Quality of care is difficult to measure. Even if you had a perfect measure of quality in terms of health outcomes, risk adjustment is imperfect. For instance, academic medical centers are often assumed to have high quality, but actual outcomes observed in the data may not be that good if they also receive the sickest, most severely ill patients. If some measures of illness severity are not observable, the quality of these centers may be underestimated.
A paper by Gewenke et al. (2003) addresses this selection bias issue using Bayesian approach. The paper uses data on hospital admissions for pneumonia in Los Angeles and measures hospital quality by whether the patient died within 10-days of the hospital admission. Hospital choice is modeled using multinomial probit model, where distance from the hospital is used to predict hospital choice. Mortality is modelled as a binary probit model which depends on hospital choice, individual characteristics and unobserved severity included in the error term of the multinomial probit specification. The authors use a Bayesian approach, leveraging a hierarchical priors to inform a Markov chain Monte Carlo (MCMC) simulation. The hierarchical priors assume that hospital quality is similar ex-ante (i.e., before going to the data). A Gibbs sampling algorithm is used to estimate all parameters and latent variables.
Using this approach, the authors find that:
…the smallest and largest hospitals to be of the highest quality. There is strong evidence of dependence between the unobserved severity of illness and the assignment of patients to hospitals, whereby patients with a high unobserved severity of illness are disproportionately admitted to high quality hospitals. Consequently a conventional probit model leads to inferences about quality that are markedly different from those in this study’s selection model.
Do read the whole paper here.
- Geweke J, Gowrisankaran G, Town RJ. Bayesian inference for hospital quality in a selection model. Econometrica. 2003 Jul;71(4):1215-38.