We build our approach on an understanding of two basic concepts used in the Comparative Risk Assessment (CRA) project (Ezzati et al. 2004), specifically relative risk (RR) and population attributable fraction (PAF). An RR is a “measure of the risk of a certain event happening in one group compared to the risk of the same event happening in another group”. ^[1]   We follow the approach taken by the CRA study, comparing our forecast population at risk to an “ideal” population with a “theoretical minimum” level of risk. For example, the WHO estimates that children under five who are moderately or severely underweight are almost nine times more likely to die of communicable causes than a population of “normal-weight” children (Blössner and de Onis 2005).

As its name suggests, a PAF or population attributable fraction reflects the degree to which a specific risk factor is associated with the occurrence of a specific health outcome.  Formally, it is the proportional reduction in disease or death rates for the total population (including those with and without the risk factor) that we would expect if we reduced a particular risk factor to a theoretically minimum level (Ezzati et al. 2004).  The further the current situation is from the ideal, the closer the value of the PAF will be to 1.

A PAF is calculated as:

(∑RR(x)P(x)-∑RR(x)P’(x)/∑RR(x)P(x)) = 1 - ∑RR(x)P’(x)/∑RR(x)P(x)                

where

RR(x) is relative risk at exposure level x; and

P(x) is the population distribution in terms of exposure level, i.e. the shares of the population exposed to each level of exposure;

P’(x) is the theoretical minimum population distribution in terms of exposure level; for certain risks this is defined as no exposure; where this is not realistic, the WHO defines an international reference population

Following this definition, multiplying the mortality from a particular disease by the PAF yields an estimate of the number of people who would not have died had the risk factor been at its theoretical minimum level.  If we assume that the values of RR(x) and P’(x) for particular risk factors and diseases do not differ across countries or change over time, ^[2] then changes in the PAF are solely a function of changes in P(x), the exposure of the population to the particular risk factor. Thus, it is necessary to be able to forecast the future levels of the risk factors. Other Help topics describe how this is done for specific risk factors such as undernutrition, obesity, smoking, and indoor air pollution.

• Mortality_Distal * PAF_Distal represents the number of people who would not have died had the risk factor been at its theoretical minimum level using the distal formulations for mortality and the proximate risk factor; and
• Mortality_Final * PAF_Full represents the number of people who would not have died had the risk factor been at its theoretical minimum level using a more complete formulation for mortality and the proximate risk factor

If we assume that no other factors influence the difference in total mortality between the distal formulation and that using the full model, then:

Mortality_Final - Mortality_Distal = Mortality_Final * PAF_Full - Mortality_Distal * PAF_Distal    

Yields:

Mortality_Final   = Mortality_Distal * ((1-PAF_Distal) / (1-PAF_Full))

                       = Mortality_Distal * ∑RR(x)P_Full(x)/∑RR(x)P_Distal(x)                             

The adjustment factor is the ratio of the weighted average relative risks based on the distributions using the distal-only versus the full formulations for estimating the value of the risk factor. A higher weighted-average relative risk based on the full formulation implies that the distal drivers overestimate our anticipated improvement (or underestimate the deterioration) in the risk factor. Thus, the mortality forecast needs to be adjusted upwards.  Alternatively, if the weighted-average relative risk is lower based on the full formulation than on the distal formulation, the mortality forecast will be adjusted downwards. Note that this property of the calculation actually obviates the need to know the theoretical minimum population.