Cardiovasc Prev Pharmacother.  2020 Jul;2(3):77-84. 10.36011/cpp.2020.2.e11.

Competing Risk Model in Survival Analysis

• Jeon Y
• Lee WK

• KMID: 2536953
• DOI: http://doi.org/10.36011/cpp.2020.2.e11

Abstract

Survival analysis is primarily used to identify the time-to-event for events of interest. However, there subjects may undergo several outcomes; competing risks occur when other events may affect the incidence rate of the event of interest. In the presence of competing risks, traditional survival analysis such as the Kaplan-Meier method or the Cox proportional hazard regression introduces biases into the estimation of survival probability. In this review, we discuss several methods that can be used to consider competing risks in survival analysis: the cumulative incidence function, the cause-specific hazard function, and Fine and Gray's Subdistribution hazard function. We also provide a guide for conducting competing risk analysis using SAS with the bone marrow transplantation dataset presented by Klein and Moeschberger (1997).

Keyword

Causality; Epidemiologic studies; Statistical models; Survival analysis

Figure

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  Figure 1. Overview of the calculation of the CSH. The risk set starts with 30 individuals (solid circles). Over time, individuals either experience event 1 (squares) or event 2 (triangles). As individuals experience either event, they are removed from the remaining risk sets. The calculation for the cause-specific hazard is given at the bottom of the figure from Lau et al.9)CSH = cause-specific hazard.

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  Figure 2. Overview of the calculation of the SDH. The risk set starts with 30 individuals (solid circles). Over time, individuals either experience event 1 (squares) or event 2 (triangles). When individuals experience a competing event (event 2, triangles), they are maintained in the risk set as triangles. Thus, over time, a greater proportion of the risk set becomes full of triangles, which represent individuals who have experienced the competing event prior to that time. The SDH for event 1 is given near the bottom of the figure along with the CSH for event 1 for comparison. Note that because individuals are maintained in the risk set, the SDH tends to be lower than the CSH from Lau et al.9)CSH = cause-specific hazard; SDH = subdistribution hazard.

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  Figure 3. SAS example (1).ALL = acute lymphoblastic leukemia; AML = acute myelocytic leukemia; BMT = bone marrow transplantation.

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  Figure 4. SAS example (2).AML = acute myelocytic leukemia; BMT = bone marrow transplantation.

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  Figure 5. SAS example (3).ALL = acute lymphoblastic leukemia; AML = acute myelocytic leukemia; BMT = bone marrow transplantation.

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  Figure 6. SAS example (4).AML = acute myelocytic leukemia; BMT = bone marrow transplantation.

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  Figure 7. SAS example (5).AML = acute myelocytic leukemia; BMT = bone marrow transplantation.

Reference

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