The goal of my research group is to develop statistical methods to estimate/learn causal and non-causal parameters of interest, based on potentially complex and high dimensional data from randomized clinical trials or observational longitudinal studies, or from cross-sectional (e.g., case-control sampling) studies. The model assumptions under which these methods are valid should be clearly formulated, so that they can be subject to scrutiny. The estimates should be accompanied by confidence regions for the true parameter values or other types of confidence measures (e.g., variability/reproducibility of clusters as measured by the bootstrap). The longitudinal data structures may involve high dimensional measurements such as whole genome profiles at various points in time; censoring and missingness of data due to a subject not responding well to treatment (or not feeling well); and changes of treatment at various points in time, based on variables related to the outcome of interest. Our methods are designed to rely on as few assumptions as possible on nuisance parameters so that they provide maximally objective statistical inference and testing procedures. To develop and refine these methods, we work with simulated and real data in collaboration with biologists, medical researchers, epidemiologists, and others.
