Increases in the availability of reliable health data are widely recognised as essential for efforts to strengthen health-care systems in resource-poor settings worldwide. Effective health-system planning requires comprehensive and up-to-date information on a range of health metrics and this requirement is generally addressed by a Health Management Information System (HMIS) that coordinates the routine collection of data at individual health facilities and their compilation into national databases. In many resource-poor settings, these systems are inadequate and national databases often contain only a small proportion of the expected records. In this paper we take an important health metric in Kenya (the proportion of outpatient treatments for malaria, MP) from the national HMIS database and predict the values of MP at facilities where monthly records are missing. The available MP data were densely distributed across a spatiotemporal domain and displayed second-order heterogeneity. We used three different kriging methodologies to make cross-validation predictions of MP in order to test the effect on prediction accuracy of (a) the extension of a spatial-only to a space-time prediction approach, and (b) the replacement of a globally-stationary with a locally-varying random function model. Space-time kriging was found to produce predictions with 98.4% less mean bias and 14.8% smaller mean imprecision than conventional spatial-only kriging. A modification of space-time kriging that allowed space-time variograms to be recalculated for every prediction location within a spatially-local neighbourhood resulted in a larger decrease in mean imprecision over ordinary kriging (18.3%) although mean bias was reduced less (87.5%).