## integrated_auc()


Time-averaged IPCW AUC across multiple time points.


Usage

``` python
integrated_auc(
    surv,
    marker,
    times,
)
```


Summarises [time_dependent_auc()](time_dependent_auc.md#greenwood.time_dependent_auc) into a single number via trapezoidal integration over the supplied time range. This provides a discrimination summary analogous to Harrell's C-statistic but with explicit IPCW bias-correction for censoring.

**Interpretation**: Same scale as [time_dependent_auc()](time_dependent_auc.md#greenwood.time_dependent_auc) (0.5 = random, 1.0 = perfect). Values of 0.6-0.7 indicate moderate and 0.7+ indicate strong discrimination.


## Parameters


`surv: Surv`  
A right-censored [Surv](Surv.md#greenwood.Surv) response.

`marker: Any`  
Risk score for each subject. Higher values indicate higher risk.

`times: Any`  
Evaluation times (at least 2). The integrated AUC is computed as the area under the AUC curve from `times[0]` to `times[-1]`, normalized by the time span. `nan` time points (no cases or controls) are dropped before integration.


## Returns


`float`  
Time-averaged AUC in \[0, 1\]. Higher is better.


## Details

The integrated AUC is computed as the area under the time-dependent AUC curve (from [time_dependent_auc()](time_dependent_auc.md#greenwood.time_dependent_auc)) divided by the time span, giving a single scalar summary of discrimination across the specified horizon. Time points that produce `nan` AUC values (no cases or no controls at that time) are dropped before integration.


## Examples

Compute the integrated AUC of a Cox model's linear predictor across three clinically relevant time horizons (6, 12, and 18 months):


``` python
import greenwood as gw

# Load data and build a right-censored response
lung = gw.load_dataset("lung", backend="polars")
y = gw.Surv.right(lung["time"], event=(lung["status"] == 2))
cox = gw.CoxPH().fit(y, lung[["age", "sex"]])

# Compute the time-averaged AUC across three horizons
lp = cox.predict(type="lp")
gw.integrated_auc(y, lp, times=[180, 365, 540])
```


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