In the United States the number of health systems that own practices or hospitals have increased in number and complexity leading to interest in assessing the relationship between health organization factors and health outcomes. However, the existence of multiple types of organizations combined with the nesting of some hospitals and practices within health systems and the nesting of some health systems within larger health systems generates numerous analytic objectives and complicates the construction of optimal survey designs. An objective function that explicitly weighs all objectives is theoretically appealing but becomes unwieldy and increasingly ad hoc as the number of objectives increases. To overcome this problem, we develop an alternative approach based on constraining the sampling design to satisfy desired statistical properties. For example, to support evaluations of the comparative importance of factors measured in different surveys on health system performance, a constraint that requires at least one organization of each type (corporate owner, hospital, practice) to be sampled whenever any component of a system is sampled may be enforced. Multiple such constraints define a nonlinear system of equations that "couples" the survey sampling designs whose solution yields the sample inclusion probabilities for each organization in each survey. A Monte Carlo algorithm is developed to solve the simultaneous system of equations to determine the sampling probabilities and extract the samples for each survey. We illustrate the new sampling methodology by developing the constraints and solving the ensuing systems of equations to obtain the sampling design for the National Surveys of United States Health Care Systems, Hospitals and Practices. We illustrate the virtues of "coupled sampling" by comparing the proportion of eligible systems for whom the corporate owner and both a hospital and a practice that are expected to be sampled to that expected under alternative sampling designs. Comparative and descriptive analyses that illustrate features of the sampling design are also presented.
Keywords: Coupled sampling; Diminishing allocation; Heuristics; Monte Carlo algorithm; Nonlinear constraints; Survey design.