Modeling General Practitioners’ Total Drug Costs through GAMLSS and Collective Risk Models

Monitoring general practitioner prescribing costs is an important topic in order to efficiently allocate National Health Insurance resources. Using generalized additive models for location, scale, and shape with random effects, we investigate how second-order variables, related to patients, contribute to estimating the frequency, severity, and hence the total amount of costs. The total cost of prescriptions associated with a general practitioner is then derived following a collective risk theory approach by aggregating cumulants of patient cost distributions. By means of the fourth-order Cornish-Fisher expansion series of quantiles of the aggregate cost distribution of general practitioners, we construct a confidence interval for each doctor, which is used to select a subset of doctors that should be monitored to identify potential inefficiencies. A case study is developed by using structured data regarding the number and cost of prescriptions of about 900,000 patients linked to corresponding general practitioners. The prescription costs considered are only those paid fully by the national health coverage.