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Calculate the expected mortality risks from a survival matrix

get_mortality.Rd

Many methods can be used to reduce a discrete survival distribution prediction (i.e. matrix) to a relative risk / ranking prediction, see Sonabend et al. (2022).

This function calculates a relative risk score as the sum of the predicted cumulative hazard function, also called ensemble/expected mortality. This risk score can be loosely interpreted as the expected number of deaths for patients with similar characteristics, see Ishwaran et al. (2008) and has no model or survival distribution assumptions.

Usage

get_mortality(x, times = NULL, eps = 1e-06, check = TRUE)

Arguments

x

(matrix())
A survival matrix. Rows correspond to observations and columns correspond to time points.

times

(numeric()|NULL)
Optional numeric vector of time points corresponding to the columns of x.

eps

(numeric(1))
Small positive constant used to bound survival probabilities away from zero and prevent infinite cumulative hazards, as H(t) = -log(S(t)).

check

(logical(1))
If TRUE (default), uses assert_prob_matrix to perform several checks on the survival matrix. Set to FALSE to skip checks (NOT recommended for external use).

Value

a numeric vector of the mortality risk scores, one per row of the input survival matrix.

References

Sonabend, Raphael, Bender, Andreas, Vollmer, Sebastian (2022). “Avoiding C-hacking when evaluating survival distribution predictions with discrimination measures.” Bioinformatics. ISSN 1367-4803, doi:10.1093/BIOINFORMATICS/BTAC451 , https://academic.oup.com/bioinformatics/advance-article/doi/10.1093/bioinformatics/btac451/6640155.

Ishwaran, Hemant, Kogalur, B U, Blackstone, H E, Lauer, S M, others (2008). “Random survival forests.” The Annals of applied statistics, 2(3), 841–860.

Examples

n = 10 # number of observations
k = 50 # time points

# Create the matrix with random values between 0 and 1
mat = matrix(runif(n * k, min = 0, max = 1), nrow = n, ncol = k)

# transform it to a survival matrix
x = t(apply(mat, 1L, function(row) sort(row, decreasing = TRUE)))
colnames(x) = 1:k # time points

# get mortality scores (larger values correspond to higher risk scores)
mort = get_mortality(x)
mort
#>  [1] 42.97823 54.82505 45.70337 43.87888 60.06472 51.07290 40.24465 58.56290
#>  [9] 47.22765 54.87452