One crucial aspect of precision medicine is to allow physicians to recommend the most suitable treatment for their patients. This requires understanding the treatment heterogeneity from a patient-centric view, quantified by estimating the individualized treatment effect (ITE). With a large amount of genetics data and medical factors being collected, a complete picture of individuals’ characteristics is forming, which provides more opportunities to accurately estimate ITE. Recent development using machine learning methods within the counterfactual outcome framework shows excellent potential in analyzing such data. In this research, we propose to extend meta-learning approaches to estimate individualized treatment effects with survival outcomes. Two meta-learning algorithms are considered, T-learner and X-learner, each combined with three types of machine learning methods: random survival forest, Bayesian accelerated failure time model and survival neural network. We examine the performance of the proposed methods and provide practical guidelines for their application in randomized clinical trials (RCTs). Moreover, we propose to use the Boruta algorithm to identify risk factors that contribute to treatment heterogeneity based on ITE estimates. The finite sample performances of these methods are compared through extensive simulations under different randomization designs. The proposed approach is applied to a large RCT of eye disease, namely, age-related macular degeneration (AMD), to estimate the ITE on delaying time-to-AMD progression and to make individualized treatment recommendations.
Bayesian methods provide direct uncertainty quantification in functional data analysis applications without reliance on bootstrap techniques. A major tool in functional data applications is the functional principal component analysis which decomposes the data around a common mean function and identifies leading directions of variation. Bayesian functional principal components analysis (BFPCA) provides uncertainty quantification on the estimated functional model components via the posterior samples obtained. We propose central posterior envelopes (CPEs) for BFPCA based on functional depth as a descriptive visualization tool to summarize variation in the posterior samples of the estimated functional model components, contributing to uncertainty quantification in BFPCA. The proposed BFPCA relies on a latent factor model and targets model parameters within a hierarchical modeling framework using modified multiplicative gamma process shrinkage priors on the variance components. Functional depth provides a center-outward order to a sample of functions. We utilize modified band depth and modified volume depth for ordering of a sample of functions and surfaces, respectively, to derive at CPEs of the mean and eigenfunctions within the BFPCA framework. The proposed CPEs are showcased in extensive simulations. Finally, the proposed CPEs are applied to the analysis of a sample of power spectral densities from resting state electroencephalography where they lead to novel insights on diagnostic group differences among children diagnosed with autism spectrum disorder and their typically developing peers across age.