Health risk modelling by transforming a multi-dimensional unknown distribution to a multi-dimensional Gaussian

Abstract

The traditional approach of health risk modelling with multiple data sources proceeds via regression-based methods assuming a marginal distribution for the outcome variable. The data is collected for $N$ subjects over a $J$ time-period or from $J$ data sources. The response obtained from $i^{th}$ subject is $\vec{Y}_i=({Y}_{i1},\cdots, {Y}_{iJ})$. For $N$ subjects we obtain a $J$ dimensional joint distribution for the subjects. In this work we propose a novel approach of transforming any $J$ dimensional joint distribution to that of a $J$ dimensional Gaussian keeping the Shannon entropy constant. This is in stark contrast to the traditional approaches of assuming a marginal distribution for each $Y_{ij}$ by treating the $Y_{ij}'$s as independent observations. The said transformation is implemented in our computer package called ENTRA.