Communities and hospitals: social capital, community accountability, and service provision in U.S. community hospitals

Health Services Research, Oct, 2004 by Shoou-Yih D. Lee, Wendy L. Chen, Bryan J. Weiner

Descriptive statistics (means and standard deviations) and correlations of variables included in the analysis are available in appendix of the electronic version of the paper available at www.blackwell-synergy.com.

Analysis

A total of 959 counties were included in our analysis and the number of hospitals clustered in these counties ranged from 1 to 23. Hospitals residing within the same county boundaries serve a similar mix of patients and operate under similar socioeconomic and political conditions. Ignoring such intra-county correlation or the cluster effect may bias the estimation of regression coefficients. To estimate the cluster effect, we first ran the unconditional means model for both dependent variables (Singer 1998). For community accountability, the analysis showed a nonsignificant intracounty correlation and a small proportion of total variance (5.9 percent) attributable to the cluster effect, suggesting that OLS regression would yield reliable estimates of coefficients. For provision of community health services, the intracounty correlation was statistically significant and accounted for a substantial portion of total variance (25 percent). Thus, the two-level hierarchical linear modeling (HLM) is preferred over OLS (Bryk and Raudenbush 1992; Singer 1998).

Hierarchical linear modeling, or the mixed-effects model, can simultaneously estimate effects within clusters (i.e., to account for the county cluster effect) and test hypotheses about cross-level effects (i.e., to examine the relationship between community social capital and hospital provision of community-oriented services). To accomplish this, HLM uses submodels to express relationships among variables within a given level and specify how variables at one level are related to relations occurring at another. In this study, the level-1 model related hospital provision of community-oriented services to hospital level covariates (e.g., ownership, size). This procedure produced a unique intercept ([[beta].sub.0j] and level-1 coefficients ([[beta].sub.qj]). In the level-2 model, which captured the influence of county factors, the intercept (and coefficients, if the relationships between level- 1 covariates and the dependent variable vary across counties) from the level-1 model became the dependent variable, as a traction of county-level variables (e.g., social capital indices, market competition). A simplified representation of the two-level models is as follows:

Level 1: [Y.sub.ij] = [[beta].sub.0j] [SIGMA][[beta].sub.qj][X.sub.ij] [r.sub.ij]

Level 2: [[beta].sub.0j] = [[gamma].sub.00] [SIGMA][[gamma].sub.0s][W.sub.j] [[mu].sub.0j],

where [Y.sub.ij] is the provision of community-oriented services in hospital i in the county j; [[beta].sub.0j] is the intercept (i.e., the average provision of community-oriented services for community hospitals in county j after controlling for the effects of hospital-level covariates); [[beta].sub.qj] is the set of level-1 estimated regression coefficients; [r.sub.ij] is the unique contribution of each hospital i in the county j; [[gamma].sub.00] is the average provision of community-oriented services (or community accountability) for all community hospitals; [[gamma].sub.0s] was the set of regression coefficients for county-level covariates in county j; and [[mu].sub.0j] was the level-2 error term or the unique contribution of each county.