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Clinicians often research complex traits in which many variables may be involved in the process underlying the disease. Nowadays, with the advent of DNA sequencing techniques, clinical studies regularly research high‐dimensional data, in which the number of variables even far exceeds the number of samples. Generic research goals are to predict certain outcomes or to select variables, using the high-dimensional data possibly in addition to clinical variables like age and sex. Examples in cancer genomics are to diagnose cancer, classify cancer type and predict survival time based on gene expression data, or to find few genes that may predict these outcomes well. While the human genome contains around 20.000 genes, clinical studies usually only include measurements for around 100 patients. This limited amount of information makes it hard to find the “right” selection or combination of variables from the vast space of options. Luckily, more prior information on the variables is often available in the form of complementary data, or co-data, e.g. from public repositories or derived from domain knowledge. Co‐data may vary in type. Genes, for example, may be grouped in non‐overlapping groups for chromosomes, overlapping groups for pathways, hierarchical groups for gene ontology or assigned a continuous summary statistic derived from a similar study. We would like to learn from co‐data to improve prediction and variable selection. This dissertation presents three statistical methods and software for co‐data learning. We consider co‐data learnt penalised generalised linear and Cox survival models for the outcome. The penalties on the variables are informed by the co‐data, such that variables for more important co‐data are penalised less. For example, some biological functions may be more important than others, such that genes corresponding to these biological functions are ideally penalised relatively less. The penalty parameters are related to prior parameters for a prior distribution on the variables, which are estimated with an empirical Bayes approach. The presented methods differ in the type of co‐data and penalty or prior that may be used.

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., Document consists of main content (20 pages, 10 figures) and supplementary material (14 pages, 13 figures)