SMARTAR (version 1.0.0)

smartest: Conduct statistical tests using a SMART data

Description

Return a message that contains the results of statistical tests to compare the values of adaptive treatment strategies defined in a SMART data. The statistical tests include (1) a global test (2) a series of pairwise tests.

Usage

smartest(data, family = "normal", method = "Gest", common = FALSE,
  alpha = 0.05, adjust = NULL, ntest = NULL)

Arguments

data

Input data frame of the SMART data used for analysis, which include the variables of stage-1 treatments (A1), intermediate outcome (O2), stage-2 treatment (A2) and final primary outcome (Y). If stage-1 treatment takes into account baseline information, baseline information (O1) also needs to be included.

family

A character string to specify the type of final primary outcome. The default is family=<U+201C>normal<U+201D>, which refers to the continuous primary outcome. If family=<U+201D>binomial<U+201D> then the primary outcome will be treated as binary variable.

method

Method used to estimate the value of adaptive treatment strategy. "Gest" for G-computation method and "IPW" for Inversed Probabiliy Weight method. Default is method="Gest".

common

If common=TRUE, the pooled variance across all the treatment sequences are used in estimation. Otherwise use the sequence-specific variance. The default is common=FALSE.

alpha

Significant level of confidence interval. The default is alpha=0.05.

adjust

A characteristic string to indicate whether the confidence intervals pairwise distance adjusted for multiple comparison. The default is adjust=<U+201D>n<U+201D>, which indicated no adjustment for multiple comparison. If adjust=<U+201D>Bon<U+201D>, the CIs are adjusted for the Bonferroni correction.

ntest

Number of pairwise tests adjusted for Bonferroni correction

Value

An objects of <U+201C>Strategy<U+201D> is return, which lists all the adaptive treatment strategy defined in the input data with an index number.

• ATS: Index of the treatment adaptive treatment strategy defined in the input dataset

• ds: the sequence of decision makings that define an adaptive treatment strategy

• N: number of subjects following an adaptive treatment strategy in the intut dataset

An objects of "Global.test" is return, which give the result of the global test.

• size: the total number of subjects in the input dataset

• nATS: the total number of adaptive treatment strategies defined in the input dataset

• df: the degrees of freedom of the global test, which is a chisquare test

• chisq: the chisquare test statistics for the global test

• Pvalue: the P-value of the global test

An object of "Pairwise.test"

• label: The labels of pairwise tests. The details of strategies are shown in $Strategy

• diff: Estimated pairwise distance between treatment and control adaptive treatment strategy

• lower.CI: Lower bound of confidence interval for pairwise distance

• upper.CI: Upper bound of confidence interval for pairwise distance

• Z: Test statistics of pairwise test

• P-value: P-value of pairwise test

References

Murphy, S. A. (2005),``An experimental design for the development of adaptive treatment strategies'' Statistics in Medicine, 24, 1455-1481.

Ogbagaber S. B., Karp, J., and Wahed A.S. (2015), ``Design of sequentially randomization trials for testing adaptive treatment strategies,'' Statistics in Medicine, DOI: 10.1002/sim.6747.

Examples

# NOT RUN {
#generate a pesudo SMART data
N=8000                       # total sample size
A1=O2=A2=Y=rep(NA,N)
Dat=data.frame(A1,O2,A2,Y)

# stage-1 treatment
Dat$A1=sample(c(0,1),size=N,prob=c(1,1),replace=TRUE)

# intermediate outcome
n0=length(Dat$A1[which(Dat$A1==0)]); n1=N-n0
Dat$O2[which(Dat$A1==0)]=rbinom(n=n0,size=1,p=0.6)
Dat$O2[which(Dat$A1==1)]=rbinom(n=n1,size=1,p=0.4)

# stage-2 treatment
n00=nrow(Dat[which(Dat$A1==0 & Dat$O2==0),]); n01=n0-n00
n10=nrow(Dat[which(Dat$A1==1 & Dat$O2==0),]); n11=n1-n10
Dat$A2[which(Dat$A1==0 & Dat$O2==0)]=sample(c(0,1),size=n00,prob=c(1,1),replace=TRUE)
Dat$A2[which(Dat$A1==0 & Dat$O2==1)]=sample(c(0,1),size=n01,prob=c(1,1),replace=TRUE)
Dat$A2[which(Dat$A1==1 & Dat$O2==0)]=sample(c(0,1),size=n10,prob=c(1,1),replace=TRUE)
Dat$A2[which(Dat$A1==1 & Dat$O2==1)]=sample(c(0,1),size=n11,prob=c(1,1),replace=TRUE)

n000=nrow(Dat[which(Dat$A1==0 & Dat$O2==0 & Dat$A2==0),]); n001=n00-n000
n010=nrow(Dat[which(Dat$A1==0 & Dat$O2==1 & Dat$A2==0),]); n011=n01-n010
n100=nrow(Dat[which(Dat$A1==1 & Dat$O2==0 & Dat$A2==0),]); n101=n10-n100
n110=nrow(Dat[which(Dat$A1==1 & Dat$O2==1 & Dat$A2==0),]); n111=n11-n110

# final primary outcome
Dat$Y[which(Dat$A1==0 & Dat$O2==0 & Dat$A2==0)]=rnorm(n=n000,mean=7,sd=6)
Dat$Y[which(Dat$A1==0 & Dat$O2==0 & Dat$A2==1)]=rnorm(n=n001,mean=7,sd=6)
Dat$Y[which(Dat$A1==0 & Dat$O2==1 & Dat$A2==0)]=rnorm(n=n010,mean=7,sd=8)
Dat$Y[which(Dat$A1==0 & Dat$O2==1 & Dat$A2==1)]=rnorm(n=n011,mean=7,sd=8)
Dat$Y[which(Dat$A1==1 & Dat$O2==0 & Dat$A2==0)]=rnorm(n=n100,mean=7,sd=6)
Dat$Y[which(Dat$A1==1 & Dat$O2==0 & Dat$A2==1)]=rnorm(n=n101,mean=7,sd=6)
Dat$Y[which(Dat$A1==1 & Dat$O2==1 & Dat$A2==0)]=rnorm(n=n110,mean=7,sd=8)
Dat$Y[which(Dat$A1==1 & Dat$O2==1 & Dat$A2==1)]=rnorm(n=n111,mean=7,sd=8)

smartest(data=Dat,family="normal",method="Gest",common=FALSE,alpha=0.05,adjust="Bon")

# }