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Multiple Risk Factors

Sometimes more than one risk factor will be linked to a particular disease. In theory, this requires estimating joint relative risks and exposure distributions. Under certain circumstances, however, a simple method can be used to calculate a combined PAF that involves multiple risk factors (Ezzati and others 2004):

PAFcombined = 1 - ∏(1-PAFi)                                                                           


PAFi is the PAF for risk factor i

The logic here is as follows. 1-PAFi represents the proportion of the disease that is not attributable to risk factor i. Multiplying these risks yields the share of the disease that is not attributable to any of the risk factors, and subtracting this from 1 leaves the share of the disease that is attributable to the set of risk factors considered.

Say that we have 2 risk factors: [1]

PAFcombined = 1 - (1-PAF1)(1-PAF2)

 Following from the discussion above, the combined adjustment factor can be calculated as:

 ((1-PAFcombined Distal) / (1-PAFcombined Full)) = [(1-PAF1 Distal)(1-PAF2 Distal)] / [(1-PAF1 Full)(1-PAF2 Full)]

 = [(1-PAF1 Distal)/(1-PAF1 Full)] * [(1-PAF2 Distal)/(1-PAF2 Full)]

 = [∑RR1(x)P1 Full(x)/∑RR1(x)P1 Distal(x)] * [∑RR2(x)P2 Full(x)/∑RR2(x)P2 Distal(x)]        

 In other words, the combined adjustment factor is a simple multiplication of the individual adjustment factors.



[1] In the sequence of our calculations we decompose this equation in practice by finding the individual PAFs, computing their individual independent effects with (1-PAFDistal)/(1-PAFFull), and multiplying mortality independently and cumulatively.