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. Author manuscript; available in PMC: 2018 May 10.
Published in final edited form as: Cell Rep. 2018 Apr 3;23(1):181–193.e7. doi: 10.1016/j.celrep.2018.03.086

Figure 6. Associations of TIL Local Spatial Structure with Cancer Type and Survival.

Figure 6

Associations are shown with cluster indices, which summarize properties of clusters derived from affinity propagation clusters of the TIL map—properties that provide details on local structure beyond simple densities.

(A) Ball-Hall cluster indices for all slide images considered in the study. The Ball-Hall index is a particular clustering index, summarizing the mean, through all the clusters, of their mean dispersion and is equivalent to the mean of the squared distances of the points of the cluster with respect to its center. In our data, the Ball-Hall index is correlated (ρSpearman = 0.95) with the mean cluster extent, CE.

(B) Table of significant associations between TIL fraction-adjusted cluster indices and overall survival based on Cox regression, accounting for age and gender as additional clinical covariates.

(C) Overall survival for median-stratified TIL fraction-adjusted Ball-Hall index in breast cancer. Significance test p value is shown in the lower left.

(D) Same as C but for adjusted Banfield-Raftery index in skin cutaneous melanoma. The Banfield-Raftery index is the weighted sum of the logarithms of the mean cluster dispersion and, in our data, often correlates with the number of clusters. See also Figure S4.