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Take now a post-merger profit function which allows for efficiencies in the form of synergies affecting marginal costs as follows: (pi _{A_{1}A_{2}}=(p_{1}-c)(X_{11}+X_{12})+(p_{2}-c)(X_{21}+X_{22})+Ec(X_{11}+X_{12}+X_{21}+X_{22}), ) where (E) stands for the merger induced marginal costs savings proportion, where (E<1).
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∥ Number of cancers needed to be detected (NND) is the reciprocal of the life-saving proportion.
The numerator of the life-saving proportion (LSP) is the screen-free absolute death risk multiplied by the RRR.
The high extreme is the life-saving proportion for women with a screen-detectable cancer of 1/1370 (7.3% at age 65/30% RRR).
Assuming a 20% RRR starting at age 50, the life-saving proportion is 4.3%, which falls to 3.7% at age 40 and increases to 4.6% at age 60.
We developed additional variations of the absolute risk reduction for a screening intervention, including the average benefit of a single screen, as well as the life-saving proportion among patients with earlier cancer detection.
The household savings ratio (the proportion of disposable income that is not spent) has been below 2.5% since 1999.
In America, the household savings ratio (the proportion of disposable income not used for consumption) has been below 2.5% since 1999; in Britain, it has been below 3% in each of the past two years.
Finally, to answer the question "Did that screening mammogram really save my life?" we derived the life-saving proportions from screening among women who develop or have a mammography-detectable breast cancer.
These variations include the average benefit from one screening exam (using airbags for a long trip), as well as the life-saving proportions among women who develop or have earlier detection of cancer (lives saved for those in traffic accidents).
Therefore, the life-saving absolute benefit in regards to screening has five forms: the RADR, number needed to screen, and the survival percentage; as well as the average benefit and the life-saving proportions.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com