Conceptual framework for classifying sources of spatial measurement errors

To discuss the spatial measurement errors systematically, we suggest the following conceptual framework as a helpful way to effectively organize the topic. We recognize that there is no way to completely capture the intricacies of all possible routes of measurement errors, however we present a basic structure, that can be expanded upon, to begin the process of systematically categorizing the types and structure of these potential errors. Spatial epidemiologic studies include two additional variables recording the locations/positions of observations in the leftmost two columns, while the other outcome and covariate variables are often similar to those used in classical epidemiology (Fig. 1).

Schematic framework for spatial measure errors in spatial epidemiology. For Location (①), the geographic coordinates are used as an example here. In practice, the Cartesian coordinates can be used instead, which is the coordinates used in the process of data analysis; For Outcome (②), a dichotomous variable is used for an example and only one column is needed. Other types of Outcome variables can also have more than one dimension, such as Poisson data, that may include a numerator (e.g., number of cases) and denominator (population at risk). For simplicity, only one column is used to indicate the Outcome. The Covariates (③) may be any combination of categorical or continuous variables. The error caused by the correspondence between Outcome and Covariates is marked as ④

The following four types of spatial measure errors are divided accordingly from the point of application:

Pure spatial location measurement errors;

Location-based outcome measurement errors;

Location-based covariate measurement errors; and;

Covariate-Outcome spatial misaligned measurement errors.