# concordance_index_compare()


Compare two concordance indices via the paired influence-function delta method.


Usage

``` python
concordance_index_compare(
    surv,
    risk_a,
    risk_b,
    *,
    data=None,
    cause=None,
    tau=None,
    conf_level=0.95,
)
```


Tests whether two risk scores (from different models) have different concordance indices on the same data. The standard error of the difference is derived from the joint influence function, which properly accounts for the correlation between the two estimates (they share the same subjects).


## Parameters


`surv: Surv | Outcome | str`  
A [Surv](Surv.md#greenwood.Surv) response (right-censored or multistate). An [Outcome](Outcome.md#greenwood.Outcome) or a formula response such as `'Surv(time, status == 2)'` is also accepted, with its columns read from `data`.

`risk_a: Any`  
Risk scores from the first model.

`risk_b: Any`  
Risk scores from the second model.

`cause: int | None = None`  
Integer cause code for competing-risks concordance. `None` for standard.

`tau: float | None = None`  
Truncation time.

`conf_level: float = ``0.95`  
Confidence level.

`data: Any = None`  
A data frame (pandas, Polars, PyArrow, DuckDB, a lazy frame, …) holding the columns named by the response, `risk_a`, and `risk_b`. When `surv` is an [Outcome](Outcome.md#greenwood.Outcome) or a formula, rows with a missing value in any column used are dropped first, along with the matching rows of any arrays passed alongside.


## Returns


`ConcordanceCompareResult`  
Difference, standard error, CI, z-statistic, and p-value.


## Examples


``` python
import greenwood as gw

lung = gw.load_dataset("lung", backend="polars")
death = gw.Outcome.surv(time="time", event="status")
cox1 = gw.CoxPH().fit(death, covariates=["age"], data=lung)
cox2 = gw.CoxPH().fit(death, covariates=["age", "sex"], data=lung)
lp1 = cox1.predict(type="lp")
lp2 = cox2.predict(type="lp")

gw.concordance_index_compare(death, risk_a=lp1, risk_b=lp2, data=lung)
```


    ConcordanceCompareResult(delta=-0.0467, se=0.0355, CI=[-0.1162, 0.0228], z=-1.318, p=0.1875)