The online version of this article (doi:10.1186/s12874-017-0327-3) contains supplementary material, which is available to authorized users.
The analysis of time-to-event data can be complicated by competing risks, which are events that alter the probability of, or completely preclude the occurrence of an event of interest. This is distinct from censoring, which merely prevents us from observing the time at which the event of interest occurs. However, the censoring distribution plays a vital role in the proportional subdistribution hazards model, a commonly used method for regression analysis of time-to-event data in the presence of competing risks.
We present the equations that underlie the proportional subdistribution hazards model to highlight the way in which the censoring distribution is included in its estimation via risk set weights. By simulating competing risk data under a proportional subdistribution hazards model with different patterns of censoring, we examine the properties of the estimates from such a model when the censoring distribution is misspecified. We use an example from stem cell transplantation in multiple myeloma to illustrate the issue in real data.
Models that correctly specified the censoring distribution performed better than those that did not, giving lower bias and variance in the estimate of the subdistribution hazard ratio. In particular, when the covariate of interest does not affect the censoring distribution but is used in calculating risk set weights, estimates from the model based on these weights may not reflect the correct likelihood structure and therefore may have suboptimal performance.
The estimation of the censoring distribution can affect the accuracy and conclusions of a competing risks analysis, so it is important that this issue is considered carefully when analysing time-to-event data in the presence of competing risks.
Additional file 1 Simulating proportional subdistribution hazards. Describes an algorithm for simulating survival data with competing risks under a proportional subdistribution hazards model with censoring, as used in the simulation study in this paper. (PDF 157 kb)12874_2017_327_MOESM1_ESM.pdf
Additional file 2 Multiple myeloma data. Survival data from the multiple myeloma example used in this paper, including the donor KIR haplotype, event times and types (0 = censored, 1 = relapse, 2 = transplant-related death [competing event]) for 35 patients. (CSV 581 bytes)12874_2017_327_MOESM2_ESM.csv
Additional file 3 Simulation results. Tables containing the complete results from the simulation study described in this paper. (PDF 92.7 kb)12874_2017_327_MOESM3_ESM.pdf
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- The importance of censoring in competing risks analysis of the subdistribution hazard
Mark W. Donoghoe
- BioMed Central
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