mb_weight: Magirr and Burman Modestly Weighted Logrank Tests

In keaven/simtrial: Clinical Trial Simulation

Magirr and Burman Modestly Weighted Logrank Tests

Description

Magirr and Burman (2019) have proposed a weighted logrank test to have better power than the logrank test when the treatment effect is delayed, but to still maintain good power under a proportional hazards assumption. In Magirr (2021), (the equivalent of) a maximum weight was proposed as opposed to a fixed time duration over which weights would increase. The weights for some early interval specified by the user are the inverse of the combined treatment group empirical survival distribution; see details. After this initial period, weights are constant at the maximum of the previous weights. Another advantage of the test is that under strong null hypothesis that the underlying survival in the control group is greater than or equal to underlying survival in the experimental group, Type I error is controlled as the specified level.

Usage

mb_weight(x, delay = 4, wmax = Inf)

Arguments

x	a counting_process-class tibble with a counting process dataset
delay	The initial delay period where weights increase; after this, weights are constant at the final weight in the delay period
wmax	Maximum weight to be returned. set delay = Inf, wmax = 2 to be consistent with recommendation of Magirr (2021).

Details

This function computes Magirr-Burman weights and adds them to a dataset created by the counting_process() function. These weights can then be used to compute a Z-statistic for the modestly weighted logrank test proposed.

We define t^* to be the input variable delay. This specifies an initial period during which weights increase. We also set a maximum weight w_max. To define specific weights, we let S(t) denote the Kaplan-Meier survival estimate at time t for the combined data (control plus experimental treatment groups). The weight at time t is then defined as

w(t)=\min(w_max, S(\min(t,t^*))^{-1}).

Value

a vector with weights for the Magirr-Burman weighted logrank test for the data in x

References

Magirr, Dominic, and Carl‐Fredrik Burman. "Modestly weighted logrank tests." Statistics in Medicine 38.20 (2019): 3782–3790.

Magirr, Dominic. "Non‐proportional hazards in immuno‐oncology: Is an old perspective needed?" Pharmaceutical Statistics 20.3 (2021): 512–527.

Examples

library(tidyr)
library(dplyr)

# Use default enrollment and event rates at cut at 100 events
# For transparency, may be good to set either `delay` or `wmax` to Inf`
x <- sim_pw_surv(n = 200) %>%
  cut_data_by_event(125) %>%
  counting_process(arm = "Experimental")

# example 1
# compute Magirr-Burman weights with `delay = 6`
ZMB <- x %>%
  mb_weight(delay = 6, wmax = Inf) %>%
  summarize(S = sum(o_minus_e * mb_weight),
            V = sum(var_o_minus_e * mb_weight^2),
            Z = S / sqrt(V))

# Compute p-value of modestly weighted logrank of Magirr-Burman
pnorm(ZMB$Z)

# example 2
# Now compute with maximum weight of 2 as recommended in Magirr, 2021
ZMB2 <- x %>%
  mb_weight(delay = Inf, wmax = 2) %>%
  summarize(S = sum(o_minus_e * mb_weight),
            V = sum(var_o_minus_e * mb_weight^2),
            Z = S / sqrt(V))

# Compute p-value of modestly weighted logrank of Magirr-Burman
pnorm(ZMB2$Z)

keaven/simtrial documentation built on April 17, 2023, 4:03 a.m.