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Background  Household surveys are the main source of demographic, health and socio-economic data in low- and middle-income countries (LMICs). To conduct such a survey, census population information mapped into enumeration areas (EAs) typically serves a sampling frame from which to generate a random sample. However, the use of census information to generate this sample frame can be problematic as in many LMIC contexts, such data are often outdated or incomplete, potentially introducing coverage issues into the sample frame. Increasingly, where census data are outdated or unavailable, modelled population datasets in the gridded form are being used to create household survey sampling frames.    Methods  Previously this process was done by either sampling from a set of the uniform grid cells (UGC) which are then manually subdivided to achieve the desired population size, or by sampling very small grid cells then aggregating cells into larger units to achieve a minimum population per survey cluster. The former approach is time and resource-intensive as well as results in substantial heterogeneity in the output sampling units, while the latter can complicate the calculation of unbiased sampling weights. Using the context of Somalia, which has not had a full census since 1987, we implemented a quadtree algorithm for the first time to create a population sampling frame. The approach uses gridded population estimates and it is based on the idea of a quadtree decomposition in which an area successively subdivided into four equal size quadrants, until the content of each quadrant is homogenous.    Results  The quadtree approach used here produced much more homogeneous sampling units than the UGC (1 × 1 km and 3 × 3 km) approach. At the national and pre-war regional scale, the standard deviation and coefficient of variation, as indications of homogeneity, were calculated for the output sampling units using quadtree and UGC 1 × 1 km and 3 × 3 km approaches to create the sampling frame and the results showed outstanding performance for quadtree approach.    Conclusion  Our approach reduces the manual burden of manually subdividing UGC into highly populated areas, while allowing for correct calculation of sampling weights. The algorithm produces a relatively homogenous population counts within the sampling units, reducing the variation in the weights and improving the precision of the resulting estimates. Furthermore, a protocol of creating approximately equal-sized blocks and using tablets for randomized selection of a household in each block mitigated potential selection bias by enumerators. The approach shows labour, time and cost-saving and points to the potential use in wider contexts.

Using gridded population and quadtree sampling units to support survey sample design in low-income settings