gs_spending_bound: Derive spending bound for group sequential boundary
In keaven/gsdmvn: Group sequential design with non-constant effect

Description Usage Arguments Value Author(s) References

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 really 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 has been modified from Chapter 19 of Jennison and Turnbull (2000).

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

`k`	analysis for which bound is to be computed
`par`	a list with the following items: sf (class spending function), timing (a vector containing values at which spending function is to be evaluated), total_spend (total spend), param (any parameters needed by the spending function)
`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)