Regression by composition

Our research group has recently proposed regression by composition, a flexible toolkit for building and understanding statistical models. Regression by composition always takes place on the original scale of the data, so offers enormous potential for clinical insight and better decision-making. We seek to enrich the mathematical theory of regression by composition, to release open-source software that expands its applicability, and to evaluate its effectiveness in biomedical science. We will... ...engage specialists in clinical trials, epidemiology, biostatistics and statistical computing to ensure regression by composition is widely applicable in biomedical research, acceptable to its scientists, and accessible to its analysts. More broadly, regression by composition affords an opportunity for reimagining teaching and training in medical statistics. ...assemble a computational engine for fitting regressions by composition. A major objective is to provide general-purpose routines suitable for specialised or user-supplied model components, while taking advantage of exact mathematical results where these are known. ...design flexible longitudinal regressions by composition that are compatible with structural nested models, and congenial for instrumental variable regression or Mendelian randomisation. Because interventions can influence health trajectories in surprising and subtle ways, we will guide scientists towards transportable findings, combining empirical evidence with careful application of mechanistic, first-principles reasoning. ...employ assumption-lean regressions by composition as tools for explainable artificial intelligence. Regression by composition is general enough to express high-dimensional machine learning models; with the addition of tuning parameters controlling regularisation, we will give users the ability to select from a spectrum of accurate and easy-to-understand models for classification, prediction or control.