We talk a lot about 'saving lives', but we shouldn't -- it's really quite misleading. At best, we may save a few decades of someone's life. Death is never banished; merely postponed. "Reducing" the number of deaths in the world is not a coherent goal: we know there will be exactly one for each life, and there's no changing that (modulo immortality research). What we really mean here is that we aim to extend life. It's worth being clear on this, since not all life-extensions are equal, but a rhetorical focus on 'death' [or 'life-saving'] occludes this fact.
It's an obvious point, but one that seems unjustly neglected in the bioethics literature. It seems very common for bioethicists to want to balance the two goals of (1) saving the most lives and (2) maximizing life-years (see, e.g., Kerstein & Bognar). But "saving the most lives" is not, strictly speaking, a coherent goal (especially when contrasted with the goal of extending people's lives as much as possible); talking this way gives an unwarranted rhetorical glow to what actually amounts to simply distributing life-years across a greater number of people. And I don't see any good reason to take that as an ultimate goal.
To bring this out, consider a case where you can either extend a 30 year old's life by three decades, or three 70 year olds' lives by one decade each. The two options are equivalent in terms of total life-years gained. So if "saving the most lives" is taken as a distinct goal on top of that, then it would seem to follow that (all else equal) we should prefer to aid the three elderly patients. But that strikes me as precisely the wrong result. Partly, I think, because not all else is equal: Those earlier years of life are more significant in welfare terms, and prioritarians should, if anything, give priority to those who have lived less over those who have lived longer.
But even so far as distribution per se is concerned: Those skeptical of utilitarian aggregation generally see a big impact to one individual as more morally significant than widely distributed welfare impacts. (As a limiting case, compare the previous options to that of extending life by a single day for each of 11000 patients, or a second for a billion people, etc.) So this points in the very opposite direction: Holding fixed the number of life-years saved, perhaps we should prefer to see this benefit distributed across a smaller number of people rather than being excessively "diluted" across a large number of people.
(For the record, I actually think it'd be a mistake to hold to any such general "distributive" principle. Distribution matters insofar as it affects welfare, but the effect is not constant: A decade of life may be more than ten times the significance of one year, insofar as the greater time period enables one to realize distinctive new values in their life. On the other hand, a century of life-extension may be of less than ten times the value of a decade of extension, insofar as one can achieve central life goals in the shorter period, and these values are not susceptible to simple repetition.)
Perhaps the most friendly case for my opponents here is one where you can either extend a 70 y/o's life by 15 years, or else extend his life by 10 years and then some other 80 y/o's life by 5 years. I personally don't see any intuitive moral difference between these two options. But I could imagine someone arguing, "We've already helped the first guy, so isn't it fairer to help the other guy instead?" I'm dubious. (I don't see why having obtained needed aid in the past would make an innocent sufferer any less deserving of aid in the future.) Maybe, as a mere tie-breaker in this sort of case, one could appeal to "fairness" in this way. But even if that's right -- and it's far from clear to me that it is -- the weight of this consideration is clearly extremely weak, so I certainly don't see any grounds for treating "saving lives" (i.e. "distributing life-extension amongst more patients rather than fewer") as a significant goal on a par with maximizing welfare (via QALYs or similar estimates).
Conclusion: There's nothing particularly desirable about distributing some fixed number of additional life-years across more rather than fewer patients. So once we understand that this is what a goal of "saving more lives" (in contrast to maximizing life-years) amounts to, we should no longer see "saving more lives" as a proper goal (to be balanced against, and sometimes override, maximizing welfare) for guiding resource-allocation decisions.
Of course, loose talk of "saving lives" is harmless in many contexts. In particular, when everyone involved is relevantly similar in terms of their age, etc., then "saving more lives" will reliably coincide with "maximizing QALYs", or doing the most good. But in the context of bioethics and the allocation of scarce medical resources, this coincidence often breaks down -- and when it does, it's simply a mistake to continue to think in terms of "saving lives". It encourages conceptual confusion that can lead to serious moral errors.
[In particular, bioethicists of an "egalitarian" bent often seem to think that the way to treat people as equals is to give them equal priority for "life-saving" treatment. But once we remember that "life-saving" is really just "life-extension", then it becomes obvious that you don't treat people as equals by ignoring how much life-extension they each stand to gain. Put another way: One does not show equal concern towards two people by being indifferent to whether one receives a papercut or the other is beheaded. We should prefer to prevent the greater harm, and nothing in the idea of "treating people as equals" warrants thinking otherwise.]