Derive spending bound for group sequential boundary

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)

Value

returns a numeric bound (possibly infinite) or, upon failure, generates an error message.

Specification

The contents of this section are shown in PDF user manual only.

References

Jennison C and Turnbull BW (2000), Group Sequential Methods with Applications to Clinical Trials. Boca Raton: Chapman and Hall.

Author

Keaven Anderson keaven_anderson@merck.com