Population shift bias in tests of space-time interaction

Tests of space-time interaction detect clustering of events in space and time in excess of “any purely spatial or purely temporal clustering” (Kulldorff, 1998, pg. 58). These tests are widely employed in studies of crime (e.g. Knox, 2002; Grubesic and Mack, 2008) and disease (e.g. Petridou et al., 1996; Rogerson, 2001). By simultaneously considering both the spatial and temporal dimensions of the event patterns, these methods are capable of identifying certain data generating processes and, as a result, are often used to inform etiological work (Ward and Carpenter, 2000). Most of these tests, however, dubiously assume the underlying susceptible population within a study area to be invariant through time and across space. In settings where this assumption does not hold, these tests will detect space-time interaction due to population changes in addition to interaction resulting from the data generating process of interest. The excess interaction observed due to violating this assumption and by failing to account for the changes in the underlying population is referred to as population shift bias (Kulldorff and Hjalmars, 1999). Although recognized, this bias is often not accounted for in practice and its potential impact on results is not fully explored. This paper carries out a simulation to develop a detailed understanding of the impact of population shift bias on three of the most common tests of space-time interaction: the Knox (1964), Mantel (1967), and Jacquez (1996) tests. Additionally, the simulation demonstrates that contrary to prior claims (i.e. Kulldorff and Hjalmars, 1999; Aldstadt, 2007), population shift bias is problematic even in studies with a short temporal extent. To these ends, we simulate events within the dynamic population of a hypothetical metropolitan landscape over the course of one day. We then quantify the amount of population shift bias affecting each of the space-time interaction tests for a number of different population movement scenarios.