Summary Functions for Data in the Presence of Competing Risks

Although cumulative incidence function (CIF) estimates are commonly used to describe the failure probabilities when competing risks are present, the CIF has limitations in some scenarios. The objective of our research was to propose new summary functions or modify CIF to overcome the limitations. In observational studies or nonrandomized trials, CIF estimates can be biased if the distribution of a confounding variable differs among treatment groups. To reduce the bias, we developed an adjusted CIF (ACIF) estimator that is based on the use of inverse probability weighting. We derived the estimation and inference procedures, and then used simulation studies to evaluate the performance. To illustrate the application of ACIF, we used the example of liver transplant candidates with various types of end-stage liver disease. We also developed a series of adjusted survival functions to estimate the ``net¡± survival probability for a specific outcome (the main event), based on the degree of correlation between this event and the competing events. First, for cases in which there is a perfect negative correlation, we constructed an adjusted survival function that uses the Kaplan-Meier estimator and the inverse probability of censoring weight (IPCW) for patients who experience competing events. Second, for cases in which there are imperfect negative correlations, we constructed an adjusted survival function that uses the combination of the IPCW and the adjusted number at risk under the constraints of the lower and upper bounds. Third, for cases in which there are positive correlations, we constructed an adjusted survival function that uses the adjusted number of main events under the constraints of the lower and upper bounds. To recover the contribution that the competing events make to the net survival probability, we incorporated auxiliary variables into the adjusted number at risk or the adjusted number of main events. We derived the estimation and inference procedures. We demonstrate the use of adjusted survival functions in data derived from patients who had emphysema, a severe form of chronic obstructive pulmonary disease.The public significance of this work is to provide new approaches to summarize the survival data with competing risks