Using random forests to uncover the predictive power of distance-varying cell interactions in tumor microenvironments

Tumor microenvironments (TMEs) contain vast amounts of information on patients cancer through their cellular composition and the spatial distribution of tumor cells and immune cell populations. Exploring variations in TMEs among patients and cancer types, as well as determining the extent to which this information can predict variables such as patient survival or treatment success with emerging immunotherapies, is of great interest. Moreover, in the face of a large number of potential spatial cell interactions to consider, we often wish to identify specific interactions that are useful in making such predictions. We present an approach to achieve these goals based on summarizing spatial relationships in the TME using spatial K functions, and then applying functional data analysis and random forest models to both predict outcomes of interest and identify important spatial relationships. This approach is shown to be effective in simulation experiments. We further used the proposed approach to interrogate two real data sets of Multiplexed Ion Beam Images of TMEs in triple negative breast cancer and lung cancer patients. The methods proposed are publicly available in a companion R package funkycells. Author summarySpatial data on the tumor microenvironment (TME) are becoming more prevalent. Existing methods to interrogate such data often have several deficiencies: (1) they rely on estimating the spatial relationships among cells by examining simple counts of cells within a single radius, (2) they do not come with ways to evaluate the statistical significance of any findings, or (3) they consider multiple individual interactions resulting in overly optimistic estimates of interaction importances. Our approach, which leverages techniques in spatial statistics and uses a benchmark ensemble machine learning method addresses (1), since the K functions used encode the relative densities of cells over all radii up to a user-selected maximum radius, and (2) we have developed a custom approach based on permutation and cross-validation to evaluate the statistical significance of any findings of significant spatial interactions in the TME, (3) over potentially multiple interactions. Our approach is also freely available with an R implementation called funkycells. In the analysis of two real data sets, we have seen that the method performs well, and gives the expected results. We think this will be a robust tool to add to the toolbox for researchers looking to interrogate, what can be sometimes unwieldy, TME data.