# cIndex: Concordance Index In intsurv: Integrative Survival Modeling

## 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

 `1` ```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 δ_i denote the risk score, observed time, and event indicator of i-th subject. The pair of (t_i,δ_i) and (t_j,δ_j), where i<j, are defined to be comparable if t_i<t_j,δ_i=1 or t_i=t_j,δ_i=1,δ_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,δ_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.

## Examples

 `1` ```## See examples of function 'cox_cure'. ```

### Example output

```
```

intsurv documentation built on Jan. 13, 2021, 3:46 p.m.