WOLFRAM|DEMONSTRATIONS PROJECT

Additive and Multiplicative Risks

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random trials to generate
300
seed repeatable random numbers
data
generate
clear
method
additive
multiplicative
seed value
0
r
0
minimum
0.0005
r
0
maximum
0.002
a minima
a maxima
f minima
f maxima
a
1
0.0001
a
1
0.001
f
1
0.5
f
1
0.75
a
2
0.0002
a
2
0.001
f
2
0.75
f
2
1.
a
3
0.0003
a
3
0.001
f
3
1.
f
3
1.25
a
4
0.0004
a
4
0.001
f
4
1.25
f
4
1.75
a
5
0.0005
a
5
0.001
f
5
1.5
f
5
2.
a
6
0.0006
a
6
0.001
f
6
1.5
f
6
2.5
b
0.
b
0.
This Demonstration estimates the combined effect of different risks, starting from a reference risk such as that corresponding to a person's age, gender, and so on. The combined effect of additional risks or potential health benefits can be either additive or multiplicative. In the additive case, the effects of these risks are cumulative and the benefits, if any, are expressed as probabilities, whereas in the multiplicative case, the effects are represented by factors where those greater than one account for increasing the overall risk and those less than one for reducing it. The most probable overall risk is calculated by the expanded Fermi solution based on Monte Carlo simulations, which produce an approximately normal distribution in the additive case and lognormal in the multiplicative case. The mode of the generated distribution is considered the best estimate of the overall risk.