DTR (version 1.2)

CHR.Wald.test: Function to compare dynamic treatment regimes (DTRs) based on cumulative hazard ratios (CHRs)

Description

This function compares the cumulative hazard functions of dynamic treatment regimes (DTRs) from sequentially randomized clinical trials by calculating the natural logarithms of cumulative hazard ratios (CHRs) and performing the Wald-type tests based on natural logarithms of CHRs as proposed in Tang and Wahed (2013) [Epub ahead of print]. For simplicity, and to maintain similarity to the most common sequentially randomized clinical trials, a simple two-stage randomization design allowing two treatment options at each stage is implemented in the current version of the function.

Usage

CHR.Wald.test(fdata, t=quantile(fdata$U, 0.75))

Arguments

fdata

a data frame (X, R, Z, U, delta, V) representing the full data from a simple two stage randomization design with therapies A1 and A2 available at the first stage, and B1 and B2 available at the second stage. X: first-stage indicator, X=0 if assigned to A

t

a time point of interest. For example, t=5 for the comparisons of survival estimates at 5 years among DTRs. Default t is set to be the 75th percentile of the observed time (i.e. 75th percentile of U).

Value

• The function returns a data set with columns: H0, test statistic, and p-value.
• H0
  the null hypotheses being tested, for example, H0 (t=3) for comparisons made at 3 years
• test statistic
  the calculated chi-square test statistic
• p
  the resulting p-value

Details

In sequentially randomized designs, there could be more than two therapies available at each stage. For simplicity, and to maintain similarity to the most common sequentially randomized clinical trials, a simple two-stage randomization design allowing two treatment options at each stage is used in the current version of the package. In detail, patients are initially randomized to either A1 or A2 at the first stage. Based on their response status, they are then randomized to either B1 or B2 at the second stage. Therefore, there are a total of four dynamic treatment regimes (DTRs): A1B1, A1B2, A2B1, and A2B2. Two different comparisons are performed: 1) An overall comparison H0: A1B1=A1B2=A2B1=A2B2 2) Pairwise comparisons including H0: A1B1=A1B2, H0: A1B1=A2B1, H0: A1B1=A2B2, H0: A1B2=A2B1, H0: A1B2=A2B2, and H0: A2B1=A2B2

References

Tang X, Wahed AS: Cumulative hazard ratio estimation for treatment regimes in sequentially randomized clinical trials. Statistics in Biosciences, 2013 [Epub ahead of print]

See Also

DTR, sim.CHR.data, updateBeta, CHR.estimator, DTR.CHR.plot

Examples

require(DTR)
  
#-------Example function usage-----------
n <- 800
max.c <- 5
pi.x <- 0.5
pi.r <- 0.6
pi.z <- 0.5
gamma10 <- 1
gamma11 <- 1.5
gamma12 <- 1.2
gamma20 <- 1
gamma21 <- 1.5
gamma22 <- 1.3
alpha10 <- 0.5
alpha11 <- 0.2
alpha12 <- 0.1
alpha20 <- 0.5
alpha21 <- 0.2
alpha22 <- 0.05
beta <- c(0.5, 0.5)

set.seed(123)
fdata <- sim.CHR.data(n,max.c,pi.x,pi.r,pi.z,gamma10,gamma11,gamma12,
gamma20,gamma21,gamma22,alpha10,alpha11,alpha12,alpha20,alpha21,alpha22,beta)

CHR.Wald.test(fdata, t=3) # Testing