mb {simtrial}

Magirr and Burman weighting function

Description

Magirr and Burman weighting function

Usage

mb(delay = 4, w_max = Inf)

Arguments

delay

The initial delay period where weights increase; after this, weights are constant at the final weight in the delay period.

w_max

Maximum weight to be returned. Set delay = Inf, w_max = 2 to be consistent with recommendation of Magirr (2021).

Details

Magirr and Burman (2019) 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.

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 list of parameters of the Magirr and Burman weighting function

References

Magirr, Dominic, and Carl‐Fredrik Burman. 2019. "Modestly weighted logrank tests." Statistics in Medicine 38 (20): 3782–3790.

Magirr, Dominic. 2021. "Non‐proportional hazards in immuno‐oncology: Is an old perspective needed?" Pharmaceutical Statistics 20 (3): 512–527.

Examples

sim_pw_surv(n = 200) |>
  cut_data_by_event(100) |>
  wlr(weight = mb(delay = 8, w_max = Inf))