A Hotel Model for Studying the Effect of State Policies on Nursing Home Hospitalizations
*Orna Intrator, Brown Univesrity and Providence VAMC 
Tony Lancaster, Brown University 

Keywords: Bayesian methods, random effects, fixed effects, joint modeling

Rates of hospitalizations from nursing homes have received much attention as they are costly, and have been suggested as important indicators of quality of care. As organizations, nursing homes must deliver a quality product measured, at times, by the rate of hospitalizations of their residents. Several studies have examined the effects of nursing home organizational structure and processes as well as the effect of states' policies on individual residents’ likelihood of hospitalization. The effect of state policies on the aggregate behavior of the nursing homes had not been studied.

The purpose of this paper is to present a model for testing the causal effect of bedhold policies and other state policies on nursing homes’ hospitalization practices addressing the issues of casemix adjustment, joint outcomes of death and hospitalization, and taking advantage of longitudinal observational data. By assuming that the unmeasured effects are fixed in time, we can exploit the time variation in bed-hold policies and other state policies to provide consistent estimates of the effect of such policies. We present a simple linear model with unmeasured facility effects together with measured time-varying covariates such as measures of casemix severity and time. We focus on nursing home beds and not residents and thus avoid the modeling issues involved in the impact of bed-hold and state policies on mortality, if such exists.

We study 17102 nursing homes in the 48 contiguous U.S. states in quarterly time periods during 2000-2004 with a total of 386335 quarterly facility observations. The outcome variable is the total number of hospitalizations from each of these nursing homes during each time period. A model with facility "(econometric) fixed effects" has over 17102 parameters. Modeling these parameters with uniform priors enables us to estimate the facility effects while being agnostic about any dependence between unmeasured facility effects and covariates, and to examine empirically whether they are, in fact, related. Such a connection invalidates a "random effects" approach which assumes independence of the facility effects and the measured covariates.

Findings suggests that indeed covariates are correlated with parameters, invalidating the random effects assumption and providing conflicting estimates for the effect of bedhold (positively or negatively related to hospitalizations). A method for estimating the large number of parameters is also presented.