carat (version 1.1)

boot.test: Bootstrap t-test

Description

Performs bootstrap t-test on treatment effects. This test is proposed by Shao et al. (2010) <doi:10.1093/biomet/asq014>.

Usage

boot.test(data, B = 200, method = HuHuCAR, conf = 0.95, …)

Arguments

data

a dataframe. It consists of patients' profiles, treatment assignments and outputs. See getData.

B

an integer. It indicates the number of bootstrap samples. The default is 200.

method

the method of randomization to be used in allocating patients. The default randomization method HuHuCAR uses Hu and Hu's general covariate-adaptive randomization; the alternatives are PocSimMIN, StrBCD, StrPBR, DoptBCD, and AdjBCD.

conf

confidence level of the interval. The default is 0.95.

…

arguments to be passed to methods. These depend on the method used and the following arguments are accepted:

omega

a vector of weights at the overall, within-stratum, and maginal levels. It is required that at least one element is larger than 0. Note that omega is only needed when HuHuCAR is to be used.

weight

a vector of weights for marginal imbalances. It is required that at least one element is larger than 0. Note that weight is only needed when PocSimMIN is to be used.

p

the probabillty of assigning one patient to treatment 1. p should be larger than 1/2 to obtain balance. Note that p is only needed when "HuHuCAR", "PocSimMIN" and "StrBCD" are to be used.

a

a design parameter. As a goes to \(\infty\), the design becomes more deterministic.

bsize

the block size for stratified randomization. It is required to be a multiple of 2. Note that bsize is only needed when "StrPBR" is to be used.

Value

It returns an object of class "htest".

The function print is used to obtain results. The generic accessor functions statistic, p.value, conf.int and others extract various useful features of the value returned by boot.test.

An object of class "htest" is a list containing at least the following components:

data.name

a character string giving the name(s) of the data.

statistic

the value of the t-statistic.

pval

the p-value of the test,the null hypothesis is rejected if p-value is less than the pre-determined significance level.

conf.int

a confidence interval under the chosen level conf for the difference in treatment effect between treatment 1 and treatment 2.

estimate

the estimated treatment effect difference between treatment 1 and treatment 2.

method

a character string indicating what type of test was performed.

Details

The bootstrap t-test is described as follows:

1) Generate bootstrap data (\(Y_1^*,Z_1^*), \dots, (Y_n^*,Z_n^*)\) as a simple random sample with replacement from the original data \((Y_1,Z_1), \dots,(Y_n,Z_n)\), where \(Y_i\) denotes the outcome and \(Z_i\) denotes the profile of the \(i\)th patient.

2) Perform covariate-adaptive procedures on the patients' profiles to obtain new treatment assignments \(T_1^*,\dots,T_n^*\), and define $$\hat{\theta}^* = -\frac{1}{n_1^*}\sum\limits_{i=1}^n (T_i^*-2) \times Y_i^* - \frac{1}{n_0^*}\sum\limits_{i=1}^n (T_i^*-1) \times Y_i$$ where \(n_1^*\) is the number of patients assigned to treatment \(1\) and \(n_0^*\) is the number of patients assigned to treatment \(2\).

3) Repeat step 2 \(B\) times to generate \(B\) independent boostrap samples to obtain \(\hat{\theta}^*_b\), \(b = 1,\dots,B\). The variance of \(\bar{Y}_1 - \bar{Y}_0\) can then be approximated by the sample variance of \(\hat{\theta}^*_b\).

References

Shao J, Yu X, Zhong B. A theory for testing hypotheses under covariate-adaptive randomization[J]. Biometrika, 2010, 97(2): 347-360.

Examples

# NOT RUN {
#Suppose the data used is patients' profile from real world, 
#  while it is generated here. Data needs to be preprocessed 
#  and then get assignments following certain randomization.
set.seed(100)
df<- data.frame("gender" = sample(c("female", "male"), 100, TRUE, c(1 / 3, 2 / 3)),
                "age" = sample(c("0-30", "30-50", ">50"), 100, TRUE),
                "jobs" = sample(c("stu.", "teac.", "other"), 100, TRUE, c(0.4, 0.2, 0.4)), 
                stringsAsFactors = TRUE)
##data preprocessing
data.pd <- StrPBR(data = df, bsize = 4)$Cov_Assig

#Then we need to combine patients' profiles and outcomes after randomization and treatments.
outcome = runif(100)
data.combined = data.frame(rbind(data.pd,outcome), stringsAsFactors = TRUE)

#run the bootstrap t-test
B = 200
Strbt = boot.test(data.combined, B, StrPBR, bsize = 4)
Strbt
# }