Estimating cumulative event probabilities in time-to-event data can be complicated by competing events. Competing events occur when individuals can experience events other than the primary event of interest. These “other events” are often treated as censored observations.
This thesis compares point estimates and relative differences between two cumulative event probability estimators, the Kaplan-Meier complement (KMC) and the cumulative incidence (CI), in the presence of competing events. The KMC does not allow for the possibility of experiencing competing events, whereas the CI does. Consequently, the KMC overestimates the CI in the presence of competing events.
In this thesis, data were simulated with different combinations of primary event hazards, competing event hazards, random censoring hazards, and sample sizes. Cumulative event probabilities using the KMC and CI methods were calculated over a time period of 10 years.
Several conclusions were drawn. High primary event hazards resulted in high KMC’s and CI’s and slightly narrowed the variability of the relative differences between the two estimates. High competing event hazards did not affect KMC’s but resulted in low CI’s, causing high relative differences. High random censoring hazards did not affect KMC’s, CI’s, or relative differences. Large sample sizes did not affect the median relative differences but did narrow the variability of the relative differences.
The public health relevance of this thesis is to help medical clinicians and researchers understand the advantages and disadvantages of different approaches of calculating cumulative event probabilities in situations where competing events occur. This is particularly important in the area of personalized medicine in diseases like cancer where clinicians attempt to predict their patients' mortality or recurrence probabilities over time given certain clinical, pathologic, or demographic characteristics
