Flexible parametric modelling of cause-specific hazards to estimate cumulative incidence functions

Sally R Hinchliffe,Paul C Lambert

doi:10.1186/1471-2288-13-13

Abstract

BackgroundCompeting risks are a common occurrence in survival analysis. They arise when a patient is at risk of more than one mutually exclusive event, such as death from different causes, and the occurrence of one of these may prevent any other event from ever happening.MethodsThere are two main approaches to modelling competing risks: the first is to model the cause-specific hazards and transform these to the cumulative incidence function; the second is to model directly on a transformation of the cumulative incidence function. We focus on the first approach in this paper. This paper advocates the use of the flexible parametric survival model in this competing risk framework.ResultsAn illustrative example on the survival of breast cancer patients has shown that the flexible parametric proportional hazards model has almost perfect agreement with the Cox proportional hazards model. However, the large epidemiological data set used here shows clear evidence of non-proportional hazards. The flexible parametric model is able to adequately account for these through the incorporation of time-dependent effects.ConclusionA key advantage of using this approach is that smooth estimates of both the cause-specific hazard rates and the cumulative incidence functions can be obtained. It is also relatively easy to incorporate time-dependent effects which are commonly seen in epidemiological studies.

Highlights

Competing risks are a common occurrence in survival analysis
In this paper we focus on situations where the events are deaths from different causes and so it follows that any event will prevent the others from occurring
Competing risks If we assume that a patient is at risk from K different causes, the cause-specific hazard for the kth cause, hk(t) is the rate of failure at time t given that no failure from cause k or any of the K-1 other causes has occurred [3]

Summary

Introduction

Competing risks are a common occurrence in survival analysis They arise when a patient is at risk of more than one mutually exclusive event, such as death from different causes, and the occurrence of one of these may prevent any other event from ever happening. In this paper we focus on situations where the events are deaths from different causes and so it follows that any event will prevent the others from occurring In this competing risks scenario, the cause-specific hazard will give the cause-specific mortality rate and the cumulative incidence function will. Cause--specific hazards can inform us about the impact of risk factors on rates of disease or mortality, while the cumulative incidence functions provide an absolute measure with which to base prognosis and clinical decisions on [6]

Methods

Results

Conclusion