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Blinded Sample Size Re-Estimation from Paired Interim Data

Source: R/PairedBSSR.R
PairedBSSR.Rd

Re-estimates the number of pairs of a matched-pairs trial from the number of discordant pairs observed at an interim analysis, without the direction in which they are discordant.

Usage

PairedBSSR(
  n1,
  D1,
  Delta.A,
  alpha,
  tar.power,
  Test,
  restricted = FALSE,
  N = NULL,
  alternative = c("greater", "less", "two.sided", "equivalence"),
  n.grid = 100,
  bb.gamma = 0,
  ss.method = c("exact", "standard", "conditional.power"),
  ss.Test = Test,
  ss.alpha = alpha,
  search = c("crossing", "smallest", "stable"),
  search.limit = c(2, 50),
  N.min = NULL,
  N.max = NULL,
  margin = 0,
  ref.pvalue = FALSE
)

Arguments

n1

Number of pairs at the interim analysis

D1

Number of discordant pairs among them

Delta.A

Assumed difference p10 - p01 used in the re-estimation

alpha

Level of significance for the alternative specified by alternative

tar.power

Target power of the re-estimation

Test

Type of statistical test. Options: 'McNemar', 'McNemar-cc', 'McNemar-exact', 'McNemar-midP', 'McNemar-uncond' or 'Paired-Score'

restricted

Logical. If TRUE, the final number of pairs is at least N. Default is FALSE

N

Planned number of pairs. Required when restricted = TRUE, otherwise optional

alternative

Direction of the alternative hypothesis. Options: 'greater' (default) for p10 - p01 > -margin, 'less' for p10 - p01 < margin, 'two.sided' for p10 != p01, or 'equivalence' for -lower < p10 - p01 < upper

n.grid

Number of grid points used to search over the probability of a discordant pair in the test 'McNemar-uncond'. Default is 100

bb.gamma

Confidence level parameter of the Berger-Boos procedure for the test 'McNemar-uncond'. The default of 0 disables the procedure

ss.method

Re-estimation rule. 'exact' (default) and 'standard' re-estimate the number of pairs of PairedSampleSize with the method of that name. 'conditional.power' takes the smallest number of pairs at which the conditional power given the interim number of discordant pairs attains tar.power, the rule of Schepers et al. (2026); it requires N.max. See Details

ss.Test

Test used in the re-estimation. Default is Test

ss.alpha

Level used in the re-estimation. Default is alpha

Search of the exact re-estimation, see PairedSampleSize; it does not go beyond N.max

search.limit

Limit of the search 'stable', see PairedSampleSize

N.min

Smallest final number of pairs, or NULL

N.max

Largest final number of pairs, or NULL

margin

Margin on the scale of the difference p10 - p01. The default of 0 gives a test of superiority, and a value other than 0 tests the null hypothesis p10 - p01 <= -margin against p10 - p01 > -margin when alternative is 'greater', and p10 - p01 >= margin against p10 - p01 < margin when it is 'less'. A negative value tests for superiority by more than its absolute value. A margin other than 0 requires Test = 'Paired-Score' and a one-sided alternative. For alternative = 'equivalence' the margin is the pair c(lower, upper), both in (0, 1), or a single value used for both, and the null hypothesis p10 - p01 <= -lower or p10 - p01 >= upper is tested

ref.pvalue

Logical. If TRUE, the maximization over the probability of a discordant pair in the test 'McNemar-uncond' is refined between the grid points, see Details. Default is FALSE

Value

An object of class bbssr_pbssr, a data frame with one row containing the interim data n1 and D1, the blinded estimate psi.hat of the probability of a discordant pair, the value psi.plan used in the re-estimation, the planning probabilities p10.plan and p01.plan, the re-estimated number of pairs N.re before the bounds are applied (at most N.max with ss.method = 'exact', whose search does not go beyond it, and within the bounds with ss.method = 'conditional.power'), the number n.stage2 of pairs still to be enrolled, the final number of pairs N.final, the power Power of the final analysis with N.final pairs under the planning probabilities, and its conditional power CP given D1, computed with ss.Test at the level ss.alpha. The attributes hold the design settings.

Details

The re-estimation is that of PairedPowerBSSR: the blinded estimate D1 / n1 of the probability of a discordant pair, raised to |Delta.A| when it is smaller, and the assumed difference Delta.A give the planning probabilities, from which the number of pairs follows by the rule ss.method. The conditional power is sum over D2 of b(D2; N.final - n1, psi.plan) g(D1 + D2), the probability of rejection given D1 under the planning probabilities, formula (4) of Schepers et al. (2026) for the exact conditional McNemar test.

References

Schepers M, Brannath W, Hoffmann E, Stingl J, Schmidtmann I (2026). Blinded sample size review for McNemar's test based on primary and surrogate endpoints. arXiv:2608.17784.

Examples

# 25 interim pairs of which 5 are discordant, assumed difference 0.15
PairedBSSR(n1 = 25, D1 = 5, Delta.A = 0.15, alpha = 0.05, tar.power = 0.8,
           Test = 'McNemar-exact', alternative = 'two.sided',
           ss.method = 'conditional.power', N.max = 150)
#> Blinded sample size re-estimation from paired interim data
#> 
#>   Test             : McNemar-exact
#>   Alternative      : two.sided
#>   Re-estimation    : conditional power (unrestricted)
#>   Assumed effect   : 0.15
#>   Alpha            : 0.05, target power 0.8
#> 
#> Interim data
#>   Pairs            : n1 = 25, discordant D1 = 5
#>   Discordance      : estimate 0.2, used 0.2
#>   Planning values  : p10 = 0.175, p01 = 0.025
#> 
#> Re-estimation
#>   Re-estimated N   : 70
#>   Still to enrol   : 45 pairs
#>   Final N          : 70
#>   Power at final N : 0.7911
#>   Conditional power: 0.8019