Predicting correlated outcomes from molecular data

Abstract

Motivation: Multivariate (multi-target) regression has the potential to outperform univariate (single-target) regression at predicting correlated outcomes, which frequently occur in biomedical and clinical research. Here we implement multivariate lasso and ridge regression using stacked generalization.

Results: Our flexible approach leads to predictive and interpretable models in high-dimensional settings, with a single estimate for each input-output effect. In the simulation, we compare the predictive performance of several state-of-the-art methods for multivariate regression. In the application, we use clinical and genomic data to predict multiple motor and non-motor symptoms in Parkinson's disease patients. We conclude that stacked multivariate regression, with our adaptations, is a competitive method for predicting correlated outcomes.

Availability and implementation: The R package joinet is available on GitHub (https://github.com/rauschenberger/joinet) and cran (https://cran.r-project.org/package=joinet).

Supplementary information: Supplementary data are available at Bioinformatics online.

Fig. 1.

To estimate the effect of input j on the linear predictor for output k, we first estimate the effects of input j on the linear predictor for each output (base layer) and then estimate the effects of all cross-validated linear predictors on the linear predictor for output k (meta layer)

Fig. 2.

Spearman’s rank correlation coefficients. Left: correlation between outputs from the same tool at different visits (averaged across combinations of visits). Right: correlation between outputs from different tools at the same visit (averaged across visits)

Fig. 3.

Percentage change in cross-validated mean squared error from univariate to multivariate regression. Left: we support the prediction for one tool at one visit with the same tool at other visits. Right: we support the prediction for one tool at one visit (row) with another tool at the same visit (column). All values are averaged across visits (1/2/3), regularization methods (lasso/ridge) and data types (clinical/omics/both), i.e. 18 settings

Fig. 4.

Percentage change in cross-validated mean squared error from prediction by the mean to univariate (first row) and multivariate regression (second row: support from other visits; third row: support from other tool). All values are averaged across visits (1/2/3), regularization methods (lasso/ridge), data types (clinical/omics/both) and coaching variables (third row only), i.e. 18 settings (first and second row) or 18 × 7 = 126 settings (third row)