On https://youtu.be/wiAnk3pt-Lc?t=44m00s Curt Ficenec claims that:
If you eliminate cancer, you would only change the average lifespan by 2.5 years
The same claim was made by David Sinclair in https://youtu.be/WglnKCJG9cw
Is that true?
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The actual number of 3.2 years comes from a US Health and Human Services report examining causes of mortality from a period between 1999-2001, and does not include any additional advances in medicine besides simply removing cancer deaths.
Most sources online that make a claim of a certain number of years are ultimately citing a May 2013 paper entitled United States Life Tables Eliminating Certain Causes of Death, 1999-2001.
The report's authors are
The full document is available to download here (publication reference: Arias, Elizabeth, Melonie Heron, and Betzaida Tejada-Vera. "United States life tables eliminating certain causes of death, 1999-2001." National vital statistics reports: from the Centers for Disease Control and Prevention, National Center for Health Statistics, National Vital Statistics System 61, no. 9 (2013): 1-128.).
In particular, we are looking at Table B, titled "Gain in life expectancy at birth due to eliminating specified causes of death, by race and sex: United States, 1999–2001", in the row titled "Malignant neoplasms".
In the section under "Total Population", we see a number of 3.20, for the number of years gained in life expectancy. This is broken down further by gender and by ethnicity, with the number hovering around the 3.20 level for all groups.
There seems to be another report available that comes to a similar results cited as "Olshansky & Carnes, 1990" that could have served as the precursor to this report, but I have not been able to find a copy of it online.