Comparison of the spatial organization in colorectal tumors using second-order statistics and functional ANOVA

Abstract

Abstract-We propose an automatic method to quantitatively describe the spatial organization governing populations of biological objects, such as cells, which exist in stationary histology images. This quantification is of prime importance when striving to compare different tumoral models in order to evaluate potential therapies. We compare two animal models of colorectal cancer. Our approach is based on the topographic map to automatically extract the location of the relevant biological objects. We describe their spatial organization along a continuous range of scales using second-order statistics. Using a functional analysis of variance test, we show that there are significant differences in these statistics depending on cancer model, and on the day after tumor implant.

Multiple Monte Carlo testing, with applications in spatial point processes

“…The last procedure was applied to a point pattern data of colorectal tumors in Aliy et al (2013). There is also a possibility to transform the function into one number and apply a classical anova but such procedures can be blind against some alternatives.…”

“…In the point patterns literature the group comparison is done either using functional anova as in Aliy et al (2013) or using a bootstrap procedure as in Diggle et al (1991), Diggle et al (2000) or Schladitz et al (2003). Furthermore, Hahn (2012) proposed a pure permutation procedure to correct the inaccurate significance level of the bootstrap procedure.…”