A short answer is, not very. In contrast to economic growth, where the free market is commonly viewed as a prime mover, mortality in the last two centuries has not been greatly helped by market forces. The classic sources of market failure – information failures, externalities, public goods, principal-agent, and free rider problems – have been pervasive. Nor has economic growth itself been behind the worldwide improvement in life expectancy. In the primitive state of nineteenth century health knowledge, the immense rise in urbanisation engendered by economic growth largely vitiated any positive level-of-living effects by increasing exposure to disease. Instead, public policy initiatives, based on new knowledge of disease and new institutions, have been essential to the improvement of life expectancy, both in urban areas and nationwide.
Sweepings from butchers' stalls, dung, guts, and blood, Drowned puppies, stinking sprats, all drenched in mud, Dead cats, and turnip tops, come tumbling down the flood. – Jonathan Swift, A Description of a City Shower, 1710