gs_power_npe: Group sequential bound computation with non-constant effect
In keaven/gsdmvn: Group sequential design with non-constant effect

Description Usage Arguments Author(s) Examples

gs_power_npe() derives group sequential bounds and boundary crossing probabilities for a design. It allows a non-constant treatment effect over time, but also can be applied for the usual homogeneous effect size designs. It requires treatment effect and statistical information at each analysis as well as a method of deriving bounds, such as spending. The routine enables two things not available in the gsDesign package: 1) non-constant effect, 2) more flexibility in boundary selection. For many applications, the non-proportional-hazards design function gs_design_nph() will be used; it calls this function. Initial bound types supported are 1) spending bounds, 2) fixed bounds, and 3) Haybittle-Peto-like bounds. The requirement is to have a boundary update method that can each bound without knowledge of future bounds. As an example, bounds based on conditional power that require knowledge of all future bounds are not supported by this routine; a more limited conditional power method will be demonstrated. Boundary family designs Wang-Tsiatis designs including the original (non-spending-function-based) O'Brien-Fleming and Pocock designs are not supported by gs_power_npe().

gs_power_npe(
  theta = 0.1,
  theta1 = NULL,
  info = 1,
  info1 = NULL,
  info0 = NULL,
  binding = FALSE,
  upper = gs_b,
  lower = gs_b,
  upar = qnorm(0.975),
  lpar = -Inf,
  test_upper = TRUE,
  test_lower = TRUE,
  r = 18,
  tol = 1e-06
)

`theta`	natural parameter for group sequential design representing expected incremental drift at all analyses; used for power calculation
`theta1`	natural parameter for alternate hypothesis, if needed for lower bound computation
`info`	statistical information at all analyses for input `theta`
`info1`	statistical information under hypothesis used for futility bound calculation if different from `info`; impacts futility hypothesis bound calculation
`info0`	statistical information under null hypothesis, if different than `info`; impacts null hypothesis bound calculation
`binding`	indicator of whether futility bound is binding; default of FALSE is recommended
`upper`	function to compute upper bound
`lower`	function to compare lower bound
`upar`	parameter to pass to upper
`lpar`	parameter to pass to lower
`test_upper`	indicator of which analyses should include an upper (efficacy) bound; single value of TRUE (default) indicates all analyses; otherwise, a logical vector of the same length as `info` should indicate which analyses will have an efficacy bound
`test_lower`	indicator of which analyses should include a lower bound; single value of TRUE (default) indicates all analyses; single value FALSE indicated no lower bound; otherwise, a logical vector of the same length as `info` should indicate which analyses will have a lower bound
`r`	Integer, at least 2; default of 18 recommended by Jennison and Turnbull
`tol`	Tolerance parameter for boundary convergence (on Z-scale)

Keaven Anderson keaven\_anderson@merck.

library(gsDesign)
# Default (single analysis; Type I error controlled)
gs_power_npe(theta=0) %>% filter(Bound=="Upper")

# Fixed bound
gs_power_npe(theta = c(.1, .2, .3), info = (1:3) * 40, info0 = (1:3) * 40,
              upper = gs_b, upar = gsDesign::gsDesign(k=3,sfu=gsDesign::sfLDOF)$upper$bound,
              lower = gs_b, lpar = c(-1, 0, 0))

# Same fixed efficacy bounds, no futility bound (i.e., non-binding bound), null hypothesis
gs_power_npe(theta = rep(0,3), info = (1:3) * 40,
upar = gsDesign::gsDesign(k=3,sfu=gsDesign::sfLDOF)$upper$bound,
lpar = rep(-Inf, 3)) %>% filter(Bound=="Upper")

# Fixed bound with futility only at analysis 1; efficacy only at analyses 2, 3
gs_power_npe(theta = c(.1, .2, .3), info = (1:3) * 40, upar = c(Inf, 3, 2), lpar = c(qnorm(.1), -Inf, -Inf))

# Spending function bounds
# Lower spending based on non-zero effect
gs_power_npe(theta = c(.1, .2, .3), info = (1:3) * 40,
             upper = gs_spending_bound,
             upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
             lower = gs_spending_bound,
             lpar = list(sf = gsDesign::sfHSD, total_spend = 0.1, param = -1, timing = NULL))

# Same bounds, but power under different theta
gs_power_npe(theta = c(.15, .25, .35), theta1 = c(.1, .2, .3), info = (1:3) * 40,
             upper = gs_spending_bound,
             upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
             lower = gs_spending_bound,
             lpar = list(sf = gsDesign::sfHSD, total_spend = 0.1, param = -1, timing = NULL))

# Two-sided symmetric spend, O'Brien-Fleming spending
# Typically, 2-sided bounds are binding
xx <- gs_power_npe(theta = rep(0, 3), theta1 = rep(0, 3), info = (1:3) * 40,
                   upper = gs_spending_bound,
                   binding = TRUE,
                   upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
                   lower = gs_spending_bound,
                   lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL))
xx

# Re-use these bounds under alternate hypothesis
# Always use binding = TRUE for power calculations
upar <- (xx %>% filter(Bound=="Upper"))$Z
gs_power_npe(theta = c(.1, .2, .3), info = (1:3) * 40,
             binding = TRUE,
             upar = upar,
             lpar = -upar)