EX1gXK {PwrGSD}

A function for computing the bias adjusted point estimate for a statistic observed to cross the efficacy boundary.

Description

A function for computing the bias adjusted point estimate for a statistic, on the Brownian scale, observed to cross the efficacy boundary.

Usage

EX1gXK(xk, b.eff, frac)

Arguments

xk

The observed value of the statistic, on the “Brownian” scale.

b.eff

Efficacy boundary points at current and prior analyses

frac

Information fraction at current and prior analyses

Value

Returns the expected value of X_1 given X_K, which is the bias adjusted point estimate

Note

This works for the unweighted, proportional hazards case, but also works in the case of the weighted log-rank statistic when we assume the chosen weights are proportional to the true shape.

Author(s)

Grant Izmirlian <[e-mail]>

References

Emerson, S. S. (1993). Computation of the uniform minimum variance unibiased estimator of a normal mean following a group sequential trialdiscrete sequential boundaries for clinical trials. Computers and Biomedical Research 26 68–73.

Izmirlian, G. (2014). Estimation of the relative risk following group sequential procedure based upon the weighted log-rank statistic. Statistics and its Interface 00 00–00

See Also

gsd.dens

Examples

# if Z.K = U_K/V_K^0.5 is the log-rank statistic on the standard normal
# scale, then we obtain an estimate of the logged relative risk as follows
# Suppose we've stopped at analysis number K=4, and Z.K = 2.5
# suppose the end of trial variance of the log-rank statistic
# (specified in design and used to compute 'frac') is V.end = 100

K <- 4
Z.K <- 2.5
V.end <- 100

# Information fraction
frac <- c(0.15, 0.37, 0.64, 0.76)

# Efficacy Boundary 
gsb <- GrpSeqBnds(frac=frac, EfficacyBoundary=LanDemets(spending=ObrienFleming, alpha=0.05))

# Efficacy boundary points
be <- gsb$table[,"b.e"] 

# Brownian scale
X.K <- Z.K*frac[K]

# expected value of X_1 given X_K
ex1gxk <- EX1gXK(X.K, be, frac)

# Crude estimate of logged relative risk
X.K/(frac[K]*V.end^0.5)

# Bias adjusted estimate of logged relative risk
ex1gxk/(frac[1]*V.end^0.5)