I believe that a much stronger statement is true. For almost every viral disease with a vaccine, there was a 90% reduction in mortality before the advent of the vaccine. The only graph I have on hand is measles:
Of course, if A causes a 90% reduction in mortality and B causes a 90% reduction in mortality, and they are independent, in a causal sense they are equal and you shouldn’t judge their effects based on which one is deployed first. But once one is deployed, the marginal value of adding the other is only 10% as much. Even if B causes a 100% reduction, its marginal value beyond A is only 10% of the initial value of A.
(There is also a theory that measles resets your immune system and wipes out acquired immunity, so avoiding measles saves even more lives. So then a vaccine would be much more valuable than surviving measles.)
I’ve done more research since I wrote this. I’m not sure if this is true “for almost every viral disease with a vaccine”, but it might be true for many or most of them.
The big ones I know of where it’s not true are smallpox and polio. Smallpox we don’t have great data on because its vaccine was invented so early (1700s), but there’s no reason to believe that its mortality rate was dropping significantly; in general big mortality rate drops didn’t occur until later.
Polio we do have good data on, and it’s clear that the epidemics continued, and indeed got worse, until the introduction of the vaccine in 1955. Polio is something of a special case in that it was not improved by sanitation.
Other diseases seem to have been ameliorated through sanitation, hygiene, and perhaps nutrition. I go into more detail on this in “Draining the swamp: How sanitation fought disease long before vaccines or antibiotics”.