| When profiling healthcare providers' effects on multiple response variables, fitting a multivariate model, rather than a series of univariate models, can capture associations among responses at both the provider and patient levels. When responses are charges for healthcare services and sampled patients include non-users of service, charge variables are a mix of zeros and highly-skewed positive values that present a modeling challenge. For estimating covariate effects on charges for a single service, a frequently used approach is a two-part model that combines logistic or probit regression on any use of service and linear regression on the log of positive charges given use of service.; Here, we extend the two-part model to the case of charges for multiple services, using a log-linear model and a general multivariate lognormal model, and employ the resultant, multivariate two-part model as the likelihood component of a hierarchical model. The log linear likelihood is reparameterized so that covariate effects on any use of each service are marginal with respect to any use of other services. The general multivariate log-normal likelihood is structured so that variances of log of positive charges for each service are provider-specific but correlations between logs of positive charges for different services are constant across providers. A data augmentation step is included in the Gibbs sampler used for model fitting, to accommodate the fact that values of log of positive charges are undefined for unused services.; We use this hierarchical, multivariate two-part model to analyze effects of primary care physicians (PCPs) on their patients' annual charges for two services, primary care and specialty care, and find that PCPs that are more likely to see their patients at least once each year, provide more service to patients that they see, and are less likely to have their patients visit specialists. Additionally, we find that independent of these PCP effects, patients who visit their PCPs' at least once each year, are less likely to visit specialists. We also demonstrate an approach for incorporating prior information about the effects of patient morbidity on response variables, to improve the accuracy of provider profiles based on patient samples of limited size. |
