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Efficacy Boundaries for Two-Stage Seamless Sequential Design (TSSSD)

Source: R/RcppExports.R
getBound_tsssd.Rd

Calculates the efficacy stopping boundaries for a two-stage seamless sequential design, accounting for the selection of the best arm at the end of Phase 2 and sequential testing in Phase 3.

Usage

getBound_tsssd(
  M = NA_integer_,
  r = 1,
  corr_known = TRUE,
  k = NA_integer_,
  informationRates = NA_real_,
  alpha = 0.025,
  typeAlphaSpending = "sfOF",
  parameterAlphaSpending = NA_real_,
  userAlphaSpending = NA_real_,
  spendingTime = NA_real_,
  efficacyStopping = NA_integer_
)

Arguments

M

Number of active treatment arms in Phase 2 (\(M \ge 2\)).

r

Randomization ratio of each active arm to the common control in Phase 2.

corr_known

Logical. If TRUE, the correlation between Wald statistics in Phase 2 is derived from the randomization ratio \(r\) as \(r / (r + 1)\). If FALSE, a conservative correlation of 0 is assumed.

k

The index of the current look in Phase 3.

informationRates

A numeric vector of information rates up to the current look. Values must be strictly increasing and \(\le 1\).

alpha

The significance level. Defaults to 0.025.

typeAlphaSpending

The type of alpha spending. One of the following: "OF" for O'Brien-Fleming boundaries, "P" for Pocock boundaries, "WT" for Wang & Tsiatis boundaries, "sfOF" for O'Brien-Fleming type spending function, "sfP" for Pocock type spending function, "sfKD" for Kim & DeMets spending function, "sfHSD" for Hwang, Shi & DeCani spending function, "user" for user defined spending, and "none" for no early efficacy stopping. Defaults to "sfOF".

parameterAlphaSpending

The parameter value for the alpha spending. Corresponds to \(\Delta\) for "WT", \(\rho\) for "sfKD", and \(\gamma\) for "sfHSD".

userAlphaSpending

The user defined alpha spending. Cumulative alpha spent up to each stage.

spendingTime

A numeric vector of length \(k+1\) specifying the error spending time at each analysis. Values must be strictly increasing and \(\le 1\). If omitted, defaults to informationRates.

efficacyStopping

Indicators of whether efficacy stopping is allowed at each stage. Defaults to TRUE if left unspecified.

Value

A numeric vector of length \(k + 1\) containing the critical values (on the standard normal Z-scale) for each analysis up to the current look.

Details

The function determines critical values by solving for the boundary that satisfies the alpha-spending requirement, given the selection of the "best" arm at the end of Phase 2.

If typeAlphaSpending is specified as "OF" (O'Brien-Fleming), "P" (Pocock), or "WT" (Wang-Tsiatis), the boundaries are calculated assuming the looks are equally spaced in terms of information.

Author

Kaifeng Lu, kaifenglu@gmail.com

Examples


# Determine O'Brien-Fleming boundaries for a TSSSD with
# 2 active arms in Phase 2 and 2 looks in Phase 3 (3 looks total).
getBound_tsssd(M = 2, k = 2, informationRates = seq(1, 3)/3,
              alpha = 0.025, typeAlphaSpending = "OF")
#> [1] 3.776605 2.670463 2.180424