bpp_1interim_t2e {bpp}

Bayesian Predictive Power (BPP) for Time-to-Event Endpoint

Description

Compute BPP and posterior density for a time-to-event endpoint, e.g. hazard ratio, assuming either an unblinded or blinded interim result.

Usage

bpp_1interim_t2e(prior = c("normal", "flat"), successHR, d,
                             IntEffBoundary, IntFutBoundary, IntFixHR, 
                             priorHR, propA = 0.5, thetas, ...)

Arguments

prior

Prior density on effect sizes.

successHR

The hazard ratio that defines success at the final analysis. We assume that hazard ratios below 1 are beneficial. Typically chosen to be the minimal detectable difference, i.e. the critical on the scale of the effect size of interest corresponding to the significance level at the final analysis.

d

2-d vector with number of events at interim and final analysis. Used to compute standard errors.

IntEffBoundary

Efficacy boundary at the interim analysis, hazard ratio.

IntFutBoundary

Futility boundary at the interim analysis, hazard ratio.

IntFixHR

Effect sizes observed at the interim analyis, to compute BPP for an unblinded interim analysis.

priorHR

Hazard ratio at which prior is centered.

propA

Proportion of subjects randomized to arm A.

thetas

Grid to compute posterior density on.

...

Further arguments specific to the chosen prior (see bpp_1interim_t2e for examples).

Value

A list containing the following elements:

initial BPP

BPP based on the prior.

BPP after not stopping at interim interval

BPP after not stopping at a blinded interim, provides the results corresponding to IntEffBoundary and IntFutBoundary.

BPP after not stopping at interim exact

BPP after not stopping at an unblinded interim, provides the results corresponding to IntFix.

posterior density interval

The posterior density, interval knowledge, i.e. corresponding to IntEffBoundary and IntFutBoundary.

posterior power interval

The posterior power, interval knowledge, i.e. corresponding to IntEffBoundary and IntFutBoundary.

posterior density exact

The posterior density, exact knowledge of interim result, i.e. corresponding to IntFix.

Author(s)

Kaspar Rufibach (maintainer)
[e-mail]

References

Rufibach, K., Jordan, P., Abt, M. (2016a). Sequentially Updating the Likelihood of Success of a Phase 3 Pivotal Time-to-Event Trial based on Interim Analyses or External Information. J. Biopharm. Stat., 26(2), 191–201.

Rufibach, K., Burger, H.U., Abt, M. (2016b). Bayesian Predictive Power: Choice of Prior and some Recommendations for its Use as Probability of Success in Drug Development. Pharm. Stat., 15, 438–446.

Examples

# number of events 
nevents <- c(191, 381)

# MDD at final analysis
hrMDD <-  0.8172823

# efficacy boundary
hrEffi <- 0.6508829

# futility boundary --> chosen informally
hrFuti <- 1

# prior specifications

# Normal prior corresponding to information of 50 events in 1:1 randomized trial
hr0 <- 0.7
sd0 <- sqrt(4 / 50)

# flat prior
width1 <- 0.5
height1 <- 1

# compute bpps
thetas <- seq(0.5, 1.35, by = 0.01)
bpp1b <- bpp_1interim_t2e(prior = "normal", successHR = hrMDD, d = nevents,
                          IntEffBoundary = hrEffi, IntFutBoundary = hrFuti, 
                          IntFixHR = 1, priorHR = hr0, propA = 0.5, thetas = thetas, 
                          priorsigma = sd0)[[1]]
bpp1_1b <- bpp_1interim_t2e(prior = "flat", successHR = hrMDD, d = nevents, 
                            IntEffBoundary = hrEffi, IntFutBoundary = hrFuti, 
                            IntFixHR = 1, priorHR = hr0, propA = 0.5, thetas = thetas, 
                            width = width1, height = height1)[[1]]