cIndex: Concordance Index
In intsurv: Integrative Survival Modeling

cIndex

R Documentation

Concordance Index

Description

Compute concordance index (C-index or C-statistic) that allows weights for right-censored survival data. For example, Asano and Hirakawa (2017) proposed cure status weighting for cure models, which reduces to Harrell's C-index if weighs are all ones.

Usage

cIndex(time, event = NULL, risk_score, weight = NULL)

Arguments

`time`	A numeric vector for observed times
`event`	A numeric vector for event indicators. If it is `NULL` (by default) or `NA`, `event` will be treated all as ones and the function will compute concordance index for uncensored survival data.
`risk_score`	A numeric vector representing the risk scores of events.
`weight`	A optional numeric vector for weights. If it is `NULL` (by default) or `NA`, equal weights will be used.

Details

Let r_i, t_i, and \delta_i denote the risk score, observed time, and event indicator of i-th subject. The pair of (t_i,\delta_i) and (t_j,\delta_j), where i<j, are defined to be comparable if t_i<t_j,\delta_i=1 or t_i=t_j,\delta_i=1,\delta_j=0. In the context of survival analysis, the risk scores of a comparable pair are said to be concordant with the survival outcomes if r_i>r_j. The C-index is defined as the proportion of the concordant pairs among the comparable pairs. For comparable pair satisfying t_i<t_j,\delta_i=1, we count 0.5 in the numerator of the concordance index for tied risk scores (r_i=r_j).

Value

A named numeric vector that consists of

index: the concordance index.
concordant: the number of concordant pairs.
comparable: the number of comparable pairs.
tied_tisk: the number of comparable pairs having tied risks.

References

Asano, J., & Hirakawa, A. (2017). Assessing the prediction accuracy of a cure model for censored survival data with long-term survivors: Application to breast cancer data. Journal of Biopharmaceutical Statistics, 27(6), 918–932.

Harrell, F. E., Lee, K. L., & Mark, D. B. (1996). Multivariable prognostic models: Issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors. Statistics in medicine, 15(4), 361–387.