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Competing risk analysis using R: an easy guide for clinicians

Bone Marrow Transplantation volume 40, pages 381–387 (2007)Cite this article

Abstract

In the last decade with widespread use of quantitative analyses in medical research, close co-operation between statisticians and physicians has become essential from the experimental design through all phases of complex statistical analysis. On the other hand, easy-to-use statistical packages allow clinicians to perform basic statistical analyses themselves. Since the software they most commonly use does not perform in depth competing risk analysis, we recommend an add-on package for the R statistical software. We provide all the instructions for downloading it from internet and illustrate how to use it for analysis of a sample dataset of patients who underwent haematopoietic stem cell transplantation for acute leukaemia.

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Acknowledgements

We thank Dr Geraldine Anne Boyd, University of Perugia, for editing this paper.

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Authors and Affiliations

  1. Department of Economy Finance and Statistics, Statistics Section, University of Perugia, Perugia, Italy

    L Scrucca

  2. Department of Clinical and Experimental Medicine, Hematology and Clinical Immunology Section, University of Perugia, Perugia, Italy

    A Santucci & F Aversa

Authors
  1. L Scrucca
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  2. A Santucci
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  3. F Aversa
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Correspondence to F Aversa.

Appendices

Appendix A

Competing risk analysis is dedicated to the study of failure probabilities when each individual may fail due to one of several causes, called competing events. The cumulative incidence function is defined as the probability of failing from cause r (r=1 ,…, k where k is the number of causes of failure) up to a certain time point t. Formally, it may be written as

where λr(t) is the cause specific hazard rate and S(t)=Pr(T⩾t) is the survival function. Non-parametric MLE of (cause specific) CIF is computed as follows:

where drj is the number of failures at time tj from cause r, nj is the number of individuals at risk at time tj, and Ŝ(tj) is the Kaplan–Meier estimate of the overall survival function. It is interesting to note that ∑kr=1Îr(t)=1−Ŝ(tj), that is the sum of cumulative incidence from all causes is equal to 1 minus the Kaplan–Meier estimate of survival.

Confidence interval estimation can be derived10 based on the ln(−ln) transformation, so the (1−α)100% confidence interval for the cumulative incidence function at time t for cause r is given by

where zα/2 is the upper α/2 percentile of the standard normal distribution, and σr(t) is the square root of the estimated variance of Îr(t). This can be calculated as follows (see Marubini and Valsecchi, p 341, eq. 10.12):12

where dj=∑kr=1drj.

Finally, comparison of cause-specific CIFs in different groups can be performed using one of the tests proposed, among others, by Gray,5 Pepe and Mori,13 and Lin.14

Appendix B

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Scrucca, L., Santucci, A. & Aversa, F. Competing risk analysis using R: an easy guide for clinicians. Bone Marrow Transplant 40, 381–387 (2007). https://doi.org/10.1038/sj.bmt.1705727

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