases where events are not strictly mutually exclusive but are so in the sense that one will be the first failure). For example, localized prostate cancer patients may either die due to prostate cancer or from other causes, due to comorbid conditions or natural causes. Another example arises in locally advanced lung cancer, where the first failure after definite localized treatment (such as radiotherapy) could be in-field failure (local recurrence), out-of-field failure (distant metastases or second primary cancer), or death without disease. While in such setting, individuals may have multiple events (e.g., distant followed by local failure, or vice versa), since the disease natural history is largely dependent on the pattern and sequence of the multiple events as well as the subsequent treatment options, competing risks analysis (e.g., of time to first event and its type) may still offer the most clinically relevant information regarding failure patterns and prognosis. Two principal types of competing risks analysis are often used in a complementary fashion as each addresses important aspects of competing risks observations. In a nutshell, one is based on the cause-specific hazards (CSHs), while the other is based on cumulative incidence (Kalbfleisch and Prentice, 2002). We review their distinctionswith an emphasis of theoretical and practical implications and argue the importance of using the right methods to answer different questions of interest. The associated estimable quantities and corresponding statistical inference methods are discussed accordingly. We illustrate the analytic methods through a reanalysis of a Radiation Therapy Oncology Group (RTOG) clinical trial.
