Residual Partial Least Squares Learning: Brain Cortical Thickness Simultaneously Predicts Eight Non-pairwise-correlated Behavioural and Disease Outcomes in Alzheimer's Disease.

Alzheimer's Disease (AD) is the leading cause of dementia. It results in cortical thickness changes and is associated with a decline in cognition and behaviour. Such decline affects multiple important day-to-day functions, including memory, language, orientation, judgment and problem-solving. Recent research has made important progress in identifying brain regions associated with single outcomes, such as individual AD status and general cognitive decline. The complex projection from multiple brain areas to multiple AD outcomes, however, remains poorly understood. This makes the assessment and especially the prediction of multiple AD outcomes - each of which may unveil an integral yet different aspect of the disease - challenging, particularly when some are not strongly correlated. Here, uniting residual learning, partial least squares (PLS), and predictive modelling, we develop an explainable, generalisable, and reproducible method called the Residual Partial Least Squares Learning (the re-PLS Learning) to (1) chart the pathways between large-scale multivariate brain cortical thickness data (inputs) and multivariate disease and behaviour data (outcomes); (2) simultaneously predict multiple, non-pairwise-correlated outcomes; (3) control for confounding variables (e.g., age and gender) affecting both inputs and outcomes and the pathways in-between; (4) perform longitudinal AD disease status classification and disease severity prediction. We evaluate the performance of the proposed method against a variety of alternatives on data from AD patients, subjects with mild cognitive impairment (MCI), and cognitively normal individuals (n=1,196) from the Alzheimer's Disease Neuroimaging Initiative (ADNI). Our results unveil pockets of brain areas in the temporal, frontal, sensorimotor, and cingulate areas whose cortical thickness may be respectively associated with declines in different cognitive and behavioural subdomains in AD. Finally, we characterise re-PLS' geometric interpretation and mathematical support for delivering meaningful neurobiological insights and provide an open software package (re-PLS) available at https://github.com/thanhvd18/rePLS.

The roles, challenges, and merits of the p value.

Since the 18th century, the p value has been an important part of hypothesis-based scientific investigation. As statistical and data science engines accelerate, questions emerge: to what extent are scientific discoveries based on p values reliable and reproducible? Should one adjust the significance level or find alternatives for the p value? Inspired by these questions and everlasting attempts to address them, here, we provide a systematic examination of the p value from its roles and merits to its misuses and misinterpretations. For the latter, we summarize modest recommendations to handle them. In parallel, we present the Bayesian alternatives for seeking evidence and discuss the pooling of p values from multiple studies and datasets. Overall, we argue that the p value and hypothesis testing form a useful probabilistic decision-making mechanism, facilitating causal inference, feature selection, and predictive modeling, but that the interpretation of the p value must be contextual, considering the scientific question, experimental design, and statistical principles.