Topological Kernel Association Test (TopKAT)

Perform global test of association between the geometric (topological) structures of spatially-resolved images of cells with continuous, binary, or survival outcomes.

Usage

TopKAT(
  y,
  X = NULL,
  cens = NULL,
  K.list,
  omega.list,
  outcome.type = "continuous"
)

Arguments

y

Vector of outcomes. Must be numeric. For continuous and survival data, should be a numeric vector. For a binary outcome, must consist of 0s and 1s.

X

Matrix of covariates to adjust for. May be left as NULL.

cens

Vector of event indicators for a survival outcome. 1 indicates a sample experienced the event, 0 otherwise. If not using a survival outcome, leave as NULL.

K.list

List of 2 kernel matrices corresponding to similarities among connected components and among loops. May provide only 1 kernel matrix if interested in a specific homology.

omega.list

Vector of weights to create different combinations of the kernel matrices. Some suggested options: c(0, 1) then TopKAT will combine the p-values for a test associating the connected components with y and the loops with y separately; c(0, 0.5, 1) will combine p-values across just the connected components, an even split of connected components and loops, and just loops.

outcome.type

What kind of outcome is y? Options include "continuous", "binary", or "survival"

Value

Returns a list of the following objects: overall.pval: the overall p-value describing the association between similarities in topological structures and clinical outcomes, p.vals: the vector of individual p-values for each weight in omega.list, y: the outcome provided, X: the covariates provided, omega.list: the vector of weights provided, outcome.type: the outcome type specified

Examples

# First, construct the similarity matrix
simmat <- rips_similarity_matrix(data1.df, max.threshold = 100, print.progress = TRUE)
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# Then, run TopKAT
res <- TopKAT(y = y,
              cens = cens,
              K.list = simmat$K.list,
              omega.list = c(0, 0.5, 1),
              outcome.type = "survival")

# Check result
res$overall.pval
#> [1] 3.443675e-05