The Clinical E-Science Framework (CLEF) project has built a system to extract clinically significant information from the textual component of medical records, for clinical research, evidence-based healthcare and genotype-meets-phenotype informatics. One part of this system is the identification of relationships between clinically important entities in the text. Typical approaches to relationship extraction in this domain have used full parses, domain-specific grammars, and large knowledge bases encoding domain knowledge. In other areas of biomedical NLP, statistical machine learning approaches are now routinely applied to relationship extraction. We report on the novel application of these statistical techniques to clinical relationships. We describe a supervised machine learning system, trained with a corpus of oncology narratives hand-annotated with clinically important relationships. Various shallow features are extracted from these texts, and used to train statistical classifiers. We compare the suitability of these features for clinical relationship extraction, how extraction varies between inter- and intra-sentential relationships, and examine the amount of training data needed to learn various relationships.