Essays in Applied Insurance Economics

The papers included in this thesis deal with a few aspects of insurance economics that have seldom been dealt with in the applied literature. In the first paper I apply for the first time the tools of the economics of crime to study the determinants of frauds, using data on Italian provinces. The contributions to the literature are manifold: -The price of insuring has a positive correlation with the propensity to defraud -Social norms constraint fraudulent behavior, but their strength is curtailed in economic downturns -I apply a simple extension of the Random Coefficient model, which allows for the presence of time invariant covariates and asymmetries in the impact of the regressors. The second paper assesses how the evolution of macro prudential regulation of insurance companies has been reflected in their equity price. I employ a standard event study methodology, deriving the definition of the “control” and “treatment” groups from what is implied by the regulatory framework. The main results are: -Markets care about the evolution of the legislation. Their perception has shifted from a first positive assessment of a possible implicit “too big to fail” subsidy to a more negative one related to its cost in terms of stricter capital requirement -The size of this phenomenon is positively related to leverage, size and on the geographical location of the insurance companies The third paper introduces a novel methodology to forecast non-life insurance premiums and profitability as function of macroeconomic variables, using the simultaneous equation framework traditionally employed macroeconometric models and a simple theoretical model of insurance pricing to derive a long term relationship between premiums, claims expenses and short term rates. The model is shown to provide a better forecast of premiums and profitability compared with the single equation specifications commonly used in applied analysis.

Prediction Nomogram for 68Ga-PSMA-11 PET/CT in different clinical settings of PSA failure after radical treatment for Prostate Cancer

Objective The objective of this study was to develop a clinical nomogram to predict gallium-68 prostate-specific membrane antigen positron emission tomography/computed tomography (68Ga-PSMA-11-PET/CT) positivity in different clinical settings of PSA failure. Materials and methods Seven hundred three (n = 703) prostate cancer (PCa) patients with confirmed PSA failure after radical therapy were enrolled. Patients were stratified according to different clinical settings (first-time biochemical recurrence [BCR]: group 1; BCR after salvage therapy: group 2; biochemical persistence after radical prostatectomy [BCP]: group 3; advanced stage PCa before second-line systemic therapies: group 4). First, we assessed 68Ga-PSMA-11-PET/CT positivity rate. Second, multivariable logistic regression analyses were used to determine predictors of positive scan. Third, regression-based coefficients were used to develop a nomogram predicting positive 68Ga-PSMA-11-PET/CT result and 200 bootstrap resamples were used for internal validation. Fourth, receiver operating characteristic (ROC) analysis was used to identify the most informative nomogram’s derived cut-off. Decision curve analysis (DCA) was implemented to quantify nomogram’s clinical benefit. Results 68Ga-PSMA-11-PET/CT overall positivity rate was 51.2%, while it was 40.3% in group 1, 54% in group 2, 60.5% in group 3, and 86.9% in group 4 (p < 0.001). At multivariable analyses, ISUP grade, PSA, PSA doubling time, and clinical setting were independent predictors of a positive scan (all p ≤ 0.04). A nomogram based on covariates included in the multivariate model demonstrated a bootstrap-corrected accuracy of 82%. The nomogram-derived best cut-off value was 40%. In DCA, the nomogram revealed clinical net benefit of > 10%. Conclusions This novel nomogram proved its good accuracy in predicting a positive scan, with values ≥ 40% providing the most informative cut-off in counselling patients to 68Ga-PSMA-11-PET/CT. This tool might be important as a guide to clinicians in the best use of PSMA-based PET imaging.

On the effect of confounding in linear regression models: an approach based on the theory of quadratic forms

The main topic of this thesis is confounding in linear regression models. It arises when a relationship between an observed process, the covariate, and an outcome process, the response, is influenced by an unmeasured process, the confounder, associated with both. Consequently, the estimators for the regression coefficients of the measured covariates might be severely biased, less efficient and characterized by misleading interpretations. Confounding is an issue when the primary target of the work is the estimation of the regression parameters. The central point of the dissertation is the evaluation of the sampling properties of parameter estimators. This work aims to extend the spatial confounding framework to general structured settings and to understand the behaviour of confounding as a function of the data generating process structure parameters in several scenarios focusing on the joint covariate-confounder structure. In line with the spatial statistics literature, our purpose is to quantify the sampling properties of the regression coefficient estimators and, in turn, to identify the most prominent quantities depending on the generative mechanism impacting confounding. Once the sampling properties of the estimator conditionally on the covariate process are derived as ratios of dependent quadratic forms in Gaussian random variables, we provide an analytic expression of the marginal sampling properties of the estimator using Carlson’s R function. Additionally, we propose a representative quantity for the magnitude of confounding as a proxy of the bias, its first-order Laplace approximation. To conclude, we work under several frameworks considering spatial and temporal data with specific assumptions regarding the covariance and cross-covariance functions used to generate the processes involved. This study allows us to claim that the variability of the confounder-covariate interaction and of the covariate plays the most relevant role in determining the principal marker of the magnitude of confounding.

Seemingly unrelated linear regression for contaminated data based on Gaussian mixtures

In this thesis, new classes of models for multivariate linear regression defined by finite mixtures of seemingly unrelated contaminated normal regression models and seemingly unrelated contaminated normal cluster-weighted models are illustrated. The main difference between such families is that the covariates are treated as fixed in the former class of models and as random in the latter. Thus, in cluster-weighted models the assignment of the data points to the unknown groups of observations depends also by the covariates. These classes provide an extension to mixture-based regression analysis for modelling multivariate and correlated responses in the presence of mild outliers that allows to specify a different vector of regressors for the prediction of each response. Expectation-conditional maximisation algorithms for the calculation of the maximum likelihood estimate of the model parameters have been derived. As the number of free parameters incresases quadratically with the number of responses and the covariates, analyses based on the proposed models can become unfeasible in practical applications. These problems have been overcome by introducing constraints on the elements of the covariance matrices according to an approach based on the eigen-decomposition of the covariance matrices. The performances of the new models have been studied by simulations and using real datasets in comparison with other models. In order to gain additional flexibility, mixtures of seemingly unrelated contaminated normal regressions models have also been specified so as to allow mixing proportions to be expressed as functions of concomitant covariates. An illustration of the new models with concomitant variables and a study on housing tension in the municipalities of the Emilia-Romagna region based on different types of multivariate linear regression models have been performed.

Economic preferences in the health setting. Three case studies concerning the needs of breast cancer patients, pain management in oncology and extreme end-of-life decisions

The thesis describes three studies concerning the role of the Economic Preference set investigated in the Global Preference Survey (GPS) in the following cases: 1) the needs of women with breast cancer; 2) pain undertreament in oncology; 3) legal status of euthanasia and assisted suicide. The analyses, based on regression techniques, were always conducted on the basis of aggregate data and revealed in all cases a possible role of the Economic Preferences studied, also resisting the concomitant effect of the other covariates that were considered from time to time. Regarding individual studies, the related conclusion are: 1) Economic Preferences appear to play a role in influencing the needs of women with breast cancer, albeit of non-trivial interpretation, statistically "resisting" the concomitant effect of the other independent variables considered. However, these results should be considered preliminary and need further confirmation, possibly with prospective studies conducted at the level of the individual; 2) the results show a good degree of internal consistency with regard to pro-social GPS scores, since they are all found to be non-statistically significant and united, albeit only weakly in trend, by a negative correlation with the % of pain undertreated patients. Sharper, at least statistically, is the role of Patience and Willingness to Take Risk, although of more complex empirical interpretation. 3) the results seem to indicate an obvious role of Economic Preferences, however difficult to interpret empirically. Less evidence, at least on the inferential level, emerged, however, regarding variables that, based on common sense, should play an even more obvious role than Economic Preferences in orienting attitudes toward euthanasia and assisted suicide, namely Healthcare System, Legal Origin, and Kinship Tightness; striking, in particular, is the inability to prove a role for the dominant religious orientation even with a simple bivariate analysis.

Developing a radiomic based machine learning model to identify patients with resected non-small-cell lung cancer at high risk of relapse

Background There is a wide variation of recurrence risk of Non-small-cell lung cancer (NSCLC) within the same Tumor Node Metastasis (TNM) stage, suggesting that other parameters are involved in determining this probability. Radiomics allows extraction of quantitative information from images that can be used for clinical purposes. The primary objective of this study is to develop a radiomic prognostic model that predicts a 3 year disease free-survival (DFS) of resected Early Stage (ES) NSCLC patients. Material and Methods 56 pre-surgery non contrast Computed Tomography (CT) scans were retrieved from the PACS of our institution and anonymized. Then they were automatically segmented with an open access deep learning pipeline and reviewed by an experienced radiologist to obtain 3D masks of the NSCLC. Images and masks underwent to resampling normalization and discretization. From the masks hundreds Radiomic Features (RF) were extracted using Py-Radiomics. Hence, RF were reduced to select the most representative features. The remaining RF were used in combination with Clinical parameters to build a DFS prediction model using Leave-one-out cross-validation (LOOCV) with Random Forest. Results and Conclusion A poor agreement between the radiologist and the automatic segmentation algorithm (DICE score of 0.37) was found. Therefore, another experienced radiologist manually segmented the lesions and only stable and reproducible RF were kept. 50 RF demonstrated a high correlation with the DFS but only one was confirmed when clinicopathological covariates were added: Busyness a Neighbouring Gray Tone Difference Matrix (HR 9.610). 16 clinical variables (which comprised TNM) were used to build the LOOCV model demonstrating a higher Area Under the Curve (AUC) when RF were included in the analysis (0.67 vs 0.60) but the difference was not statistically significant (p=0,5147).