  Clinical research often focuses on complex traits in which many variables
play a role in mechanisms driving, or curing, diseases. Clinical prediction is
hard when data is high-dimensional, but additional information, like domain
knowledge and previously published studies, may be helpful to improve
predictions. Such complementary data, or co-data, provide information on the
covariates, such as genomic location or p-values from external studies. Our
method enables exploiting multiple and various co-data sources to improve
predictions. We use discrete or continuous co-data to define possibly
overlapping or hierarchically structured groups of covariates. These are then
used to estimate adaptive multi-group ridge penalties for generalised linear
and Cox models. We combine empirical Bayes estimation of group penalty
hyperparameters with an extra level of shrinkage. This renders a uniquely
flexible framework as any type of shrinkage can be used on the group level. The
hyperparameter shrinkage learns how relevant a specific co-data source is,
counters overfitting of hyperparameters for many groups, and accounts for
structured co-data. We describe various types of co-data and propose suitable
forms of hypershrinkage. The method is very versatile, as it allows for
integration and weighting of multiple co-data sets, inclusion of unpenalised
covariates and posterior variable selection. We demonstrate it on two cancer
genomics applications and show that it may improve the performance of other
dense and parsimonious prognostic models substantially, and stabilises variable
selection.
