ltrmst2adapt {survRM2adapt}

Long-Term Restricted Mean Survival Times with Adaptively Selected Lower End of Time Window

Description

This function performs the method proposed by Horiguchi, Tian, and Uno. (2023) <doi:10.1002/sim.9662>. Specifically, it estimates the restricted mean survival time (RMST) within a prespecified time window (from tau1 to tau2) to quantify the long-term treatment benefit. Instead of choosing one specific time point as the lower end of the time window (tau1), the procedure allows users to prespecify a set of time points. The procedure picks one time point among the set of tau1 values that gives the most significant difference in the long-term RMST between the two groups. It then performs testing for equality of the long-term RMSTs between the two groups and estimates the difference in RMST within the adaptively selected time window [tau1, tau2] between the two groups. Multiplicity as a result of specifying several values for tau1 is taken into account in this procedure.

Usage

ltrmst2adapt(indata, tau1, tau2, iteration=50000, seed=NULL, test="2_side", conf.int=0.95)

Arguments

indata

A data matrix (data frame). The 1st column is the time-to-event variable, the 2nd column is the event indicator (1=event, 0=censor), and the 3rd column is the treatment indicator (1=treatment, 0=control). No missing values are allowed in this data matrix.

tau1

An integer value or a vector indicating a set of tau1 values for the lower end of the time window.

tau2

An integer value indicating the upper end of the time window. When tau2 = NULL, the default value is used. See Details for the definition of the default value for tau2.

iteration

A number of iterations for the resampling (the multivariate normal distribution-based perturbation method). It is recommended to specify at least 50000 (default) or larger.

seed

An integer value used for random number generation in the resampling procedure. Default is NULL.

test

Specify "1_side" for the one-sided test where the alternative hypothesis is that the treatment group is superior to the control group with respect to survival time. Specify "2_side" for the two-sided test where the alternative hypothesis is that the treatment group is not equal to the control group with respect to survival time. Default is "2_side".

conf.int

Specify a confidence coefficient for calculating confidence bands for the differences in long-term RMST. Default is 0.95.

Details

The definition of the default value for tau2. Let x1 and x0 be the maximum observed time in Group 1 and Group 0, respectively. Case 1: If the last observations in Group 1 and Group 0 are "event," then tau = max(x1, x0). Case 2-1: If the last observation in Group 1 is "event," the last observation in Group 0 is "censor," and x1 <= x0, tau2 = max(x1, x0) = x0. Case 2-2: If the last observation in Group 0 is "event," the last observation in Group 1 is "censor," and x1 > x0, tau2 = max(x1, x0) = x1. Case 3-1: If the last observation in Group 1 is "event," the last observation in Group 0 is "censor," and x1 > x0, tau2 = min(x1, x0) = x0. Case 3-2: If the last observation in Group 0 is "event," the last observation in Group 1 is "censor," and x1 <= x0, tau2 = min(x1, x0) = x1. Case 4: If the last observations in Group 1 and Group 0 are "censor," then tau = min(x1, x0).

Value

an object of class ltrmst2adapt.

iteration

The number of iterations for resampling from a multivariate normal distribution with a mean 0 and a variance-covariance matrix.

test

The type of test used in the analyses

arm1

The RMST [tau1, tau2] estimation for arm1

arm0

The RMST [tau1, tau2] estimation for arm0

diff10

The difference in RMST [tau1, tau2] between the two groups (arm1 minus arm0)

diff10_selected

The difference in RMST within the selected time window [tau1, tau2] between the two groups (arm1 minus arm0) with the normal confidence interval considering the randomness of selecting one time window. The p-value for the RMST difference test within the selected time window [tau1, tau2] is also provided.

Author(s)

Miki Horiguchi, Lu Tian, Hajime Uno

References

Horiguchi M, Tian L, Uno H. On assessing survival benefit of immunotherapy using long-term restricted mean survival time. Statistics in Medicine 2023. DOI:10.1002/sim.9662.

Examples

#--- sample data ---#
data = cm214_pfs
b    = ltrmst2adapt(indata=data, tau1=c(0,1,2,3), tau2=10, 
               test="2_side", seed=123)
print(b)