Traditional versus Competing Risks Approaches in the Modeling of Survival Time Open Access

Zhang, Chao (Spring 2019)

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      In survival analysis, it is often the case that competing events may preclude the event of interest. In our specific case, death was the competing event to our outcome of interest, hospital readmission after CABG surgery. In these situations, the usage of competing risks methods becomes necessary, as traditional survival analysis methods inaccurately assume competing events as censored observations. We first outline the fundamental quantities and models associated with competing risks analysis, which are largely based from the Kaplan-Meier estimator and Cox proportional hazards model in traditional survival analysis: the cumulative incidence function (subdistribution), cause-specific hazard function, and their respective generalizations of the Cox model, the Fine-Gray subdistribution hazard function and cause-specific hazards regression. We then compare the results of the Kaplan-Meier estimate with those of the cumulative incidence function, and then extend the Cox model to the cause-specific hazard function and subdistribution hazard function.

              The hazard ratios from the Fine-Gray and cause-specific hazards regression models were largely similar and identified several significant risk factors for readmission, including, but not limited to, gender (male), race (black), history of diabetes, and prior myocardial infarction. However, due to the low amount of competing events in our dataset, the results between traditional and competing risks methods differed minimally. As such, the data was modified to increase the incidence of deaths and readmissions. When there a large number of observations experiencing competing events, the Kaplan-Meier estimator becomes increasingly inaccurate, and its complement can no longer be interpreted as the probability of experiencing the event of interest; instead, the cumulative incidence function and its models are necessary here. Additionally, the distribution of competing events within a covariate was also found to lead to differences in results between the cause-specific hazards and Fine-Gray models. Overall, we can conclude that competing risks methods are largely trivial when the number of competing events is minimal, but can provide a meaningful prospective to the problem when a large number of competing event(s) exist, and the results of traditional estimators are no longer accurate.

Table of Contents


           I.         The Competing Risks Problem                                                                      1

           II.      Data Background                                                                                           4


           III.     Data Overview                                                                                               6

           IV.     Kaplan-Meier (KM) Estimator                                                                      9

           V.       Cox Proportional Hazards Model                                                                  11       

           VI.      Representation of Competing Risks                                                              13

           VII.    Cumulative Incidence Function (Subdistribution)                                        15

           VIII.   Cause-Specific Hazard Function                                                                   17

           IX.      Fine-Gray Subdistribution Hazard Function                                                 19

           X.       Cause-Specific Hazards Regression                                                              21

           XI.      Implementation in SAS and R                                                                       22


           XII.    Results from Original Data                                                                           24

           XIII.   Comparison of Simulation Results                                                               30       

Discussion                                                                                                                             34

References                                                                                                                            37

Appendix                                                                                                                             38

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