Contributions to Evolutionary Dynamics and Causal Inference

Abstract

In this dissertation, we investigate topics in two different quantitative disciplines, both of which have profound impact in biomedical sciences. The first area is evolutionary dynamical systems to model biological systems; the second area is causal inference, with the primary goal of drawing causal conclusions from experimental and observational studies. In Chapter 1, we investigate the dynamical behavior of reprogramming of somatic cells to induced pluripotent stem cells (iPSCs). In order to define a unified framework to study and compare the dynamics of reprogramming under different conditions, we developed an in silico analysis platform based on evolutionary modeling. Our approach takes into account the variability in experimental results stemming from probabilistic growth and death of cells and potentially heterogeneous reprogramming rates. We found that reprogramming driven by the Yamanaka factors alone is a more heterogeneous process possibly due to cell-specific reprogramming rates, which can be homogenized by the addition of additional factors. In Chapter 2, we study the problem of data-driven confounder selection in causal inference. The recently proposed Collaborative Targeted Minimum Loss Estimation (CTMLE) provides a framework of constructing doubly-robust estimators by selecting appropriate covariates into the propensity score model. We focus on the asymptotic (large-sample) theory of CTMLE, together with some other alternatives such as Focused Information Criterion (FIC) and the Lepski’s method (or equivalently, hypothesis testing). The algebraic connections among these selection statistics are presented. In Chapter 3, we investigate some practical issues in the application of higher-order influence functions (HOIFs) in the problem semi-/non-parametric functional estimation, which is closely connected to literature of estimating causal estimand of interest with modern machine learning technique. We discuss several ideas of stabilizing the finite-sample performance of HOIF-based estimators and demonstrate the superiority of these modifications to the original construction of HOIF-based estimator in simulation studies.