Robust (potentially stratified) logrank adjustment — robincar

Perform a robust covariate-adjusted logrank test ("CL") that can be stratified ("CSL") if desired.

robincar_logrank(adj_method, ...)

Arguments

adj_method: Adjustment method, one of "CL", "CSL"
...: Additional arguments to `robincar_tte`

Value

A result object with the following attributes:

result: A list: "statistic" is the adjusted logrank test statistic which can be used to obtain p-values; "U" and "se" are the numerator and denominator of the test statistic, respectively.
settings: The covariate adjustment settings used.
original_df: The dataset supplied by the user.

Details

Note: Since RobinCar version 0.4.0, the variance of the test statistic has changed to better accommodate tied event times.

$\hat{\sigma}_{\rm CL}^2$ and $\hat{\sigma}_{\rm CSL}^2$ for the covariate-adjusted stratified log-rank test are given by Ye, Shao, and Yi (2024) after equation (8) on page 700, with $\hat{\sigma}_{\rm SL}^2$ replaced by the following estimator, which is the standard denominator of the logrank test:

$$\frac1n \sum_{j} \sum_{i} v_j(t_i)$$ $$v_j(t_i) = \frac{Y_{0,j}(t)Y_{1,j}(t)d_j(t)\left[Y_j(t) - d_j(t)\right]}{Y_j(t)^2\left[Y_j(t) - 1 \right]}$$ where $t_i$ are strata-specific unique failure times, $d_j(t)$ is the number of events at time $t$ in strata $j$, $Y_j(t)$ is the number at risk within strata $j$ at time $t$, and $Y_{a,j}(t)$ is the number at risk within strata $j$ and treatment $a$ at time $t$.

Please see Ye, Shao, and Yi (2024)'s "Covariate-adjusted log-rank test: guaranteed efficiency gain and universal applicability" in Biometrika for more details about $\hat{\sigma}_{\rm CSL}^2$.

Examples

library(magrittr)
library(dplyr)
library(forcats)
set.seed(0)
n=100
data.simu0=data_gen(n=n,
                    theta=0,
                    randomization="permuted_block",
                    p_trt=0.5,
                    case="case2") %>% mutate(strata1=sample(letters[1:3],n,replace=TRUE),
                                             strata2=sample(LETTERS[4:5],n,replace=TRUE))

out <- robincar_logrank(df=data.simu0,
                        treat_col="I1",
                        p_trt=0.5,
                        ref_arm=0,
                        response_col="t",
                        event_col="delta",
                        covariate_cols=c("model_z1", "model_z2"),
                        car_scheme="simple",
                        adj_method=c("CL"))

set.seed(0)
n=100
data.simu0=data_gen(n=n,
                    theta=0,
                    randomization="permuted_block",
                    p_trt=0.5,
                    case="case1")

data.simu <- data.simu0 %>%
  tidyr::pivot_longer(cols=starts_with("car_strata"),
                      names_prefix="car_strata",
                      names_to="strt") %>%
  filter(value==1) %>% select(-value) %>%
  mutate(strt=forcats::as_factor(strt)) %>%
  select(t,strt) %>%
  left_join(data.simu0, .)
#> Joining with `by = join_by(t)`

out1 <- robincar_logrank(df=data.simu,
                         treat_col="I1",
                         p_trt=0.5,
                         ref_arm=0,
                         response_col="t",
                         event_col="delta",
                         car_strata_cols="strt",
                         covariate_cols=NULL,
                         car_scheme=c("permuted-block"),
                         adj_method=c("CSL")
)