cpower(tref, n, mc, r, accrual, tmin, noncomp.c=0, noncomp.i=0, alpha=0.05, nc, ni, pr=TRUE)
n/2
observations in each group, you may specify
the sample sizes in
nc
and
ni
.
mc
by intervention
nc
and
ni
are specified
exclusive of
n
.
FALSE
to suppress printing of details
For handling noncompliance, uses a modification of formula (5.4) of
Lachin and Foulkes. Their method is based on a test for the difference
in two hazard rates, whereas
cpower
is based on testing the difference
in two log hazards. It is assumed here that the same correction factor
can be approximately applied to the log hazard ratio as Lachin and Foulkes applied to
the hazard difference.
Note that Schoenfeld approximates the variance
of the log hazard ratio by
4/m
, where
m
is the total number of events,
whereas the George-Desu method uses the slightly better
1/m1 + 1/m2
.
Power from this function will thus differ slightly from that obtained with
the SAS
samsizc
program.
Frank Harrell
Department of Biostatistics
Vanderbilt University
f.harrell@vanderbilt.edu
Peterson B, George SL: Controlled Clinical Trials 14:511–522; 1993.
Lachin JM, Foulkes MA: Biometrics 42:507–519; 1986.
Schoenfeld D: Biometrics 39:499–503; 1983.
#In this example, 4 plots are drawn on one page, one plot for each #combination of noncompliance percentage. Within a plot, the #5-year mortality % in the control group is on the x-axis, and #separate curves are drawn for several % reductions in mortality #with the intervention. The accrual period is 1.5y, with all #patients followed at least 5y and some 6.5y. par(mfrow=c(2,2),oma=c(3,0,3,0)) morts <- seq(10,25,length=50) red <- c(10,15,20,25) for(noncomp in c(0,10,15,-1)) { if(noncomp>=0) nc.i <- nc.c <- noncomp else {nc.i <- 25; nc.c <- 15} z <- paste("Drop-in ",nc.c,"%, Non-adherence ",nc.i,"%",sep="") plot(0,0,xlim=range(morts),ylim=c(0,1), xlab="5-year Mortality in Control Patients (%)", ylab="Power",type="n") title(z) cat(z,"\n") lty <- 0 for(r in red) { lty <- lty+1 power <- morts i <- 0 for(m in morts) { i <- i+1 power[i] <- cpower(5, 14000, m/100, r, 1.5, 5, nc.c, nc.i, pr=FALSE) } lines(morts, power, lty=lty) } if(noncomp==0)legend(18,.55,rev(paste(red,"% reduction",sep="")), lty=4:1,bty="n") } mtitle("Power vs Non-Adherence for Main Comparison", ll="alpha=.05, 2-tailed, Total N=14000",cex.l=.8) # # Point sample size requirement vs. mortality reduction # Root finder (uniroot()) assumes needed sample size is between # 1000 and 40000 # nc.i <- 25; nc.c <- 15; mort <- .18 red <- seq(10,25,by=.25) samsiz <- red i <- 0 for(r in red) { i <- i+1 samsiz[i] <- uniroot(function(x) cpower(5, x, mort, r, 1.5, 5, nc.c, nc.i, pr=FALSE) - .8, c(1000,40000))$root } samsiz <- samsiz/1000 par(mfrow=c(1,1)) plot(red, samsiz, xlab='% Reduction in 5-Year Mortality', ylab='Total Sample Size (Thousands)', type='n') lines(red, samsiz, lwd=2) title('Sample Size for Power=0.80\nDrop-in 15%, Non-adherence 25%') title(sub='alpha=0.05, 2-tailed', adj=0)