Risk assessment for hospital-acquired diseases: a risk-theory approach

We introduce a new approach to hospital-acquired disease risk assessment from public health databases. In a spirit similar to actuarial risk theory, we define an adjustment coefficient that can quantify the risk associated with a hospital department, allowing comparisons of similar departments. The adjustment coefficient characterizes the tail of the distribution of the total patient length of stay in a department before the first disease event occurs. We show that this coefficient is the solution of a Lundberg-like equation, and we provide a nonparametric estimation procedure for this measure, based on a Cramér-Lundberg approximation for the tail of the distribution. Using simulations, we provide evidence of the robustness of the approximation to various individual risk models. In addition, we illustrate the relevance of this approach by evaluating the risk associated with a standard patient safety indicator in 20 hospitals of southeastern France.