Re: "Attributable risk in practice"

Attributing the burden of cancer at work: three areas of concern when examining the example of shift-work

This commentary intends to instigate discussions about epidemiologic estimates and their interpretation of attributable fractions (AFs) and the burden of disease (BOD) of cancers due to factors at workplaces. By examining recent work that aims to estimate the number of cancers attributable to shift-work in Britain, we suggest that (i) causal, (ii) practical and (iii) methodological areas of concern may deter us from attributable caseload estimations of cancers at this point in time. Regarding (i), such calculations may have to be avoided as long as we lack established causality between shift-work and the development of internal cancers. Regarding (ii), such calculations may have to be avoided as long as we can neither abandon shift-work nor identify personnel that may be unaffected by shift-work factors. Regarding (iii), there are at least four methodological pitfalls which are likely to make AF calculations uninterpretable at this stage. The four pitfalls are: (1) The use of Levin's 1953 formula in case of adjusted relative risks; (2) The use of broad definitions of exposure in calculations of AFs; (3) The non-additivity of AFs across different levels of exposure and covariables; (4) The fact that excess mortality counts are misleading due to the fact that a human being dies exactly once - a death may occur earlier or later, but a death cannot occur more than once nor can it be avoided altogether for any given individual. Overall, causal, practical and methodological areas of concern should be diligently considered when performing and interpreting AF or BOD computations which - at least at the present time - may not be defensible.

Average Attributable Fractions: A Coherent Theory for Apportioning Excess Risk to Individual Risk Factors and Subpopulations

The attributable fraction in a population and the attributable fraction in exposed are different epidemiologic measures for quantifying the contribution of a risk factor to the risk of disease. While the attributable fraction in a population depends on both the relative risk of disease and the risk of being exposed in the population, the attributable fraction in exposed depends only on the relative risk. Similar relationships apply to the combined attributable fraction in a population and in exposed, respectively, for quantifying the total contribution of a group of risk factors. Eide and Gefeller (1995) showed how the sequential and average attributable fractions could be applied to quantify the contributions of the individual risk factors to a combined attributable fraction in a population. The present paper shows how this methodology can be extended to the combined attributable fraction in exposed. The resulting average attributable fractions in exposed are compared to other proposed methods. The relationship between the average attributable fractions in a population and in exposed is outlined, thus establishing a coherent theory for apportioning attributable fractions in individuals, groups of individuals and populations, to single risk factors or groups of risk factors like modifiable versus nonmodifiable factors.

How much downside? Quantifying the relative harm from tobacco taxation

OBJECTIVE

To estimate the loss of life expectancy attributable to tobacco taxation (via financial hardship and flow-on health effect) in New Zealand.

DESIGN

Data were used on the gradients in life expectancy and smoking by neighbourhood socioeconomic deprivation and survey data on tobacco expenditure. Three estimates were modelled of the percentage of the crude association of neighbourhood deprivation with life expectancy that might be mediated via financial hardship: 100%, 50%, and 25% (best estimate). From this information the impact of tobacco taxation on life expectancy was estimated.

MAIN RESULTS

For the total population, the estimated loss of life expectancy due to tobacco tax ranged from 0.005 years to 0.027 years. For people living in the most deprived 30% of neighbourhoods, the range was 0.009 to 0.044 years (that is, 3 to 16 days of lost life expectancy). For the total population the loss of life expectancy attributable to tobacco tax ranged from 119 to 460 times less than that attributable to deprivation. The loss of life expectancy attributable to tobacco tax was 42 to 257 times less than that attributable to smoking.

CONCLUSIONS

The estimated harm to life expectancy from tobacco taxation (via financial hardship) is orders of magnitude smaller than the harm from smoking. Although the analyses involve a number of simplistic assumptions, this conclusion is likely to be robust. Policy makers should be reassured that tobacco taxation is likely to be achieving far more benefit than harm in the general population and in socioeconomically deprived populations.

A new way to estimate the contribution of a risk factor in populations avoided nonadditivity

OBJECTIVE

Attributable fraction in the exposed and (population) attributable fraction have been extensively used to determine the proportion of cases of a particular disease that can be attributable to any risk factor. Epidemiologists know that these measurements can add up to more than 100%; nevertheless, in a clinical context or in mass media, this characteristic is sometimes misinterpreted. This article provides a way to estimate the contribution of a risk factor in populations.

STUDY DESIGN AND SETTING

McElduff et al. have suggested a method for estimating the contribution of a risk factor in a person with more than one risk factor. We extend their suggestion to populations where risk factors are mixed in different proportions. We illustrate the usage of this method by enlarging the example provided by them and compare it with the average attributable fraction suggested by Eide and Gefeller.

RESULTS

Population attributable fraction can be modified to obtain additivity; therefore, the contribution of a risk factor in populations can be estimated, which would be of interest, for example, in clinical or in court settings.

CONCLUSION

The suggested method and the average attributable fraction provide different results, and would be applicable under different assumptions.

Attributable fractions: fundamental concepts and their visualization

A general methodology for visualizing attributable fractions in epidemiology is described. The methodology applies to the multifactorial exposure situation and embraces various types of attributable fractions including adjusted, sequential and average attributable fractions. The concept of the scaled Venn diagram plays a central role, illustrating total disease risk and excess disease risk attributable to the exposures as areas in a unit square. This forms the ground for making simple pie charts of attributable fractions summing to 1 (or 100%). The potential applications extend from cohort and cross-sectional data to data from case-control studies. The methodology is illustrated by theoretical as well as empirical examples including the risk of motor fatalities attributable to driver's blood alcohol concentration and age, and the prevalence of chronic cough attributable to smoking habits, occupational exposure to dust or gas, and residence. A total of 40 figures illustrate the methodology.

A review of adjusted estimators of attributable risk

This paper reviews adjusted methods of estimation of attributable risk (AR), that is methods that allow one to obtain estimates of AR while controlling for other factors. Estimability and basic principles of AR estimation are first considered and the rationale for adjusted AR estimators is discussed. Then, adjusted AR estimators are reviewed focusing on cross-sectional, cohort and case-control studies. Two inconsistent adjusted estimators are briefly commented upon. Next, adjusted estimators based on stratification, namely the weighted-sum and Mantel-Haenszel (MH) approaches, are reviewed and contrasted. It appears that the weighted-sum approach, which allows for full interaction between exposure and adjustment factors, can be affected by small-sample bias. By contrast, the MH approach, which rests on the assumption of no interaction between exposure and adjustment factors may be misleading if interaction between exposure and adjustment factors is present. Model-based adjusted estimators represent a more general and flexible approach that includes both stratification approaches as special cases and offers intermediate options. Bruzzi et al.'s and Greenland and Drescher's estimators are reviewed and contrasted. Finally, special problems of adjusted estimation are considered, namely estimation from case-cohort data, estimation for risk factors with multiple levels, for multiple risk factors, for recurrent events, estimation of the prevented and preventable fractions, and estimation of the generalized impact fraction. Comments on future directions are presented.