The influence of resolution on the predictive power of spatial heterogeneity measures as biomarkers of liver fibrosis

Spatial heterogeneity of cells in liver biopsies can be used as biomarker for disease severity of patients. This heterogeneity can be quantified by non -parametric statistics of point pattern data, which make use of an aggregation of the point locations. The method and scale of aggregation are usually chosen ad hoc, despite values of the aforementioned statistics being heavily dependent on them. Moreover, in the context of measuring heterogeneity, increasing spatial resolution will not endlessly provide more accuracy. The question then becomes how changes in resolution influence heterogeneity indicators, and subsequently how they influence their predictive abilities. In this paper, cell level data of liver biopsy tissue taken from chronic Hepatitis B patients is used to analyze this issue. Firstly, Morisita-Horn indices, Shannon indices and Getis-Ord statistics were evaluated as heterogeneity indicators of different types of cells, using multiple resolutions. Secondly, the effect of resolution on the predictive performance of the indices in an ordinal regression model was investigated, as well as their importance in the model. A simulation study was subsequently performed to validate the aforementioned methods. In general, for specific heterogeneity indicators, a downward trend in predictive performance could be observed. While for local measures of heterogeneity a smaller grid -size is outperforming, global measures have a better performance with medium-sized grids. In addition, the use of both local and global measures of heterogeneity is recommended to improve the predictive performance.