An essential ingredient in the evaluation of policies concerning health services is knowledge of the impact of health services and other factors on the health of the population. One method of obtaining this information is from the regression analysis of international cross-section data on mortality rates, health service provision, income levels, consumption patterns, and other variables hypothesised to affect population health. The investigation of the determinants of population health is in many ways akin to the estimation of production functions which describe the relationship between the output of goods or services and the mix of inputs used in their production. The purpose of our paper is to use this analogy to discuss, and provide examples of, the problems which arise with the statistical investigation of mortality rates. Issues raised include simultaneous equation bias, multicollinearity, selection of explanatory variables, omitted variable bias, definition and measurement of variables, functional forms, lagged relationships and temporal stability. These problems are illustrated by replication and re-analysis, using new data, of the well known study by Cochrane, St Leger and Moore.