"For the average person enrolled in the experiment, we observed two significant positive effects of free care relative to cost-sharing: corrected far vision … was better by 0.1 Snellen lines (p = 0.001) and diagnostic blood pressure was lower by 0.8mm HG (p = 0.03). For the remaining measures … any true differences would be clinically and socially negligible. For the five general health measures, we could detect no significant positive effect of free care for persons who differed by income .. and by initial health status. … Among participants who were judged to be at elevated risk with respect to smoking habits, cholesterol levels, and weight, free care had no detectable effect" http://www.rand.org/pubs/reports/R3055.html

"Average baseline health status of cohort members was similar across regions of differing spending levels, but patients in higher-spending regions received approximately 60% more care." http://annals.org/article.aspx?articleid=716066


Not from a study, but from a blog post by an economist summarizing and discussing these studies:
"It found that variations across the 50 U.S. states of 1960 age-sex-adjusted death rates were significantly predicted by variations in income, education, fractions of white collar and female workers, and the existence of a local medical school, but not by variations in medical spending, urbanization, and alcohol and cigarette consumption.
Later studies using robust controls to compare similar regions tend to give similar results. For example, a Byrne, Pietz, Woodard, & Petersen Health Economics 2007 study found no significant mortality effects of funding variations across 22 U.S. Veterans Affairs regions over six years. And a Fisher, et al. Annals of Internal Medicine 2003 study of 18,000 patients confirmed a Fisher et. al. Health Services Research 2000 study, and a related Skinner and Wennberg 1998 study, which together used the largest dataset I know of: five million Medicare patients in 1989 and 1990 across 3,400 U.S. hospital regions.
Regions that paid more to have patients stay in intensive care rooms for one more day during their last six months of life were estimated, at a 2% significance level, to make patients live roughly forty fewer days, even after controlling for: individual age, gender, and race; zipcode urbanity, education, poverty, income, disability, and marital and employment status; and hospital-area illness rates."

"In the aggregate, variations in medical spending usually show no statistically significant medical effect on health. (At least they do not in studies with enough good controls.) It has long been nearly a consensus among those who have reviewed the relevant studies that differences in aggregate medical spending show little relation to differences in health, compared to other factors like exercise or diet."
http://www.cato-unbound.org/2007/09/10/robin-hanson/cut-medicine-half