Update group sequential bounds with observed information

Given a planned gsNB (or gsDesign) object and observed statistical information at one or more analyses, recompute the group sequential boundaries and return an updated design object together with a gsDesign::gsBoundSummary()-style table.

Usage

update_gsNB(design, observed_info, spending_time = NULL)

Arguments

design: A gsNB or gsDesign object produced by gsNBCalendar() (or gsDesign::gsDesign()).
observed_info: Numeric vector of observed statistical information at each analysis conducted so far. Its length must be between 1 and design$k. If shorter than design$k, information at future analyses is projected from the planned design.
spending_time: Optional numeric vector the same length as observed_info giving the spending time (between 0 and 1) for each analysis. When NULL, spending time equals the information fraction. If shorter than design$k, future spending times are taken from the planned design.

Value

A list with components:

design: The updated gsDesign object with recalculated boundaries.
bounds: A data frame from gsDesign::gsBoundSummary() showing Z-boundaries, nominal p-values, approximate treatment effects at the boundary, and cumulative crossing probabilities at each analysis.
info: A data frame with one row per analysis containing the information fraction (IF), spending time (spending_time), upper and lower Z-boundaries, and cumulative upper and lower spending.

Details

The observed information determines the covariance structure of the test statistics (via the information fraction timing), while spending_time controls how much of the error-spending budget has been used. When spending_time is NULL (the default), spending is driven by the observed information fraction. Supplying an explicit spending_time is useful when the monitoring charter specifies calendar-driven spending that differs from the observed information fraction.

Examples

library(gsDesign)
#> 
#> Attaching package: ‘gsDesign’
#> The following object is masked from ‘package:gsDesignNB’:
#> 
#>     toInteger
nb_ss <- sample_size_nbinom(
  lambda1 = 0.5, lambda2 = 0.3, dispersion = 0.1, power = 0.9,
  accrual_rate = 10, accrual_duration = 20, trial_duration = 24
)
gs <- gsNBCalendar(nb_ss, k = 3, analysis_times = c(12, 18, 24))

# After observing information at the first interim
upd <- update_gsNB(gs, observed_info = gs$n.I[1] * 0.95)
upd$bounds
#>   Analysis               Value Efficacy Futility
#>  IA 1: 32%                   Z   3.0253  -0.2814
#>      N: 15         p (1-sided)   0.0012   0.6108
#>                ~delta at bound   1.5860  -0.1475
#>            P(Cross) if delta=0   0.0012   0.3892
#>            P(Cross) if delta=1   0.1318   0.0143
#>  IA 2: 64%                   Z   2.5838   0.8587
#>      N: 28         p (1-sided)   0.0049   0.1953
#>                ~delta at bound   0.9615   0.3195
#>            P(Cross) if delta=0   0.0057   0.8138
#>            P(Cross) if delta=1   0.5475   0.0411
#>      Final                   Z   1.9967   1.9967
#>      N: 44         p (1-sided)   0.0229   0.0229
#>                ~delta at bound   0.5963   0.5963
#>            P(Cross) if delta=0   0.0234   0.9766
#>            P(Cross) if delta=1   0.9000   0.1000
upd$info
#>   Analysis     IF spending_time upper_bound lower_bound cum_upper_spend
#> 1        1 0.3245        0.3245      3.0253     -0.2814        0.001242
#> 2        2 0.6441        0.6441      2.5838      0.8587        0.005668
#> 3        3 1.0000        1.0000      1.9967      1.9967        0.025000
#>   cum_lower_spend
#> 1        0.014302
#> 2        0.041108
#> 3        0.100000