Sample Size Calculation under Non-Proportional Hazards

Performs combination tests and sample size calculation for fixed design with survival endpoints using combination tests under either proportional hazards or non-proportional hazards. The combination tests include maximum weighted log-rank test and projection test. The sample size calculation procedure is very flexible, allowing for user-defined hazard ratio function and considering various trial conditions like staggered entry, drop-out etc. The sample size calculation also applies to various cure models such as proportional hazards cure model, cure model with (random) delayed treatments effects. Trial simulation function is also provided to facilitate the empirical power calculation. The references for projection test and maximum weighted logrank test include Brendel et al. (2014) and Cheng and He (2021) . The references for sample size calculation under proportional hazard include Schoenfeld (1981) and Freedman (1982) . The references for calculation under non-proportional hazards include Lakatos (1988) and Cheng and He (2023) .

package: nphPower

Package: nphPower provides functions to perform combination test including maximum weighted logrank test (MWLR) and projection test, to calculate sample size with MWLR in a simulation-free approach allowing for staggered entry, drop-out etc, to visualize the design parameters and to simulate survival data with flexible design input.

Installation

You can install the released version of nphPower from CRAN with:

install.packages("nphPower")

library("nphPower")

And the development version from GitHub with:

# install.packages("devtools")
#devtools::install_github("hcheng99/nphPower")

Example 1 - perform maximum weighted logrank test

This is a basic example which shows you how to perform maximum weighted logrank test.

Load the lung data and only keep columns for analysis.

lung <- nphPower::lung
tmpd <- with(lung, data.frame(time = SurvTime, stat = 1-censor, grp = Treatment))

Generate the weight functions for maxcombo test

wmax <- gen.wgt(method = "Maxcombo")

Perform the test using pooled Kaplan-Meier estimate of CDF as base function and visualize the weight functions

t1 <- MaxLRtest(tmpd, Wlist = wmax, base = c("KM"),
  alternative = c("two.sided"))
plot(t1)

## Example 2 - sample size under proportional hazard The design setting is: 5 years’ entry time and 5 years’ follow-up time; Median survival for control group is 10 years. The hazard ratio comparing treatment and control is 0.5.

t_enrl <- 5; t_fup <- 5 ; lmd0 <- -log(0.2)/10 ; HR <- 0.5
eg1 <- pwr2n.LR(method = "schoenfeld", lambda0 = lmd0,
  lambda1 = lmd0*HR, entry = t_enrl, fup = t_fup)
#> ------------------------------------------ 
#>  -----Summary of the Input Parameters----- 
#> ------------------------------------------ 
#>        __Parameter__      __Value__
#>              Method     schoenfeld
#>  Lambda1/Lambda0/HR 0.08/0.161/0.5
#>          Entry Time              5
#>      Follow-up Time              5
#>    Allocation Ratio              1
#>        Type I Error           0.05
#>       Type II Error            0.1
#>         Alternative      two.sided
#>  Drop-out Parameter   Not Provided
#> ------------------------------------------ 
#>  -----Summary of the Output Parameters----- 
#>  ------------------------------------------ 
#>                __Parameter__ __Value__
#>            Number of Events    87.479
#>  Number of Total Sampe Size   153.173
#>          Overall Event Rate     0.571

Example 3 - sample size under nonproportional hazard

Design setting: patients are enrolled within 12 months and the last enrolled patient has at least 18 months’ follow-up. The medial survival time for control group is 12 months. The treatment has delayed effects. The hazard ratio is 0.75 after 6 months. Maxcombo test is used.

t_enrl <- 12; t_fup <- 18; lmd0 <- log(2)/12
f_hr_delay <- function(x){(x<=6)+(x>6)*0.75}
f_haz0 <- function(x){lmd0*x^0}
snph1 <- pwr2n.NPH(entry = t_enrl, fup = t_fup, Wlist = wmax,
 k = 50, ratio = 2, CtrlHaz = f_haz0, hazR = f_hr_delay)
#> -----Summary of the Input Parameters----- 
#>          parameter     value
#>             Method     MaxLR
#>         Entry Time        12
#>     Follow-up Time        18
#>   Allocation Ratio         2
#>       Type I Error      0.05
#>      Type II Error       0.1
#>        Alternative two.sided
#>  Number of Weights         4
#> -----Summary of the Output Parameters----- 
#>                    parameter    value
#>            Number of Events 1198.779
#>  Number of Total Sampe Size 1720.967
#>            Asymptotic Power    0.900
#>          Overall Event Rate    0.697

Example 4 - trial data simulation

A time-to-event data set with settings in example 3 is simulated.

N <- round(snph1$totalN, digits = 0)
set.seed(12345)
simu1 <- simu.trial(type = "time", trial_param = c(N,t_enrl,
  t_fup), bsl_dist = "weibull", bsl_param = c(1,lmd0),
  HR_fun = f_hr_delay, ratio = 1)
#> Notes: Drop-outs are not considered in the simulation.
#>  -------- Summary of the Simulation -------- 
#>                 parameter value
#> 1             Trial Type:  time
#> 2             Entry Time:    12
#> 3 Maximum Study Duration:    30
#> 4     Number of Subjects:  1721
#> 5       Number of Events:  1259

More functions can be found in the package.