gs_spending_bound: Derive spending bound for group sequential boundary
In keaven/gsDesign2: Group Sequential Design with Non-Constant Effect

gs_spending_bound

R Documentation

Derive spending bound for group sequential boundary

Description

Computes one bound at a time based on spending under given distributional assumptions. While user specifies gs_spending_bound() for use with other functions, it is not intended for use on its own. Most important user specifications are made through a list provided to functions using gs_spending_bound(). Function uses numerical integration and Newton-Raphson iteration to derive an individual bound for a group sequential design that satisfies a targeted boundary crossing probability. Algorithm is a simple extension of that in Chapter 19 of Jennison and Turnbull (2000).

Usage

gs_spending_bound(
  k = 1,
  par = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL,
    max_info = NULL),
  hgm1 = NULL,
  theta = 0.1,
  info = 1:3,
  efficacy = TRUE,
  test_bound = TRUE,
  r = 18,
  tol = 1e-06
)

Arguments

`k`	analysis for which bound is to be computed
`par`	a list with the following items: `sf` (class spending function), `total_spend` (total spend), `param` (any parameters needed by the spending function `sf()`), `timing` (a vector containing values at which spending function is to be evaluated or NULL if information-based spending is used), `max_info` (when `timing` is NULL, this can be input as positive number to be used with `info` for information fraction at each analysis)
`hgm1`	subdensity grid from h1 (k=2) or hupdate (k>2) for analysis k-1; if k=1, this is not used and may be NULL
`theta`	natural parameter used for lower bound only spending; represents average drift at each time of analysis at least up to analysis k; upper bound spending is always set under null hypothesis (theta = 0)
`info`	statistical information at all analyses, at least up to analysis k
`efficacy`	TRUE (default) for efficacy bound, FALSE otherwise
`test_bound`	a logical vector of the same length as `info` should indicate which analyses will have a bound
`r`	Integer, at least 2; default of 18 recommended by Jennison and Turnbull
`tol`	Tolerance parameter for convergence (on Z-scale)