Finite-Sample Two-Group Composite Hypothesis Testing via Machine Learning

A general, flexible, and harmonious framework to construct interpretable functions in regression analysis

An interpretable model or method has several appealing features, such as reliability to adversarial examples, transparency of decision-making, and communication facilitator. However, interpretability is a subjective concept, and even its definition can be diverse. The same model may be deemed as interpretable by a study team, but regarded as a black-box algorithm by another squad. Simplicity, accuracy and generalizability are some additional important aspects of evaluating interpretability. In this work, we present a general, flexible and harmonious framework to construct interpretable functions in regression analysis with a focus on continuous outcomes. We formulate a functional skeleton in light of users' expectations of interpretability. A new measure based on Mallows's $C_p$-statistic is proposed for model selection to balance approximation, generalizability, and interpretability. We apply this approach to derive a sample size formula in adaptive clinical trial designs to demonstrate the general workflow, and to explain operating characteristics in a Bayesian Go/No-Go paradigm to show the potential advantages of using meaningful intermediate variables. Generalization to categorical outcomes is illustrated in an example of hypothesis testing based on Fisher's exact test. A real data analysis of NHANES (National Health and Nutrition Examination Survey) is conducted to investigate relationships between some important laboratory measurements. We also discuss some extensions of this method.

DL 101: Basic introduction to deep learning with its application in biomedical related fields

Deep learning is a subfield of machine learning used to learn representations of data by successive layers. Remarkable achievements and breakthroughs have been made in image classification, speech recognition, et cetera, but the full capability of deep learning is still under exploration. As statistical researchers and practitioners, we are especially interested in leveraging and advancing deep learning techniques to address important and impactive problems in biomedical and other related fields. In this article, we provide a basic introduction to Feedforward Neural Networks (FNN) along with some intuitive explanations behind its strong functional representation. Guidance is provided on how to choose quite a few hyperparameters in neural networks for a specific problem. We further discuss several more advanced frameworks in deep learning. Some successful applications of deep learning in biomedical fields are also demonstrated. With this beginner's guide, we hope that interested readers can include deep learning in their toolbox to tackle future real-world questions and challenges.