Optimal personalized treatment learning models with insurance applications

Leo Guelman

March 2, 2015

Montserrat Guillén

In many important settings, subjects can show significant heterogeneity in response to a stimulus or “treatment”. For instance, a treatment that works for the overall population might be highly inefiective, or even harmful, for a subgroup of subjects with specific characteristics. Similarly, a new treatment may not be better than an existing treatment in the overall population, but there is likely a subgroup of subjects who would benefit from it. The notion that “one size may not fit all” is becoming increasingly recognized in a wide variety of fields, ranging from economics to medicine. This has drawn significant attention to personalize the choice of treatment, so it is optimal for each individual. An optimal personalized treatment is the one that maximizes the probability of a desirable outcome. We call the task of learning the optimal personalized treatment personalized treatment learning (PTL). From the statistical learning perspective, building PTL models imposes important challenges, primarily because the optimal treatment is unknown on a given training data set. In this thesis, we formalize the PTL problem from a causal inference perspective and provide a comprehensive description of the existing methods to solve this problem. We contribute to the PTL literature by proposing two novel methods, namely uplift random forests and causal conditional inference forests. Our proposal outperforms the existing methods based on an extensive numerical simulation and real-world data. Next, we introduce the concept of PTL models to insurance marketing and pricing applications. In particular, we contribute to the Insurance literature in these areas by proposing PTL methods to optimize client retention and cross-selling in insurance from experimental data. We also illustrate an application of these methods to price-elasticity estimation and insurance economic price optimization in the context of observational data. In the insurance field, the selection of the optimal personalized treatment also requires consideration of the expected insurance losses of each individual policyholder within the portfolio. We contribute to the non-life insurance ratemaking literature by proposing a novel application of gradient boosting models to estimate insurance loss cost, with key important advantages over the conventional generalized linear model approach. A key problem facing research in this field, has been the lack of publicly available statistical software to estimate PTL models. We implement most of the existing methods for fitting these models, as well as our proposed ones, in a package named uplift, which is now released and freely available from the CRAN (Comprehensive R Archive Network) repository under the R statistical computing environment.