Basic health system data such as the number of patients utilising different health facilities and the types of illness for which they are being treated are critical for managing service provision. These data requirements are generally addressed with some form of national Health Management Information System (HMIS) which coordinates the routine collection and compilation of data from national health facilities. HMIS in most developing countries are characterised by widespread under-reporting. Here we present a method to adjust incomplete data to allow prediction of national outpatient treatment burdens. We demonstrate this method with the example of outpatient treatments for malaria within the Kenyan HMIS. Three alternative modelling frameworks were developed and tested in which space-time geostatistical prediction algorithms were used to predict the monthly tally of treatments for presumed malaria cases (MC) at facilities where such records were missing. Models were compared by a cross-validation exercise and the model found to most accurately predict MC incorporated available data on the total number of patients visiting each facility each month. A space-time stochastic simulation framework to accompany this model was developed and tested in order to provide estimates of both local and regional prediction uncertainty. The level of accuracy provided by the predictive model, and the accompanying estimates of uncertainty around the predictions, demonstrate how this tool can mitigate the uncertainties caused by missing data, substantially enhancing the utility of existing HMIS data to health-service decision-makers.