For instance, suppose you get cancer in 2000 and it is the one that will not self-cure. Under older diagnostics, you might be diagnosed in 2014 with 2 years left to live. Despite treatment, you die in 2016 after 2 years. Under newer screenings, you are diagnosed in 2002 and get chemo. The chemo takes out that cancer, and in 2005 or 2006 you get another cancer because your immune system was trashed. The second cancer takes you out in 2008, or 6 years after the initial diagnosis but still some 8 years before you would have died from the first cancer. Have they extended your life by 4 years, or shortened it by 8?
Wow, that's a pretty provocative conclusion! Can you please point me to the empirical evidence used to support this? I mean no disrespect and information like this needs to be substantiated, otherwise it is conjecture.
Additionally, how do you know that the person in the later situation would have lived longer had he received treatment later in life? Your hypothesis can't really be tested for verification or falsification. Thus, I suspect there is no empirical evidence.