Here the data analysis challenges for pharmacosurveillance and pharmacogenomics are reviewed. Four interrelated tools to tackle the ubiquitous problems of high dimensionality and sparsity are outlined: the contribution of negative or contrary evidence in the four pillars of evidence established in the early days of epidemiology, information and decision theory, the zeta function, and hyperbolic-complex algebra. These four tools are described in a fairly integrated way, and this order basically reflects the degree of novelty and degree of acceptance in biomedicine, the most recent and controversial coming last. The zeta function is essentially an estimate in information theory, an extension to express the expected information in a system, the amount of available to the observer via the data, and in one guise has been in use in bioinformatics since the early 1970s. Hyperbolic-complex algebra is concerned with encoding information in two directions of conditionality, of potential importance in inference about etiology, considerations derivable mathematically from the zeta function. It takes on importance when many zeta function terms as estimates of information terms are used in an inference network. Its usefulness remains to be, although it essentially represents the method of inference due to Dirac and already established in quantum field and particle theory. Including negative evidence in inference using estimates based on multiple factors, however, requires that we are careful in interpretation.