README.md

In Knusprikus/BSSRed: Blinded Sample Size Reestimation For Event Driven Trials

BSSRed (Blinded Sample Size Reestimation with Event-Driven Data.)

The goal of BSSRed is to provide the methods published by T. Friede et al. (Friede and Schmidli 2010), which main aspect lies on reestimation procedures.

Installation

You can install the released version of BSSRed from GITHUB with:

library("devtools")
install_git(url="https://github.com/ChristophAnten/BSSRed.git",
            upgrade=FALSE)
library("BSSRed")

Study Exapmle

This is a basic example to evaluate and varify a study plan with event driven data.

For this example it is assumed, that we have some prior information from other studies on witch we base our assumptions on the hazard and drop out rates.

We assume, that 30% of the patients in the control group have an event after 24 month and 20% of the patients across both group drop out of the study within 24 month. Assuming a 30% reduction of hazard in the treatment group.

library(BSSRed)

# assumed reduction of hazard by 30% 
# defining the hazard ratio 'theta'
theta = 1-.3

# hazard rate of control group is 30% after 24 month
lambdaC <- get_hazardRate(.3,24)
lambdaC
#> [1] 0.01486146

# the treatment group has a reduction of 30% after 24 month
lambdaT <- lambdaC*theta
lambdaT
#> [1] 0.01040302

# the overall dropout proportion is 20% after 24 months
gamma <- get_hazardRate(.2,24)
gamma
#> [1] 0.009297648

With a nominal alpha niveau of 5% (two-sided), the study aims for a power of 90%. The treatment allocation is planned to be 2:1 (treatment:control). With these additional assumptions we can calculate the required number of events to achive the targetet power as follows.

# define the alpha and beta error
alpha = .05
beta = .1

# set the alternative 
alternative = "two-sided"

# define the allocation parameter
k=2

# calculating the required number of events
nEvents <- nschoenfeld(theta = theta, k=k, alpha=alpha, beta=beta, alternative = "two-sided")
nEvents
#> [1] 371.6752

nEvents <- ceiling(nEvents)
nEvents
#> [1] 372

The recruitment is assumed to be linear with with a total of 1071 patients and an treatment allocation of 2:1 (tratment:control). The recruitment is assumend to be available at the start of each month.

# define the recruitment table
N_recruit <- set_recruitment(targetN=1071, k=2, timePoints=0:23)
head(N_recruit,5)
#>    T  C time
#> 1 30 15    0
#> 2 29 15    1
#> 3 30 15    2
#> 4 30 14    3
#> 5 30 15    4

colSums(N_recruit[,c("T","C")])
#>   T   C 
#> 714 357

# short overview of recruitments
barplot(names.arg =N_recruit$time,height=(t(cumsum(N_recruit[,c("T","C")]))),
        main = "Cummulative number of recruitments",col=c("grey33","grey88"))
legend("topleft",legend = c("T","C"),fill = c("grey33","grey88"),bty="n")

The study is planned to run for 48 months. With these information we can check if our recruitments will suffice to achieve the calculated number of events before 48 months.

# define the administrative censoring at the end of the study
L = 48

# calculate expected number of events
calc_expEvents(N_recruit[,1:2],theta,L,N_recruit[,3],lambdaC,gamma = gamma)
#>         T         C 
#> 254.79327  95.80526

Thes are not enough events to hold the assumptions. With we can calculate the additional recruitements we need.

# that is not enough we need
rEstimate(N=N_recruit[,1:2], tn=N_recruit[,3], theta=theta, nEvents=nEvents, L=L,
                  lambda=lambdaC, gamma = gamma, distC="exponential",distS="exponential")
#> $rec_batch
#> [1] 26
#> 
#> $rec_time
#> [1] 25
#> 
#> $rec_total_number
#>   T   C 
#> 774 387

So we need to recruit 1161 patients or we need 26 batches of recruits. The last recruitment arrives at timepoint 25.

AS the final step we can simulate the study and observe the impact of misspecification of the assumed hazard ratio theta on the study duration.

# simulating the study
res <- sim_BSSRed(N=N_recruit[,1:2],tn=N_recruit[,3],M=as.matrix(N_recruit[24,1:2,drop=F]),
                  tm=25,addRecT=c(2,4,6),
                  sim.lambdaP = get_hazardRate(seq(.2,.4,length.out = 9),24), sigma=1,
                  theta=theta,gamma=gamma,kappa=1,distS="exponential",distC="exponential",nEvents=nEvents,
                  L=L,nSim=100, par.est=FALSE, fixed.min.studytime=FALSE, seed=235711)

Show the results …

library(plyr)
#> Warning: package 'plyr' was built under R version 3.6.3
library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:plyr':
#> 
#>     arrange, count, desc, failwith, id, mutate, rename, summarise,
#>     summarize
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
library(ggplot2)
#> Warning: package 'ggplot2' was built under R version 3.6.3
res$results %>%
  group_by(lambda,type) %>%
  summarise_all(mean) %>%
  ungroup() %>%
  mutate(lambda = 1-exp(-lambda*24)) %>%
  ggplot(aes(x=lambda,y=study.end,col=factor(type))) +
  geom_point() +
  geom_hline(yintercept = L,lty=2,col="darkgrey") +
  geom_line() +
  ggtitle(sprintf("Mean Time to End of Study (nEvent=%i)",ceiling(nEvents))) +
  theme_bw() +
  ylab("Mean study duration") +
  xlab("24 month conifrmed progression probability")# +

# scale_y_continuous(breaks = seq(30,70,by=10),limits = c(30,70))
res$results %>%
  group_by(lambda,type) %>%
  summarise_all(mean) %>%
  ungroup() %>%
  mutate(lambda = 1-exp(-lambda*24)) %>%
  ggplot(aes(x=lambda,y=nPop-1161,col=factor(type))) +
  geom_point() +
  geom_line() +
  ggtitle(sprintf("Mean number of Additional Patients (nEvent=%i)",ceiling(nEvents))) +
  ylab("Mean number of additional patients") +
  xlab("24 month conifrmed progression probability") +
  theme_bw()# +

# scale_y_continuous(breaks = seq(0,700,by=100),limits = c(0,700))

res$results %>%
  group_by(lambda,type) %>%
  mutate(power = BSSRed::pschoenfeld(theta = theta,
                                     nEvent = events,
                                     k = 2,
                                     alpha = .05,
                                     alternative = "two-sided")) %>%
  summarise_all(mean) %>%
  ungroup() %>%
  mutate(lambda = 1-exp(-lambda*24)) %>%
  ggplot(aes(x=lambda,y=power,col=factor(type))) +
  geom_point() +
  geom_line() +
  geom_hline(yintercept = 1-.1,lty=2,col="darkgrey") +
  ggtitle(sprintf("Power at End of Study (nEvent=%i)",ceiling(nEvents))) +
  ylab("Mean power") +
  xlab("24 month conifrmed progression probability") +
  theme_bw()

References

Friede, Tim, and Heinz Schmidli. 2010. “Blinded Sample Size Reestimation with Count Data: Methods and Applications in Multiple Sclerosis.” *Statistics in Medicine* 29 (10): 1145–56.

Knusprikus/BSSRed documentation built on July 6, 2020, 11:02 p.m.