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.

中文翻译：

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分辨率对空间异质性指标作为肝纤维化生物标志物预测能力的影响

肝活检中细胞的空间异质性可以用作患者疾病严重程度的生物标志物。这种异质性可以通过点模式数据的非参数统计来量化，该统计利用点位置的聚合。尽管上述统计数据的值在很大程度上取决于它们，但聚合的方法和规模通常是临时选择的。此外，在测量异质性的背景下，增加空间分辨率并不会无休止地提供更高的准确性。那么问题就变成分辨率的变化如何影响异质性指标，以及随后它们如何影响其预测能力。本文利用慢性乙型肝炎患者肝活检组织的细胞水平数据来分析这个问题。首先，使用多种分辨率评估Morisita-Horn指数、Shannon指数和Getis-Ord统计量作为不同类型细胞的异质性指标。其次，研究了分辨率对序数回归模型中指数的预测性能的影响，以及它们在模型中的重要性。随后进行了模拟研究以验证上述方法。一般来说，对于特定的异质性指标，可以观察到预测性能下降的趋势。虽然对于异质性的局部度量来说，较小的网格尺寸表现更好，但对于中等规模的网格，全局度量具有更好的性能。此外，建议使用局部和全局异质性测量来提高预测性能。