Over the last few decades, many countries, especially Caribbean island ones, have been challenged by the devastating consequences of natural disasters, which pose a significant threat to human health and safety. Timely information related to the distribution of vulnerable population and critical infrastructure are key for an effective disaster relief. OpenStreetMap (OSM) has repeatedly been shown to be highly suitable for disaster mapping and management. However, large portions of the world, including countries exposed to natural disasters, remain unmapped. In this study, we propose a methodology that relies on remotely sensed measurements (e.g. VIIRS, Sentinel-2 and Sentinel-1) and derived classification schemes (e.g. forest and built-up land cover) to predict the completeness of OSM building footprints in three small island states (Haiti, Dominica and St. Lucia). We find that the combinatorial effects of these predictors explain up to 94% of the variation of the completeness of OSM building footprints. Our study extends the existing literature by demonstrating how remotely sensed measurements could be leveraged to evaluate the completeness of OSM database, especially in countries at high risk of natural disasters. Identifying areas that lack coverage of OSM features could help prioritize mapping efforts, especially in areas vulnerable to natural hazards and where current data gaps pose an obstacle to timely and evidence-based disaster risk management actions.