In this project we consider the problem of building a quantile regression model to analyze risks in medical malpractice contest when the right predictors explaining the phenomenon have to be selected. As well known, quantile regression is an important method for implementing the impact of regressors on the whole conditional distribution of a response variable in particular on its tails. For this reason quantile regression is particular attractive when risk assessment is the main concern i.e. when the events are extreme. How to select the best predictors and estimate the right parameters in model building is critically important and here we will consider the penalized regression approach propose by Tibishirani in 1996 focusing the attention on the lasso and the elastic net framework. We will use those tools in the quantile regression contest building specific algorithms to implement the frequentist and the Bayesian statistical inference. Once the methodological part is implemented, we will use those tools in the medical malpractice risk assessment which is particular important for the risk managers of health care institutions involved in measuring frequencies, claims intensities of damages and amount of costs for them. Since several variables are involved in explain those phenomena it seems quite interesting to choose the right ones by using a penalizing quantile regression approach. This would be, to the best of our knowledge, the first quantile regression approach to face the medical malpractice issue.
The research project that we propose can be embedded in a wide recent literature related with building regression methods
in terms of simultaneous variable selection and coefficient estimation. The idea is pretty new and not related with the traditional stepwise variable selection or AIC methods to choose a preferable model. What we propose is to use the lasso and the elastic net methodology in the regular quantile regression framework and in the generalized quantile regression models in order to efficiently analyze risky phenomena. This approach is particularly new and can be realized by proposing new statistical algorithms both from a Bayesian and from a frequentist point of view. From a more applied point of view since the literature on medical malpractice is quite poor we propose to deep analyze the problem in a more statistical and mathematical point of view in order to provide a formal and structure to the problem. To do that we propose to build quantiles models which are never been used to face this problem.
A better understanding of such a phenomenon can have positive effects for hospitals and clinics in terms of quality assurance, service improvement, cost reduction and new ways for risk management procedures. At the same time, such understanding is essential for insurance companies to be able to reliably price their policies, in order to implement a more efficient risk management approach to losses. The data that we will analyze are collected from databases of insurers, brokers and Italian public and private health care organizations.
For sure this would be, to the best of our knowledge, the first quantile regression approach to analyze the medical malpractice issue.