Assess discriminative performance of predictions obtained from a conventional or competing risks time-to-event model using time-dependent concordance index.
Usage
CIndexCRisks(
predictions,
time,
cens.code = 0,
status,
cause,
tau,
method = c("survival", "cifs")
)Arguments
- predictions
Numeric vector of model predictions.
- time
Numeric vector describing the time to the event of interest or censoring.
- cens.code
Value used to denote censoring in
status. Defaults to 0.- status
Vector of censoring status.
- cause
Event of interest.
- tau
Time c-index is evaluated.
- method
'survival'if the predictions are survival probabilities or'cifs'if they are cumulative incidence functions
Details
Uses the proportion of correctly ordered risk pairs for the event \(k\), based on the predicted risk of the event up to time \(\tau\).
$$C_k(\tau) = \frac{\sum_{i=1}^N \sum_{j=1}^N (A_{ij} + B_{ij}) \cdot Q_{ij} \cdot N_i^k(\tau)}{\sum_{i=1}^N \sum_{j=1}^N (A_{ij} + B_{ij}) \cdot N_i^k(\tau)}$$
A == risk ordering of patients, small time means patient 'i' at higher risk than patient 'j' experiencing event of interest \(A[i,j] = 0\) for tied event times.
B == risk ordering of patients, large time for patient 'i' means lower risk than patient 'j' if not experienced the event of interest. Ties are included in B
Q == the risk ordering of the subjects, i.e., is subject i assigned a higher risk by the model than the subject j, for event \(E_k\) until time \(t\). \(Q[i,j] = 0\) for tied predictions.
N_t == number of subjects with survival time < time point and experience event of interest Tied event times are included
References
Ahuja K, Schaar M van der. Joint Concordance Index. Published online August 17, 2019. doi:10.48550/arXiv.1810.11207