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.
cIndex(time, event = NULL, risk_score, weight = NULL)
| time | A numeric vector for observed times |
|---|---|
| event | A numeric vector for event indicators. If it is |
| risk_score | A numeric vector representing the risk scores of events. |
| weight | A optional numeric vector for weights. If it is |
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.
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 (\(r_i=r_j\)).
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.
## See examples of function 'cox_cure'.