To check the answers of the goal seek in scenario 4 and 5, the example summary explains the results of a mortality reduction of 51% and 9% are reasonable as: 1. 51% : "The magnitude is broadly as would be expected, since a 20% reduction factor resulted in an increase of 0.7 years to 8.5 years, and therefore approximately a further 30% would be required in order to increase it by another 1.5 years to 10.0 years." 2. 9% "The magnitude is not unreasonable: a 20% reduction factor resulted in an increase of 6.2 years to 14.0 years, and therefore between a third and a half of this would be appropriate to increase it by the 2.2 years required to achieve the target of 10.0 years." Can someone please explain how the futher 30% in part 1 above and "between a third and a half" in part 2 are found? Thanks!
We are told that 20% reduction caused a change of 0.7 years. We need to work out the mortality reduction that would lead to the target life expectancy of 10 years (a change of 1.5 years), so that is just over twice as much. However, we know it isn't a linear relationship, so the increase being calculated at 51% appears a reasonable value given the shape of the distribution. Similarly a 20% reduction caused an increase of 6.2 years. We again need to work out the reduction that would give the target of 10 years and instead increase it by just 2.2 years. If we do 20/6.2 x 2.2 it gives us an estimate of 7%, so 9% appears reasonable (being between a half and a third of 20%). I think the half to a third has been given as a suggested reasonable range given it is not a linear relationship. The more important point here is that a reasonableness check has been carried out and documented. Any sensible test and reasonable argument would have been fine.
