A comparison of approaches for estimating combined population attributable risks (PARs) for multiple risk factors

Abstract Objectives The methods to estimate the population attributable risk (PAR) of a single risk factor or the combined PAR of multiple risk factors have been extensively studied and well developed. Ideally, the estimation of combined PAR of multiple risk factors should be based on large cohort studies, which account for both the joint distributions of risk exposures and for their interactions. However, because such individual-level data are often lacking, many studies estimate the combined PAR using a comparative risk assessment framework. It involves estimating PAR of each risk factor based on its prevalence and relative risk, and then combining the individual PARs using an approach that relies on two key assumptions: that the distributions of exposures to the risk factors are independent and that the relative risks are multiplicative. While such assumptions rarely hold true in practice, no studies have investigated the magnitude of bias incurred if the assumptions are violated. Methods Using simulation-based models, we compared the combined PARs obtained with this approach to the more accurate estimates of PARs that are available when the joint distributions of exposures and risks can be established. Results We show that the assumptions of exposure independence and risk multiplicativity are sufficient but not necessary for the combined PAR to be unbiased. In the simplest situation of two risk factors, the bias of this approach is a function of the strength of association and the magnitude of risk interaction, for any values of exposure prevalence and their associated risks. In some cases, the combined PAR can be strongly under- or over-estimated, even if the two assumptions are only slightly violated. Conclusions We encourage researchers to quantify likely biases in their use of the M–S method, and here, we provided level plots and R code to assist.