SMARTAR (version 1.0.0)

atsmeans: Identify adaptive treatment strategy and estimate strategy values

Description

Return a message that lists all the adaptive treatment strategy embedded in SMART design. It also gives the estiamted strategy values and the variance-covariance matrix of estimated values.

Usage

atsmeans(data, family = "normal", method = "Gest", common = FALSE,
  conf = TRUE, alpha = 0.05, plot = FALSE)

Arguments

data

Input data frame of the sequential randomized trial (SMART) data used for analysis. The data should include the variables of stage-specific treatments (At; t=1,2,3), intermediate evaluation (Ot; t=1,2,3) and final primary outcome (Y), where t represent the number of stages embedded in design. If stage-1 treatment (A1) takes into account the information of baseline evaluation, O1 needed to be include in data, otherwise not.

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

A character string to specify the method of estimation. If method=``Gest'' then G-computation method is used. If method=``IPW'' then Inversed Probability Weighting method is used.

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.

conf

If conf=TRUE, output confidence intervals for estimate strategy values. The default is conf=FALSE.

alpha

Type I error rate control for confidence interval. The default is alpha=0.05.

plot

If plot=TRUE, output the graphs of treatment effects with CIs.

Value

An object of ``value<U+201D> is return, which contain the index of all the adaptive treatment strategies, strategy-specific sample sizes and estimated values with standardized errors.

• ATS: Index of adaptive treatment strategy from 1 to G, where G is total number of strategies defined in SMART

• ds: Stage-specific decision makings given certain histories corresponding to each strategy. The number of columns of ``ds'' is defined by strategy and details are shown in the output.

• N: Number of subjects following a strategy.

• value: Estimated strategy values.

• se: standard errors of estimation

• lower.CI: Lower bound of (1-alpha) level confidence interval for strategy values

• upper.CI: Upper bound of (1-alpha) level confidence interval for strategy values

An object of ``vmat'' is return, which is variance-covariance matrix of estimated strategy values

References

Lavori P.W. and Dawson R. (2007). Improving the efficiency of estimation in randomization trials of adaptive treatment strategies. Clinical Trials, 4: 297-308.

Ko and Wahed A.S. (2015). Design of sequentially randomization trials for testing adaptive treatment strategies. Statistics in Medicine, 31, 812-830.

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)

atsmeans(data=Dat,family="normal",method="Gest",conf=TRUE,common=TRUE,alpha=0.05,plot=TRUE)

# }