The need for data privacy and security -- enforced through increasingly strict data protection regulations -- renders the use of healthcare data for machine learning difficult. In particular, the transfer of data between different hospitals is often not permissible and thus cross-site pooling of data not an option. The Personal Health Train (PHT) paradigm proposed within the GO-FAIR initiative implements an 'algorithm to the data' paradigm that ensures that distributed data can be accessed for analysis without transferring any sensitive data. We present PHT-meDIC, a productively deployed open-source implementation of the PHT concept. Containerization allows us to easily deploy even complex data analysis pipelines (e.g, genomics, image analysis) across multiple sites in a secure and scalable manner. We discuss the underlying technological concepts, security models, and governance processes. The implementation has been successfully applied to distributed analyses of large-scale data, including applications of deep neural networks to medical image data.