Comparison of methods for estimating the attributable risk in the context of survival analysis

Malamine Gassama,Laureen Dartois,Anne C M Thiébaut,Jacques Bénichou

doi:10.1186/s12874-016-0285-1

Abstract

BackgroundThe attributable risk (AR) measures the proportion of disease cases that can be attributed to an exposure in the population. Several definitions and estimation methods have been proposed for survival data.MethodsUsing simulations, we compared four methods for estimating AR defined in terms of survival functions: two nonparametric methods based on Kaplan-Meier’s estimator, one semiparametric based on Cox’s model, and one parametric based on the piecewise constant hazards model, as well as one simpler method based on estimated exposure prevalence at baseline and Cox’s model hazard ratio. We considered a fixed binary exposure with varying exposure probabilities and strengths of association, and generated event times from a proportional hazards model with constant or monotonic (decreasing or increasing) Weibull baseline hazard, as well as from a nonproportional hazards model. We simulated 1,000 independent samples of size 1,000 or 10,000. The methods were compared in terms of mean bias, mean estimated standard error, empirical standard deviation and 95% confidence interval coverage probability at four equally spaced time points.ResultsUnder proportional hazards, all five methods yielded unbiased results regardless of sample size. Nonparametric methods displayed greater variability than other approaches. All methods showed satisfactory coverage except for nonparametric methods at the end of follow-up for a sample size of 1,000 especially. With nonproportional hazards, nonparametric methods yielded similar results to those under proportional hazards, whereas semiparametric and parametric approaches that both relied on the proportional hazards assumption performed poorly. These methods were applied to estimate the AR of breast cancer due to menopausal hormone therapy in 38,359 women of the E3N cohort.ConclusionIn practice, our study suggests to use the semiparametric or parametric approaches to estimate AR as a function of time in cohort studies if the proportional hazards assumption appears appropriate.

Highlights

The attributable risk (AR) measures the proportion of disease cases that can be attributed to an exposure in the population
We focus on the first definition of AR based on Cumulative Distribution Function (CDF) which looks more consistent with the standard AR definition and appears to be the most used in the literature
For the purpose of our illustration, we considered 38,359 participants who were postmenopausal and free of cancer when they completed a self-administered questionnaire on their past use of any menopausal hormone therapy (MHT) in January 1992

Summary

Introduction

The attributable risk (AR) measures the proportion of disease cases that can be attributed to an exposure in the population. It is important to assess the association between one exposure and the occurrence of health events, and to quantify the impact of this exposure on the occurrence of these events This is done by estimating the attributable risk (AR) or the proportion AR =. In the context of cohort studies and time-to-event outcomes, AR measures can be defined as functions of time [4,5,6,7,8,9] a single AR estimate has been proposed alternatively [10]. Several methods of estimation have been proposed for the AR defined in this case, including nonparametric approaches based on Kaplan-Meier’s estimator of the survival function [7], a semiparametric approach based on Cox’s proportional hazards model [7] and a fully parametric approach assuming a piecewise constant hazards model [8]. Some evaluations were made for the nonparametric and semiparametric approaches [7] but, to the best of our knowledge, the performances of these various approaches have not been systematically compared

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