Consider for the moment a single measure of medical treatments, which we wish to relate to the change in disability. For concreteness, assume that the variable is the share of people in an area who receive a surgical procedure that has been shown to be effective in improving health for people with that condition. The treatment rate for area j in time period t is denoted Tj,t. We model the probability that person i will be in health state k using a multinomial logit formulation:
where Xi>t is a set of demographic variables, yk’s are the coefficient of interest. Our demographic variables include age/sex (five year age groups differentiated by gender); dummy variables for other cardiovascular disease hospitalizations, a modified Charlson index (i.e. without cardiovascular disease diagnoses) (Deyo, Cherkin et al. 1992) marital status at the beginning of the five year window (married; widowed; and divorced/separated); and race (white and nonwhite).
One issue that comes up in any estimation involving an equation like is the issue of causality. If treatments are not randomly assigned, estimates of у will be biased. We address this issue in several ways. The most important is to use area-level variation in treatments, rather than individual-level variation. Whether any individual receives a treatment is dependent on the physician’s perception of that patient’s underlying health. If the underlying severity of disease is relatively constant across areas and over time, however, variations in treatment at the area level will be good markers for exogenous changes in the use of medical care.
As is standard in the literature (O’Connor, Quinton et al. 1999; Fisher, Wennberg et al. 2003; Fisher, Wennberg et al. 2003; Stukel, Lucas et al. 2005), we group individuals into areas based on the Hospital Referral Region (HRR) they live in. HRRs are groups of zip codes where the bulk of patients go to the same set of hospitals and include at least one hospital with a tertiary cardiovascular or neurological surgical center. For example, the HRR for Chicago includes zip codes 6060160712; within this area, the vast majority of people who are hospitalized get admitted to a hospital in that region.
To facilitate interpretation of the results, we center all demographic and HRR-level covariates. This allows us to interpret the coefficients on the survey year dummy variables as the change in the log-odds of disability and death relative to being alive and non-disabled for the average person living in the average area across survey cohorts. We also begin our analyses with models that include only survey year dummy variables and demographic and health status covariates. We compare these models to models that include cardiovascular disease medical treatments to evaluate whether including treatment in the models changes the association between survey year and the likelihood of death and disability for the average patient.