A partial dependence factorial analysis to deal with selection bias in observational studis

This thesis presents a creative and practical approach to dealing with the problem of selection bias. Selection bias may be the most important vexing problem in program evaluation or in any line of research that attempts to assert causality. Some of the greatest minds in economics and statistics have scrutinized the problem of selection bias, with the resulting approaches – Rubin’s Potential Outcome Approach(Rosenbaum and Rubin,1983; Rubin, 1991,2001,2004) or Heckman’s Selection model (Heckman, 1979) – being widely accepted and used as the best fixes. These solutions to the bias that arises in particular from self selection are imperfect, and many researchers, when feasible, reserve their strongest causal inference for data from experimental rather than observational studies. The innovative aspect of this thesis is to propose a data transformation that allows measuring and testing in an automatic and multivariate way the presence of selection bias. The approach involves the construction of a multi-dimensional conditional space of the X matrix in which the bias associated with the treatment assignment has been eliminated. Specifically, we propose the use of a partial dependence analysis of the X-space as a tool for investigating the dependence relationship between a set of observable pre-treatment categorical covariates X and a treatment indicator variable T, in order to obtain a measure of bias according to their dependence structure. The measure of selection bias is then expressed in terms of inertia due to the dependence between X and T that has been eliminated. Given the measure of selection bias, we propose a multivariate test of imbalance in order to check if the detected bias is significant, by using the asymptotical distribution of inertia due to T (Estadella et al. 2005) , and by preserving the multivariate nature of data. Further, we propose the use of a clustering procedure as a tool to find groups of comparable units on which estimate local causal effects, and the use of the multivariate test of imbalance as a stopping rule in choosing the best cluster solution set. The method is non parametric, it does not call for modeling the data, based on some underlying theory or assumption about the selection process, but instead it calls for using the existing variability within the data and letting the data to speak. The idea of proposing this multivariate approach to measure selection bias and test balance comes from the consideration that in applied research all aspects of multivariate balance, not represented in the univariate variable- by-variable summaries, are ignored. The first part contains an introduction to evaluation methods as part of public and private decision process and a review of the literature of evaluation methods. The attention is focused on Rubin Potential Outcome Approach, matching methods, and briefly on Heckman’s Selection Model. The second part focuses on some resulting limitations of conventional methods, with particular attention to the problem of how testing in the correct way balancing. The third part contains the original contribution proposed , a simulation study that allows to check the performance of the method for a given dependence setting and an application to a real data set. Finally, we discuss, conclude and explain our future perspectives.

Automatic risk evaluation in elderly patients based on Autonomic Nervous System assessment

Dysfunction of Autonomic Nervous System (ANS) is a typical feature of chronic heart failure and other cardiovascular disease. As a simple non-invasive technology, heart rate variability (HRV) analysis provides reliable information on autonomic modulation of heart rate. The aim of this thesis was to research and develop automatic methods based on ANS assessment for evaluation of risk in cardiac patients. Several features selection and machine learning algorithms have been combined to achieve the goals. Automatic assessment of disease severity in Congestive Heart Failure (CHF) patients: a completely automatic method, based on long-term HRV was proposed in order to automatically assess the severity of CHF, achieving a sensitivity rate of 93% and a specificity rate of 64% in discriminating severe versus mild patients. Automatic identification of hypertensive patients at high risk of vascular events: a completely automatic system was proposed in order to identify hypertensive patients at higher risk to develop vascular events in the 12 months following the electrocardiographic recordings, achieving a sensitivity rate of 71% and a specificity rate of 86% in identifying high-risk subjects among hypertensive patients. Automatic identification of hypertensive patients with history of fall: it was explored whether an automatic identification of fallers among hypertensive patients based on HRV was feasible. The results obtained in this thesis could have implications both in clinical practice and in clinical research. The system has been designed and developed in order to be clinically feasible. Moreover, since 5-minute ECG recording is inexpensive, easy to assess, and non-invasive, future research will focus on the clinical applicability of the system as a screening tool in non-specialized ambulatories, in order to identify high-risk patients to be shortlisted for more complex investigations.