Test for equality of RMST across two or more groups.
Usage
Compares restricted mean survival time (RMST) up to a fixed time tau across groups using a z-test or t-test. Provides point estimate, standard error, confidence interval, and p-value for the null hypothesis of equal RMST.
For two groups, this is equivalent to a z-test on the RMST difference (default) or log-ratio (if estimand=“ratio”).
surv: SurvA right-censored Surv response (time-to-event data).
tau: floatThe restriction time, typically a clinically relevant horizon (e.g., 365, 1825).
group: AnyGroup membership for each observation. Can be array-like or categorical variable.
estimand: str = "difference"Type of estimand: "difference" (default, RMST1 - RMST2), "ratio" (RMST1 / RMST2), or "percentage_difference" ((RMST1 - RMST2) / RMST2 * 100).
strata: Any | None = None(Optional) Stratification variable for stratified RMST comparison. If provided, RMST estimates are combined across strata before computing the test statistic.
conf_level: float = 0.950.95 for 95% CI).
RMSTResultFor two groups (i=1,2), the RMST difference is:
\[ \Delta = \mathrm{RMST}_1(\tau) - \mathrm{RMST}_2(\tau) \]
with standard error:
\[ \mathrm{SE}(\Delta) = \sqrt{\mathrm{SE}(\mathrm{RMST}_1)^2 + \mathrm{SE}(\mathrm{RMST}_2)^2} \]
assuming independence. The z-statistic is \(Z = \Delta / \mathrm{SE}(\Delta)\), with two-tailed p-value from the standard normal.
For ratio estimand, the log-ratio variance uses the delta method:
\[ \mathrm{SE}(\log R) = \sqrt{\frac{\mathrm{SE}_1^2}{\mathrm{RMST}_1^2} + \frac{\mathrm{SE}_2^2}{\mathrm{RMST}_2^2}} \]
Test RMST difference between two treatment groups:
import greenwood as gw
lung = gw.load_dataset("lung", backend="polars")
y = gw.Surv.right(lung["time"], event=(lung["status"] == 2))
result = gw.rmst_test(y, tau=365, group=lung["sex"])
result.estimate # RMST difference
result.p_value # significance0.00018270646131113288Using ratio estimand: