Population-Weighted Exposure Assignment from Residential Postal Codes: a National Comparison of Methods

The Postal Code Conversion File Plus (PCCF+) assigns a residential postal code with several candidate locations to one location drawn at random in proportion to population. Two non-random alternatives that use the same candidates and weights, (A) the weighted mean of the exposure across candidates and (B) the exposure at the weighted centroid, were compared with (C) PCCF+ random allocation, using (D) the exposure at the address as the reference, for 12,410,638 residential addresses in the National Address Register. Exposures were greenness (MODIS Enhanced Vegetation Index) and 2021 Material and Social Deprivation Index quintiles. The weighted mean had the same greenness bias as PCCF+, and its mean absolute error was 13.5% lower overall and 20% lower for rural postal codes. The error of random allocation decomposed exactly into the error of the weighted mean and an allocation variance, which accounted for 34% of its mean squared error for greenness and 49% for the material deprivation score among postal codes with six-, five- or four-character weighted links. The weighted centroid had the smallest positional error but did not improve greenness. The quintile of the weighted mean score compressed assignments toward the middle quintiles, whereas the modal candidate quintile reduced material quintile misclassification from 12.2% to 10.2% overall and from 46.2% to 37.0% for rural postal codes. Differences were small for urban letter-carrier postal codes. The weighted mean for continuous exposures and the modal quintile for area-based quintiles are recommended in place of random allocation, and a validated R function is provided.