Detecting interpolation errors in infant mortality counts in 20th Century England and Wales

TL;DR

This study tackles the challenge of analyzing 20th century infant mortality counts by local government districts in England and Wales when boundary changes hinder direct temporal comparison. It introduces a Poisson changepoint detector with a time trend to automatically flag interpolation errors arising from areal weighting, and couples this with functional principal components analysis to cluster fine-scale mortality trajectories. The approach identifies and conservatively corrects interpolation-related distortions, and demonstrates that such corrections alter clustering patterns and reveal nuanced regional differences. The work provides a practical framework for reconstituting long-run historical series and extracting meaning from high-resolution spatial-temporal data in the presence of boundary-induced inconsistencies.

Abstract

Understanding historical datasets, such as the England and Wales infant mortality data, for local government districts can provide valuable insights into our changing society. Such analyses can prove challenging in practice, due to frequent changes in the boundaries of local government districts for which records are collected. One solution adopted in the literature to overcome such practical challenges is to pre-process data using areal interpolation to render the units consistent over the time period of focus. However, such methods are prone to errors. In this paper we introduce a novel changepoint method to detect instances where interpolation performs poorly. We demonstrate the utility of our method on original data, and also demonstrate how correcting interpolation errors can affect the clustering of the infant mortality curves.

Figures (18)

• Figure 1: Infant mortality rate England and Wales, based on the raw data. Sample of $15$ local government districts depicted GBHDB_vital_statistics: two of these are districts with populations under $500$ in $1911$ and the rest are districts with populations over $50000$.
• Figure 2: Counts of infant deaths, England and Wales, based on the raw data. Random sample of $100$ local government districts depicted GBHDB_vital_statistics.
• Figure 3: Counts of LGD names in England and Wales per year (raw data) GBHDB_vital_statistics.
• Figure 4: Raw and interpolated IM rates for local government districts in Sussex or Northumberland that are created or abolished $1911-1973$GBHDB_vital_statistics. Depicted on the left hand side is the raw data, showing large numbers of districts abolished in the mid-$1930$s and a few created that continue to have data recorded for them until $1973$. On the right hand side we see the interpolated data for $1973$ districts that were created during the period.
• Figure 5: Raw and interpolated counts of infant deaths in selected areas $1911-1973$GBHDB_vital_statistics. The areas are selected as in Figure \ref{['fig: hist im rates selected areas']}. Left image: raw counts. Right image: interpolated counts.