Mathers et al
] described two traditions for causal attribution of health determinants, outcomes, or states: categorical attribution and counterfactual analysis. In categorical attribution, an event such as death is attributed to a single cause (such as a disease or risk factor) or group of causes according to a defined set of rules (hence 100% of the event is attributed to the single cause or group of causes). The International Classification of Disease system (ICD) attribution of causes of death [24
] and attribution of some injuries to alcohol or occupational conditions are examples of categorical attribution. In counterfactual analysis, the contribution of one or a group of diseases, injuries, or risk factors to a summary measure of population health (SMPH) is estimated by comparing the current or future levels of the SMPH with the levels that would be expected under some alternative hypothetical scenario including the absence of or reduction in the disease(s) or risk factor(s) of interest. This hypothetical scenario is referred to as the counterfactual (see Maldonado and Greenland [25
] for a discussion of conceptual and methodological issues in use of a counterfactuals).
In theory, causal attribution of an SMPH to risk factors can be done using both categorical and counterfactual approaches. For example, categorical attribution has been used in attribution of diseases and injuries to occupational risk factors in occupational health registries [8
] and attribution of motor vehicle accidents to alcohol consumption. In general however, categorical attribution of SMPH to risk factors overlooks the fact that many diseases have multiple causes [26
]. The epidemiological literature has commonly used the counterfactual approach for the attribution of a SMPH to a risk factor, and compared mortality or disability under current distribution of exposure to the risk factor to those expected under an alternative exposure scenario.
The dominant counterfactual exposure distribution in these studies has been zero exposure for the whole population (or a fixed non-zero level where zero is not possible such as the case of blood pressure when defined as presence or absence of hypertension). The basic statistic obtained in this approach is the population attributable fraction (PAF) defined as the proportional reduction in disease or death that would occur if exposure to the risk factor were reduced to zero, ceteris paribus
]. As discussed by Greenland and Robins [36
], attributable fractions without a time dimension are not able to characterize those cases whose occurrence would have been delayed in the absence of exposure. The authors recommend the use of etiologic fractions with a time dimension to account for this shortcoming. Time-based measures are discussed in more detail below.
The attributable mortality, incidence, or burden of disease due to the risk factor, AB, is then given as AB = PAF × B where B is the total burden of disease from a specific cause or group of causes affected by the risk factor with a relative risk of RR.
The exposed population may itself be divided into multiple categories based on level or length of exposure each with its own relative risk. With multiple (n) exposure categories, the PAF is given by the following generalized form:
Although choosing zero as the reference exposure may be useful for some purposes, it is a restricting assumption for others. The contribution of a risk factor to disease or death can alternatively be estimated by comparing the burden due to the observed exposure distribution in a population with that from another distribution
(rather than a single reference level such as non-exposed) as described by the generalized "potential impact fraction" in Equation 2 [32
where RR(x) is the relative risk at exposure level x, P(x) is the population distribution of exposure, P' (x) is the counterfactual distribution of exposure, and m the maximum exposure level. The first and second terms in the numerator of Equation (2a) therefore represent the total exposure-weighted risk of mortality or disease in the population under current and counterfactual exposure distributions. The corresponding relationship when exposure is described as a discrete variable with n levels is given by:
In addition to relaxing the assumption of no-exposure group as the reference, analysis based on a broader range of distributions has the advantage of allowing multiple comparisons with multiple counterfactual scenarios. Equation 2a can be further generalized to consider counterfactual relative risks (i.e. relative risk may depend on other risks, new technology, medical services, etc.). For example the relative risk of injuries as a result of alcohol consumption may depend on road conditions and traffic law enforcement. Similarly, people employed in the same occupation may have different risk of occupational injuries because of different safety measures. Therefore, a more general form of Equation 2a is given by:
Counterfactual exposure distributions
Various criteria may determine the choice of the counterfactual exposure distributions. Greenland [39
] has discussed some of the criteria for the choice of counterfactuals, arguing that the counterfactuals should be limited to operationalizable actions (e.g. anti-smoking campaigns) rather than the effects of removing the outcomes targeted by those actions (e.g. smoking cessation) because in practice, the implementation of counterfactuals for one risk factor or disease, may affect other risks. The solution to Greenland's concern, however, is better analytical techniques for estimating joint risk factor effects, rather than abandoning non-intervention-based counterfactuals which, as argued by Mathers et al
], is a limiting view. An understanding of the contributions from risk factors and the benefits of their removal, even in the absence of known interventions, can provide visions of population health attributable to risk factors, and avoidable by their removal. This knowledge of risk factor effects can provide valuable input into public health policies and priorities, as well as research and development (R&D).
Murray and Lopez [20
] introduced one taxonomy of counterfactual exposure distributions which, in addition to identifying the size of risk, provides a mapping to policy implementation. These categories include the exposure distributions corresponding to theoretical
minimum risk, plausible
minimum risk, feasible
minimum risk, and cost-effective
minimum risk. Theoretical minimum risk is the exposure distribution that would result in the lowest population risk, irrespective of whether currently attainable in practice. Plausible minimum refers to a distribution which is imaginable and feasible is one that has been observed in some population. Finally, cost-effective minimum considers the cost of exposure reduction (through the set of cost-effective interventions) as an additional criterion for choosing the alternative exposure scenario.
In addition to illustrating the total magnitude of disease burden due to a risk factor, theoretical minimum risk distribution (or the current difference between theoretical and plausible or feasible risk levels) can guide R&D resources towards those risk factors for which the mechanisms of reduction (i.e. interventions) are currently underdeveloped. For example, if the reduction in the burden of disease due to improved medical injection safety is high and the methods for risk reduction are well-known so that plausible/feasible and theoretical minima are identical, then current policy may have to be focused on the implementation of such methods. On the other hand, if there are large differences between plausible/feasible and theoretical minima risk levels for blood lipids or body mass index (BMI) [40
], then research on reduction methods and their implementation should be encouraged. For this reason the total magnitude of the burden of disease due to a risk factor, as illustrated by the theoretical minimum, provides a tool for considering alternative visions of population health and setting research and implementation priorities.
Biological principles as well as considerations of equity would necessitate that, although the exposure distribution for theoretical minimum risk may depend on age and sex, it should in general be independent of geographical region or population. Exceptions to this are however unavoidable. An example would be the case of alcohol consumption, which in limited quantities and certain patterns, has beneficial effects on cardiovascular mortality, but is always harmful for other diseases such as cancers and accidents [41
]. In this case, the composition of the causes of death as well as drinking patterns in a region would determine the theoretical minimum distribution. In a population where cardiovascular diseases are a dominant cause of mortality theoretical minimum may be non-zero with moderate drinking patterns, whereas in a population with binge drinking and large burden from injuries the theoretical minimum would be zero. Feasible and cost-effective distributions, on the other hand, may vary across populations based on the current distribution of the burden of disease and the resources and institutions available for exposure reduction.
The above categories of counterfactual exposure distributions are based on the burden of disease in the population as a whole. Counterfactual exposure distributions may also be considered based on other criteria. For example, a counterfactual distributions based on equity would be one in which the highest exposure group (or the group with highest burden of disease) would be shifted towards low exposure values. Further, such equitable counterfactual distributions for each risk factor may themselves be categorized into theoretical (most equitable), plausible, feasible, and cost-effective as described above. Similarly, a counterfactual distribution which focuses on the most sensitive groups in the population is one that gives additional weight to lowering the exposure of this group. Therefore, by permitting comparison of disease burden under multiple exposure distributions, based on a range of criteria – including, but not limited to, implementation and cost, equity, and research prioritization – relaxing the assumption of constant exposure base-line provides an effective policy and planning tool.
Exposure distribution for theoretical minimum risk
In one taxonomy, risk factors such as those in the GBD project [42
] can be broadly classified into categories of physiological, behavioral, environmental, and socio-economic. Some general principles that guide the choice of theoretical minimum distribution for each category are:
1) Physiological risk factors
: This group includes those factors that are physiological attributes of humans, such as blood pressure or blood lipids, and at some levels result in increased risk. Since these factors are necessary to sustain life, their "exposure-response" relationship is J-shaped or U-shaped, and the theoretical minimum is non-zero. For such risk factors, the choice of the theoretical minimum needs to be based on empirical evidence from different scientific disciplines. For example, epidemiological research on blood pressure and cholesterol have illustrated a monotonically increasing dose-response relationship for mortality even at low levels of these risk factors [43
]. But, given the role of these factors in sustaining life, this relationship must flatten and reverse at some level. In the blood pressure and cholesterol assessment, a theoretical minimum distribution with a mean of 115 mmHg for systolic blood pressure and 3.8 mmol/l for total cholesterol (each with a small standard deviation) were used [42
]. This distribution corresponds to the lowest levels at which the dose-response relationship has been characterized in meta-analyses of cohort studies [43
]. Further, these levels of blood pressure and cholesterol are consistent with levels seen in populations which have low cardiovascular disease, such as the Yanomamo Indians [47
] and rural populations in China [48
], Papua New Guinea [47
], and Africa [51
]. Although, meta-analyses of randomized clinical trials have indicated that blood pressure and cholesterol levels may be lowered substantially with no adverse effects [52
], it is difficult to justify a theoretical minimum lower than those measured in population-based studies, since lower levels in individuals may be caused by factors such as pre-existing diseases. Inferences from evolutionary biology would also support the lower bound on the choice of optimal distribution based on historical survival of populations who are not substantially exposed to factors that raise blood pressure or cholesterol.
2) Behavioral risk factors
: the exposure-response relationship for this group of risk factors may be monotonically increasing or J-shaped. For risk factors with a monotonic exposure-response relationship, such as smoking, the theoretical minimum would be zero unless there are physical constraints that make zero risk unattainable. For example in the case of blood transfusion, there may be a lower bound on safety of blood supply process even using the best monitoring technology. With a J-shaped or U-shaped exposure-response relationship, the theoretical minimum would be the turning point of the exposure-response curve. An example of this is alcohol consumption in adult populations with high cardiovascular disease rates, since moderate consumption may result in reduction in coronary heart disease in some age groups [54
]. With a J-shaped exposure-response curve, similar to physiological risk factors, empirical evidence would have to be used to determine the theoretical minimum.
Finally, some behavioral risks are expressed as the absence of protective factors such as physical inactivity or low fruit and vegetable intake. In such cases, optimal exposure would be the level at which the benefits of these factors would no longer continue. With a monotonic exposure-response relationship or without detailed knowledge about a possible turning point, the theoretical minimum risk level would have to be chosen based on empirical evidence on the highest theoretically sustainable levels of intake or exposure (for example a purely vegetarian diet or a very active life style).
3) Environmental risk factors: The toxicity of most of the environmental risk factors are monotonically increasing functions of exposure (potentially with some threshold). Therefore, the theoretical minimum for this group would be the lowest physically achievable level of exposure, such as background particulate matter concentration due to dust.
4) Socioeconomic "risk factors"
: Socioeconomic status and factors – such as income (including levels and distribution) and associated levels of poverty and inequality, education, the existence of social support networks, etc. – are important determinants of health, often through their effects on other risk factors. The effects of each of these factors on health are, however, highly dependent on other socioeconomic variables as well as the policy context, including accessibility and effectiveness of health and welfare systems. For this reason, the theoretical minimum exposure distribution, even if meaningfully defined, is likely to change over time and space depending on a large number of other factors. With this heterogeneity of effects, the effects of socioeconomic variables are best assessed relative to counterfactual distributions defined based on policy and intervention options in specific times and settings, as discussed by Greenland [39