Quantifying the importance of scale — scale

Identify which distance is most important in characterizing an association between the topological structure in each image and outcomes.

Usage

scale_importance(
  pd.list,
  y,
  X = NULL,
  cens = NULL,
  omega.list,
  threshold,
  PIDs,
  outcome.type = "continuous",
  n.thresh = 50,
  print.progress = FALSE
)

Arguments

pd.list: List of persistence diagrams
y: Outcome vector
X: Covariates to adjust for, if desired. May be left NULL.
cens: Censoring vector for survival outcomes. May be left NULL.
omega.list: Vector of weights to combine kernel matrices
threshold: Maximum radius for Rips filtration
PIDs: Vector of patient IDs
outcome.type: Outcome type, options include "continuous", "binary", or "survival"
n.thresh: Number of distances between cells to evaluate. Default is 50
print.progress: Boolean, should progress be printed throughout analysis?

Value

Returns a list with the following elements:

min.thresh: The distance value at which the lowest TopKAT p-value was obtained
pvals: The vector of TopKAT p-values for each radius value
threshold.seq: The vector of distances considered

Details

This function identifies the distance at which the features which have been born and died during the process of filtration are most associated with the outcome.

Examples

# Generate a persistence diagram based on a Rips filtration for each image
pd.list <- generate_rips(data1.df, 100)
#> [1] "Rips diagram: 1"
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# Run the scale importance analysis
data1.scale <- scale_importance(pd.list = pd.list,
  y = y,
  cens = cens,
  omega.list = c(0, 0.5, 1),
  threshold = 100,
  PIDs = 1:100,
  outcome.type = "survival")

# Plot the results
plot(data1.scale$threshold.seq, data1.scale$pvals); abline(v = data1.scale$min.thresh)