## Attributable fractions used for partitioning risk and evaluating disease prevention. Concepts, estimation, interpretation and presentation

##### Abstract

Background:
In medical research some fundamental tasks are to study potential harmful exposures
that may give increased risk of getting some disease, potential beneficial treatments
that may increase chance of recovering from a disease, or interventions that may
reduce the extent or effect of a harmful exposure. In epidemiologic research these
questions are studied by collecting individual data for representative samples of the
population. For a specified disease (e.g. breast cancer) there will usually be many risk
factors, some may be modifiable (e.g. life style factors like smoking habits, physical
activity, dietary factors) and other factors not so easy to modify (like reproductive
factors, aging, genetic factors). Provided that enough data for the individuals in the
sample is collected on the occurrence of disease and the relevant risk factors,
statistical models are identified to estimate the effects of the various risk factors on
the prevalence or incidence of the disease in the population. Estimating the factual
situation in the population and quantifying the uncertainty in the estimates are thus
important aims of such statistical analyses. Having done so, a natural next question of
importance is what kind of exposures can be avoided, or how many diseased cases
can be prevented, if such exposure could be completely or partially eliminated. A
statistical concept that can be used to quantify this is the attributable fraction. For a
single disease caused by a single exposure the attributable fraction due to this factor
is the proportion of diseased subjects that could have been prevented if the specified
exposure had not been present. Or, in other words, one questions what would the
proportionate reduction in diseased subjects in the population be if the exposure
distribution had been different from what it actual is? For illustration, an Italian study
estimated that 15.0 % of the breast cancer cases might have been avoided if the betacarotene
intake had been increased to at least 3366 μg/day for everyone while not
changing the distribution of a number of other risk factors (low vitamin E intake,
residence, alcohol habits, physical activity, age, educational level, calorie intake and
menopausal status). Increasing also vitamin E intake (to at least 8.5 mg /day) for all subjects gave a combined attributable fraction per cent of 21.5%. Sometimes
eliminating a common exposure with a moderate increased risk of disease may have
the same effect in the population at large as eliminating a rare exposure with a highly
increased risk of disease. Thus, an attributable fraction depends both on the risk of
disease if exposed and the extent of the exposure in the population studied.
In general, the attributable fraction quantifies the proportion of cases prevented if the
factual exposure distribution were replaced with a hypothetical, so called
counterfactual, exposure distribution. The attributable fraction can also be crudely
defined as excess proportion of diseased in the population relative to the total
proportion. The attributable fraction has also several other applications, e.g. to
quantify the proportion of diseased that can be ascribed to one or more exposures
(epidemiology), to predict the effect of planned preventive interventions (health
policy) and to apportion the responsibility for the disease to various agents
responsible for the exposure (liability law). It has been used in regional and national
research, as well as in global studies like the Global Burden of Disease and
Comparative Risk Assessment projects of the World Health Organization.
Results: With multiple risk factors attributable fractions can be defined in many ways
depending on how the counterfactual situation is hypothesized. This thesis describes
how attributable fractions can be defined, interpreted and estimated for various
scenarios, e.g. one factor is eliminated while the rest is kept fixed; several factors are
eliminated; and, multiple factors are removed sequentially may be in different
orderings. It also describes convenient graphical methods to illustrate the potential
impact on disease load in a population from interventions on one or more risk factors.
The statistical and graphical methodology is potentially useful as tools in health
policy discussions illustrating possible effects of different preventive strategies under
evaluation and may ease the communication between researchers, decision takers and
the public. Which strategy will have the largest effect in a public health perspective?
Which factors should be given priority in a public health intervention or in legislation? How much can be achieved by changing personal habits versus general
prevention of environmental exposure locally, nationally or globally? Methodology
for computerized, and possibly interactive, manipulations of different scenarios is
developed to depict the estimates of possible consequences.
The statistical methodology for attributable fractions has traditionally been developed
in relation to the classical epidemiological research designs like case-control studies,
cross-sectional studies and cohort studies with fixed time to follow-up. Based on the
statistical models for analysing time-to-event data the thesis extends and reformulates
the traditional definitions of attributable fraction so as to apply also for scenarios
where the risk of disease in the population is developing through time and actions
against harmful exposure or treatment or other intervention may be implemented at
different time points. Thus immediate, later, as well as cumulative effects of an
intervention on the disease load in the population are incorporated in these new
attributable fraction concepts. Conclusions: In summary, the thesis discusses many types of attributable fractions to be used for
various purposes. The thesis provides methodology for making adequate choices for
the question at hand. It also gives new algorithms for calculating attributable fractions
extending those of standard statistical software, and it suggests graphical displays that
are useful for communicating research results concerning attributable fractions, most
of which are not found in standard statistical software of today. Finally, new
methodology for dynamic modelling of attributable fractions taking time to disease,
time of intervention, or other time-dynamic aspects, into account is suggested by
relating the methodology of attributable fractions to established theory of survival
analysis. The latter will be an interesting field for further methodological research as
will also relating the concepts of attributable fraction to the recent development in
causal statistical modelling.

##### Has part(s)

Paper I: Journal of Clinical Epidemiology 48, Eide, Geir Egil & Gefeller, Olaf, Sequential and average attributable fractions as aids in the selection of preventive strategies, pp. 645-655. Copyright 1995 Elsevier. Abstract only. Full-text not available due to publisher restrictions. Paper II: Statistical Methods in Medical Research 10(3), Eide, Geir Egil & Heuch, Ivar, Attributable fractions: fundamental concepts and their visualization, pp. 159-193. Copyright 2001 Arnold. Published by Sage Publications. Abstract only. Full-text not available due to publisher restrictions. Paper III. Biometrical Journal 48(1), Eide, Geir Egil & Heuch, Ivar, A scaled sample space cube used to illustrate attributable fractions, pp. 93-104. Copyright 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. http://dx.doi.org/10.1002/bimj.200410156 Abstract only. Full-text not available due to publisher restrictions. Paper IV. Biometrical Journal 48(5), Eide, Geir Egil & Heuch, Ivar, Average attributable fractions: a coherent theory for apportioning excess risk to individual risk factors and subpopulations, pp. 820-837. Copyright 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. http://dx.doi.org/10.1002/bimj.200410156 Abstract only. Full-text not available due to publisher restrictions. Paper V. Statistics in Medicine 27(9), Samuelsen, Sven Ove & Eide, Geir Egil, Attributable fractions with survival data, pp. 1447 – 1467. Copyright 2008 John Wiley & Sons, Ltd. http://dx.doi.org/10.1002/sim.3022 Abstract only. Full-text not available due to publisher restrictions.