General Additive Models (GAM)
GAM models with P-splines. The efficient estimation methods and the algorithms that are developed, will be implemented in a wide variety of models with covariates, particularly those where the computational aspect determines the flexibility of the models used (models involving interaction between covariates).
ROC curves with covariates
Generally speaking, the ROC curves (as well as the selection of optimal cutoff points and the optimal combination of markers) obtained by the methods are flexible. They will be useful in any clinical and epidemiological speciality where they are required in diagnostic studies, prognoses and/or classification through diagnostic tests. The flexible inclusion of covariates in calculating the Index Youden can improve the selection and comparison of biomarkers. Especially in Radiology, it is expected that the use of information from the GAM analysis, in combination with the ROC curves, allows to obtain a greater reduction in the number of false detections produced by the developed CAD system. This breakthrough is a further step in the automation of mammography screening for cancer, and telemammography systems, which allow its exploitation, given the implementation of these programs and the large volume of images to handle.
The developments in this field can be used in a variety of biomedical applications. For multistate models, especially those characterized by the study of individual progression of various stages of the disease. For example, diabetic nephropathy, cirrhosis of the liver, multi-state models for the progression of HIV, survival after a transplant, breast cancer, etc. The developments that fall within time-dependent ROC curves have direct application in all studies whose purpose is to classify individuals in the Survival context. In this regard, we will continue our collaboration with the Cardiology Service of the University Hospital Complex of Santiago.
Smooth spatio-temporal models (STAR models)
Flexible spatio-temporal regression models are applicable in many areas. The developed methodology will resolve important issues such as the comparison to models with interactions and the analysis of data with seasonal effects. In the area of the Environment, the use of these models will allow the study of the evolution of temperatures, or the spatial and temporal trends in processes of air and river pollution. In the field of medical imaging, particularly in the area of "Brain Imaging" these models allow, for instance, the identification of temporal and positional signals corresponding to cognitive responses to different stimuli.
In the field of medicine, quantile regression is essential in specialties like pediatrics, for the calculation of anthropometric variables percentiles, adjusted for age and sex. It is also of interest in any clinical laboratory, for adjusted calculation of "normal clinical" variables of different biochemical, hormones (Ex., TSH), etc. In the field of Marine Biology, its use is especially important in the study of the life cycle and growth of different species.
Flexible models for counting data
In the field of epidemiology and demography, this type of data often appear. Flexible models and at the same time computationally efficient allow pattern detection due to environmental causes, or socio-economic analysis of disease maps, and allow simultaneous analysis of mortality tables for different causes of illness or in different locations, which will allow to make comparisons which until now were not possible to obtain.