The relationship between expenditure on health and fundamental measures of benefit is pretty weak in developed countries.
The figures for some countries may be misleading, as these graphs do not include private individuals expenditure, which in some places is quite considerable. 
The relationship between expenditure and benefit is even weaker for infant mortality.
Expenditure on health in the USA is an order of magnitude greater than any other country, but life expectancy is very poor.
There is also a wider debate to be had about the relationship between health and economic growth and progress.
If my doctor gives me good advice and I stay healthy the NHS has not contributed anything to GDP. If I become a chronic invalid the NHS expenditure is counted as part of the GDP and therefore a good thing. The idea that healthcare is a business and should therefore be developed has some profound contradictions.
Health is the outcome, not an output.
Thanks to Lucy Reynolds for the very useful graphs.