Spatial sampling is widely used in environmental and social research. In this paper we consider the situation where instead of a single global estimate of the mean of an attribute for an area, estimates are required for each of many geographically defined reporting units (such as counties or grid cells) because their means cannot be assumed to be the same as the global figure. Not only may survey costs greatly increase if sample size has to be a function of the number of reporting units, estimator sampling error tends to be large if the population attribute of each reporting unit can be estimated by using only those samples actually lying inside the unit itself. This study proposes a computationally simple approach to multi-unit reporting by using analysis of variance and incorporating ‘twice-stratified’ statistics. We assume that, although the area is heterogeneous (the mean varies across the area), it can be zoned (or stratified) into homogeneous subareas (the mean is constant within each subarea) and, in addition, that it is possible to acquire prior knowledge about this partition. This zoning of the study area is independent of the reporting units. The zone estimates are transferred to the reporting units. We call the methodology sandwich estimation and we report two contrasting empirical studies to demonstrate the application of the methodology and to compare its performance against some other existing methods for tackling this problem. Our study shows that sandwich estimation performs well against two other frequently used, probabilistic, model-based approaches to multi-unit reporting on stratified heterogeneous surfaces whilst having the advantage of computational simplicity. We suggest those situations where sandwich estimation might be expected to do well.

Severe acute respiratory syndrome (SARS) originated in China in 2002, and it spread to 26 provinces in mainland China and 32 countries across five continents in a matter of months. This outbreak resulted in 774 deaths. However, the spatial features and potential determinants of SARS input-output flows remain unclear. We used an adjusted spatial interaction model to examine the spatial effects and potential factors associated with SARS input-output flows. The presence of origin-based spatial dependence positively affected SARS input-output flows from the neighbours of the origin regions. Two components of the input-output flows, migrant and hospitalization flows, exhibited distinctive features. The origin-based and destination-based spatial dependence positively affected migrant flows (i.e., due to those seeking jobs) from the neighbours of origin and destination locations. Similarly, the destination-based spatial dependence also positively affected hospitalization flows (i.e., due to those seeking treatment) from the neighbours of destination regions. However, the origin-to-destination based spatial dependence negatively affected hospitalisation flows from the neighbours of origin-to-destination regions. The direct effects accounted for 78 % of the SARS input-output flows, which was 3.56-fold greater than the indirect effects. Differences in regional income drove the SARS input-output flows. Therefore, urban income had a positive effect, whereas rural income had a negative effect. Total interregional flows increased by 3.54 % with a 1 % increase in urban income, and intraregional flows increased by 8.35 %. In contrast, the total interregional flows decreased by 3.38 % with a 1 % increase in rural income, and intraregional flows declined by 2.29 %. Railway capacity, per person gross domestic product (PGDP), urban rate and the law of distance decay also affected the input-output flows. Our results confirm that the SARS input-output flows presented significant geographic spatial heterogeneity and spatial effects. Income differences were the major cause of the flows between pairs of regions. Railway capacity, PGDP, and urban rate also played important roles. These findings provide valuable information for the Chinese government to control the future spread of nationwide epidemics.