gsDesign (version 2.4-01)

gsBoundSummary: 2.8: Bound Summary and Z-transformations

Description

Z-value test statistic transformations are commonly used as supplementary descriptions of bounds. gsBoundSummary() summarizes a bound for a group sequential design with by computing several of these design characteristics. xtable.gsDesign produces Latex output of boundary summary information; intended for use with Sweave(). Individual transformation of z-value test statistics for interim and final analyses are obtained from gsBValue(), gsDelta(), gsHR() and gsCPz() for B-values, approximate treatment effect (see details), approximate hazard ratio and conditional power, respectively.

Usage

gsBValue <- function(z, i, x, ylab="B-value", ...)
    gsDelta(z, i, x, ylab=NULL, ...)
    gsHR(z, i, x, ratio=1, ylab="Estimated hazard ratio", ...)
    gsRR(z, i, x, ratio=1, ylab="Estimated risk ratio",...)
    gsCPz(z, i, x, theta=NULL, ylab=NULL, ...)
    gsBoundSummary(x, upper=TRUE, ratio=1)
    xtable.gsDesign(x, caption=NULL, label=NULL, align=NULL, digits=c(0,0,3,4,4,4,3,3,3,3),
                             display=NULL, upper=TRUE, rnames=NULL, cnames=NULL, ratio=1,
                             sanitize.text.function=function(x){x}, 
                             sanitize.rownames.function=function(x){x},...)

Arguments

x

A gsDesign object

upper

If TRUE, upper bound is summarized. If FALSE, lower bound is summarized

z

A vector of z-statistics

i

A vector containing the analysis for each element in z; each element must be in 1 to x$k, inclusive

theta

A scalar value used for conditional power calculations; see gsDesign; if NULL, conditional power is computed at the estimated interim treatment effect based on z

ylab

Used when functions are passed to plot.gsDesign to establish default y-axis labels

ratio

Used only for time-to-event studies; randomization ratio for experimental versus control group

digits

An integer vector containing the digits to be displayed for each row

rnames

Allows user to override default row names for output matrix

cnames

Allows user to override default column names for output matrix

...

This allows many optional arguments that are standard when calling xtable and plot

caption

See dcoumentation for xtable

label

See dcoumentation for xtable

align

See dcoumentation for xtable

display

See dcoumentation for xtable

sanitize.text.function

Should be able to use default; see documentation for xtable

sanitize.rownames.function

Should be able to use default; see documentation for xtable and print

Value

• gsBValue(), gsDelta(), gsHR() and gsCPz() each returns a vector containing the B-values, approximate treatment effect (see details), approximate hazard ratio and conditional power, respectively, for each value specified by the interim test statistics in z at interim analyses specified in i. gsBoundSummary returns an matrix. The rows correspond to the analyses planned in x. For each interim, the columns provide 1) timing (%), 2) sample size ("N"), events ("Events") or sample size inflation relative to a fixed design ("r"), 3) Z, 4) nominal p-value (upper tail for upper bound, lower tail for lower bound), 5) cumulative boundary crossing probability (spend) under the null hypothesis, 6) cumulative spend under the alternate hypothesis, 7) conditional power at the bound assuming the alternate hypothesis treatment effect, 8) conditional power at the bound assuming the interim trend, 9) treatment effect at the boundary (hazard ratio for time-to-event endpoint studies), 10) B-value.

Details

See examples and manual

References

Jennison C and Turnbull BW (2000), Group Sequential Methods with Applications to Clinical Trials. Boca Raton: Chapman and Hall.

See Also

gsDesign, Plots for group sequential designs, gsProbability

Examples

# derive group sequential bound
x <- gsDesign(n.fix=100)

# upper bound summary
gsBoundSummary(x)

# lower bound summary
gsBoundSummary(x, upper=FALSE)

# print upper bound summary in latex format
xtable(x)

# print lower bound summary in latex format
xtable(x, upper=FALSE)

# now derive a design with a time-to-event endpoint
# note that by specifying endpoint="Survival", hazard ratio replaces treatment effect
ns <- nSurvival()
xs <- gsDesign(n.fix=ns$nEvents, nFixSurv=ns$n, endpoint="Survival")
gsBoundSummary(xs)
# generate some of the above summary statistics for the upper bound
z <- xs$upper$bound
# B-values
gsBValue(z=z, i=1:3, x=xs)
# hazard ratio
gsHR(z=z, i=1:3, x=xs)
# conditional power at observed treatment effect
gsCPz(z=z[1:2], i=1:2, x=xs)
# conditional power at H1 treatment effect
gsCPz(z=z[1:2], i=1:2, x=xs, theta=xs$delta)

# now look at a binomial endpoint; specify H0 treatment difference as p1-p2=.05
# now treatment effect at bound (say, thetahat) is transformed to 
# xp$delta0 + xp$delta1*(thetahat-xp$delta0)/xp$delta  
np <- nBinomial(p1=.15, p2=.10)
xp <- gsDesign(n.fix=np, endpoint="Binomial", delta1=.05)
gsBoundSummary(xp)
# estimate treatment effect at lower bound
# by setting delta0=0 (default) and delta1 above in gsDesign
# treatment effect at bounds is scaled to these differences
# in this case, this is the difference in event rates
gsDelta(z=xp$lower$bound, i=1:3, xp)
# binomial endpoint with risk ratio estimates
xrr <- gsDesign(n.fix=np, endpoint="Binomial", delta1=log(2/3))
gsRR(z=xp$lower$bound, i=1:3, xrr)
plot(xrr,plottype="RR")