medianConcordance: Estimate of median concordance for censored data
In Jeepen/biSurv: Functions related to bivariate survival data

medianConcordance

R Documentation

Estimate of median concordance for censored data

Description

Estimate of median concordance for censored data

Usage

medianConcordance(
  formula,
  data = NULL,
  gamma = NULL,
  maxIt = 100,
  method = "dabrowska"
)

Arguments

`formula`	a formula object, with the response on the left of a ~ operator, and the terms on the right. The response must be a survival object as returned by the `Surv` function. The RHS must contain a 'cluster' term.
`data`	a data.frame containing the variables in the model.
`gamma`	bandwidth for pruitt estimator. Ignored if estimator is another one.
`maxIt`	maximum number of iterations for NPMLE and pruitt estimators of bivariate survival function. Doesn't do anything if estimator is 'dabrowska' (default).
`method`	which estimator to use for the bivariate survival function.

Details

median concordance is a rank based measure of dependence which ensures that it doesn't change if we transform the marginal distributions with strictly increasing functions. Median concordance is defined as

E(sign((T1 - m1)(T_2 - m2))),

where m1 and m2 are the marginal medians. Median concordance is more intuitive than for instance Kendall's tau since you are only comparing whether one pair of observations is concordance or discordant wrt their respective medians rather than whether one pair is concordant/discordant compared to another pair. The median concordance is equal to 4*S(m1,m2)-1 where S is the bivariate survival function. This function estimates S both non-parametrically and parametrically for three frailty models. The survival function value for the frailty models at the medians are uniquely determined by the copula they imply since S(m1,m2) = C(S1(m1),S2(m2)) = C(0.5,0.5), where C is the survival copula implied by the model.