Two figures that say it all.

Death Rates (deaths per 1,000 population), New York City, c. 1800–2007. Source: NYC Department of Health & Mental Hygiene. Summary of Vital Statistics (2008). H/T to William Briggs for making me aware of this figure.

Infant Mortality Rate (deaths per 1,000 live births), New York City, 1898–2007. In 1898 IMR was estimated to be 140.9 Because of incomplete reporting of early neonatal deaths, this is almost certainly an underestimate. In 2007 IMR was 5.4 deaths per 1,000 live births. Source: NYC Department of Health & Mental Hygiene. Summary of Vital Statistics (2008)