Contributions on metric spaces with applications in personalized medicine

Esta tesis tiene como objetivo proponer nuevas representaciones distribucionales y métodos estadísticos en espacios métricos para modelar de forma eficaz los datos procedentes de la monitorización continua de los pacientes durante las actividades propias de su vida diaria. Proponemos nuevas pruebas de hipótesis para datos emparejados, modelos de regresión, algoritmos de cuantificación de la incertidumbre, pruebas de independencia estadística y algoritmos de análisis de conglomerados para las nuevas representaciones distribucionales y otros objetos estadísticos complejos. Los diferentes resultados recogidos a lo largo de la tesis muestran las ventajas en términos de predicción, interpretabilidad y capacidad de modelización de las nuevas propuestas frente a los metodos existentes

Fatigue Induced Changes in Muscle Strength and Gait Following Two Different Intensity, Energy Expenditure Matched Runs

Purpose: To investigate changes in hip and knee strength, kinematics, and running variability following two energy expenditure matched training runs; a medium intensity continuous run (MICR) and a high intensity interval training session (HIIT). Methods: Twenty (10F, 10M) healthy master class runners were recruited. Each participant completed the HIIT consisting of six repetitions of 800 meters with a 1:1 work: rest ratio. The MICR duration was set to match energy expenditure of the HIIT session. Hip and knee muscular strength were examined pre and post both HIIT and MICR. Kinematics and running variability for hip and knee, along with spatiotemporal parameters were assessed at start and end of each run-type. Changes in variables were examined using both 2 x 2 ANOVAs with repeated measures and on an individual level when the change in a variable exceeded the minimum detectable change (MDC). Results: All strength measures exhibited significant reductions at the hip and knee (P < .05) with time for both run-types; 12% following HIIT, 10.6% post MICR. Hip frontal plane kinematics increased post run for both maximum angle (P < 0.001) and range of motion (P = 0.003). Runners exhibited increased running variability for nearly all variables, with the HIIT having a greater effect. Individual assessment revealed that not all runners were effected post run and that following HIIT more runners had reduced muscular strength, altered kinematics and increased running variability. Conclusion: Runners exhibited fatigue induced changes following typical training runs, which could potentially increase risk of injury development. Group and individual assessment revealed different findings where the use of MDC is recommended over that of P values

Causal survival embeddings: non-parametric counterfactual inference under censoring

Model-free time-to-event regression under confounding presents challenges due to biases introduced by causal and censoring sampling mechanisms. This phenomenology poses problems for classical non-parametric estimators like Beran's or the k-nearest neighbours algorithm. In this study, we propose a natural framework that leverages the structure of reproducing kernel Hilbert spaces (RKHS) and, specifically, the concept of kernel mean embedding to address these limitations. Our framework has the potential to enable statistical counterfactual modeling, including counterfactual prediction and hypothesis testing, under right-censoring schemes. Through simulations and an application to the SPRINT trial, we demonstrate the practical effectiveness of our method, yielding coherent results when compared to parallel analyses in existing literature. We also provide a theoretical analysis of our estimator through an RKHS-valued empirical process. Our approach offers a novel tool for performing counterfactual survival estimation in observational studies with incomplete information. It can also be complemented by state-of-the-art algorithms based on semi-parametric and parametric models

Semiparametric functional mixture cure model for survival data

We develop a functional proportional hazards mixture cure (FPHMC) model with scalar and functional covariates measured at the baseline. The mixture cure model, useful in studying populations with a cure fraction of a particular event of interest is extended to functional data. We employ the EM algorithm and develop a semiparametric penalized spline-based approach to estimate the dynamic functional coefficients of the incidence and the latency part. The proposed method is computationally efficient and simultaneously incorporates smoothness in the estimated functional coefficients via roughness penalty. Simulation studies illustrate a satisfactory performance of the proposed method in accurately estimating the model parameters and the baseline survival function. Finally, the clinical potential of the model is demonstrated in two real data examples that incorporate rich high-dimensional biomedical signals as functional covariates measured at the baseline and constitute novel domains to apply cure survival models in contemporary medical situations. In particular, we analyze i) minute-by-minute physical activity data from the National Health and Nutrition Examination Survey (NHANES) 2011-2014 to study the association between diurnal patterns of physical activity at baseline and 9-year mortality while adjusting for other biological factors; ii) the impact of daily functional measures of disease severity collected in the intensive care unit on post ICU recovery and mortality event. Software implementation and illustration of the proposed estimation method is provided in R

Predicting distributional profiles of physical activity in the NHANES database using a Partially Linear Single-Index Fr\'echet Regression model

Object-oriented data analysis is a fascinating and developing field in modern statistical science with the potential to make significant and valuable contributions to biomedical applications. This statistical framework allows for the formalization of new methods to analyze complex data objects that capture more information than traditional clinical biomarkers. The paper applies the object-oriented framework to analyzing and predicting physical activity measured by accelerometers. As opposed to traditional summary metrics, we utilize a recently proposed representation of physical activity data as a distributional object, providing a more sophisticated and complete profile of individual energetic expenditure in all ranges of monitoring intensity. For the purpose of predicting these distributional objects, we propose a novel hybrid Frechet regression model and apply it to US population accelerometer data from NHANES 2011-2014. The semi-parametric character of the new model allows us to introduce non-linear effects for essential variables, such as age, that are known from a biological point of view to have nuanced effects on physical activity. At the same time, the inclusion of a global for linear term retains the advantage of interpretability for other variables, particularly categorical covariates such as ethnicity and sex. The results obtained in our analysis are helpful from a public health perspective and may lead to new strategies for optimizing physical activity interventions in specific American subpopulations