Population attributable fractions for continuously distributed exposures

When estimating population attributable fractions (PAF), it is common to partition a naturally continuous exposure into a categorical risk factor. While prior risk factor categorization can help estimation and interpretation, it can result in underestimation of the disease burden attributable to the exposure as well as biased comparisons across different exposures and risk factors. Here, we propose sensible PAF estimands for continuous exposures under a potential outcomes framework. In contrast to previous approaches, we incorporate estimation of the minimum risk exposure value (MREV) into our procedures. While for exposures such as tobacco usage, a sensible value of the MREV is known, often it is unknown and needs to be estimated. Second, in the setting that the MREV value is an extreme-value of the exposure lying in the distributional tail, we argue that the natural estimator of PAF may be both statistically biased and highly volatile; instead, we consider a family of modified PAFs which include the natural estimate of PAF as a limit. A graphical comparison of this set of modified PAF for differing risk factors may be a better way to rank risk factors as intervention targets, compared to the standard PAF calculation. Finally, we analyse the bias that may ensue from prior risk factor categorization, examining whether categorization is ever a good idea, and suggest interpretations of categorized-estimands within a causal inference setting.