Translate survival design bounds to exact binomial bounds

Translate survival design bounds to exact binomial bounds

Usage

toBinomialExact(x, observedEvents = NULL)

Arguments

x

An object of class gsSurv; i.e., an object generated by the gsSurv() function.

observedEvents

If NULL (default), targeted timing of analyses will come from x$n.I. Otherwise, this should be vector of increasing positive integers with at most 1 value >= x$n.IPlan and of length at least 2. Only one value can be greater than or equal to x$maxn.IPlan. This determines the case count at each analysis performed. Primarily, this is used for updating a design at the time of analysis.

Value

An object of class gsBinomialExact.

Details

The exact binomial routine gsBinomialExact has requirements that may not be satisfied by the initial asymptotic approximation. Thus, the approximations are updated to satisfy the following requirements of gsBinomialExact: a (the efficacy bound) must be positive, non-decreasing, and strictly less than n.I b (the futility bound) must be positive, non-decreasing, strictly greater than a n.I - b must be non-decreasing and >= 0

See also

gsBinomialExact

Examples

# The following code derives the group sequential design using the method
# of Lachin and Foulkes

x <- gsSurv(
  k = 3,                 # 3 analyses
  test.type = 4,         # Non-binding futility bound 1 (no futility bound) and 4 are allowable
  alpha = .025,          # 1-sided Type I error
  beta = .1,             # Type II error (1 - power)
  timing = c(0.45, 0.7), # Proportion of final planned events at interims
  sfu = sfHSD,           # Efficacy spending function
  sfupar = -4,           # Parameter for efficacy spending function
  sfl = sfLDOF,          # Futility spending function; not needed for test.type = 1
  sflpar = 0,            # Parameter for futility spending function
  lambdaC = .001,        # Exponential failure rate
  hr = 0.3,              # Assumed proportional hazard ratio (1 - vaccine efficacy = 1 - VE)
  hr0 = 0.7,             # Null hypothesis VE
  eta = 5e-04,           # Exponential dropout rate
  gamma = 10,            # Piecewise exponential enrollment rates
  R = 16,                # Time period durations for enrollment rates in gamma
  T = 24,                # Planned trial duration
  minfup = 8,            # Planned minimum follow-up
  ratio = 3              # Randomization ratio (experimental:control)
)
# Convert bounds to exact binomial bounds
toBinomialExact(x)
#>              Bounds
#>   Analysis   N   a   b
#>          1  31  12  22
#>          2  48  23  30
#>          3  69  38  39
#> 
#> Boundary crossing probabilities and expected sample size assume
#> any cross stops the trial
#> 
#> Upper boundary
#>           Analysis
#>    Theta      1      2      3  Total E{N}
#>   0.6774 0.4328 0.3960 0.1523 0.9811 44.1
#>   0.4737 0.0068 0.0206 0.0578 0.0851 52.2
#> 
#> Lower boundary
#>           Analysis
#>    Theta      1      2      3  Total
#>   0.6774 0.0008 0.0030 0.0151 0.0189
#>   0.4737 0.2167 0.3767 0.3215 0.9149
# Update bounds at time of analysis
toBinomialExact(x, observedEvents = c(20,55,80))
#>              Bounds
#>   Analysis   N   a   b
#>          1  20   6  17
#>          2  55  28  33
#>          3  80  45  46
#> 
#> Boundary crossing probabilities and expected sample size assume
#> any cross stops the trial
#> 
#> Upper boundary
#>           Analysis
#>    Theta      1      2      3  Total E{N}
#>   0.6774 0.0732 0.8400 0.0668 0.9800 54.4
#>   0.4737 0.0006 0.0404 0.0205 0.0615 57.1
#> 
#> Lower boundary
#>           Analysis
#>    Theta      1      2      3  Total
#>   0.6774 0.0006 0.0067 0.0127 0.0200
#>   0.4737 0.0903 0.6571 0.1911 0.9385