Explaining a health care paradox

The paradox of a statistically weak linkage between physician density and measures of health based on outcome has recently received much attention because of its importance to health planning policy. It is demonstrated here that the linkage is stronger than indicated by previous studies if the statistical model is more carefully specified. A single case-type is chosen so that the impact of physician services is not filtered out by the aggregation process and a quantitative variable measuring case severity is derived. When statistical techniques are applied to correct for case-risk and for the inherent heteroscedasticity in observed mortality rates across states and time, the positive effect of physician density on health is shown to be statistically highly significant. Thus the apparently paradoxical findings in previous studies may be a result of failing to correct not only for differences in case severity but also for variations in sample errors. Also, even though the magnitude of physician impact is small compared to non-medical variables, an exploratory estimate of the impact of government programs focused on prevention suggests that present allocations between prevention and treatment may approximate optimality.The project upon which this paper is based was performed pursuant to Research Grant HS01036 from the Bureau of Health Services Research and Evaluation, U.S. Department of Health, Education and Welfare. The author wishes to acknowledge the advice and encouragement of Llad Phillips and H. E. Frech.