It's easiest to think about this by picturing a randomized trial, which you would try to emulate with an observational study.
By the ENTIRE group, we mean look at the proportion dying of the target cancer in the whole screened and unscreened groups, not just in those who were diagnosed. Length bias will make the prognosis of cancers identified by screening look better, but if groups are otherwise comparable (as they would be in an RCT), the numbers of good and bad cancers in the screened and unscreened groups should be comparable, and if you compare mortality you'll get no bias.
Does that help?
Tom
It sounds reasonable. However, in practice, do you mean we need to calculate specific mortality for all people (not just in those who were diagnosed) in two seperate groups, one with screening and one without screening? If so, how could we know those who were not diagnosed and died from this specific disease?
Thanks.
Chuangzhen
Yes, calculate mortality for entire screened and unscreened groups. The numerator will presumably just included those who were diagnosed. The key is that the denominator is the whole group, which includes people not diagnosed.
Tom