Toby, the question is of course what is the evidence that at least "a tenth of this increase is due to aid," since the correlation analyses look bad.
Nica, they did not publish the part of the Framington Heart Study relating diet to heart disease. And in the RAND experiment, the initially poor and sick did not do better on average with free medicine.
The remarkable observation that medical spending has zero net marginal effect is shocking, but not completely unprecedented.
According to Spiegel in "Too Much of a Good Thing: Choking on Aid Money in Africa", the Washington Center for Global Development calculated that it would require $3,521 of marginal development aid invested, per person, in order to increase per capita yearly income by $3.65 (one penny per day).
The Kenyan economist James Shikwati is even more pessimistic in "For God's Sake, Please Stop the Aid!": The net effect of Western aid to Africa is actively destructive (even when it isn't stolen to prop up corrupt regimes), a chaotic flux of money and goods that destroys local industry.
What does aid to Africa have in common with healthcare spending? Besides, of course, that it's heartbreaking to just say no -