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O'Brien Plus: Analytical Power for Joint AND Any Individual Endpoint

Source: R/obrien_plus.R
obrien_plus.Rd

This function analytically estimates the statistical power for the scenario where both the O'Brien joint endpoint test is significant AND at least one of the individual endpoints is significant. It also calculates the power for "Joint AND a Specific Individual" (if ind_index is provided). It relies on a multivariate t-distribution approximation of the test statistics.

Usage

obrien_plus(
  n1,
  n2 = n1,
  df = n1 + n2 - 2,
  es_ind,
  cor_mtx,
  ind_index = NULL,
  method = c("ols", "gls"),
  alpha = 0.025,
  one_sided = TRUE
)

Arguments

n1

Numeric, sample size for the first treatment group.

n2

Numeric, sample size for the second treatment group.

es_ind

Numeric vector, the standardized mean differences (Cohen's d) for each individual endpoint under the alternative hypothesis.

cor_mtx

Numeric matrix, the correlation matrix (R) among the standardized individual endpoints.

ind_index

Integer, the 1-based index of a specific individual endpoint for which "Joint AND Specific Individual" power is also calculated. Set to NULL if only "Joint AND Any Individual" power is desired.

method

Character, the O'Brien test method to use ("ols" or "gls").

alpha

Numeric, the significance level for each test (e.g., 0.05). Assumes no explicit multiplicity adjustment for the 'AND' or 'OR' conditions.

one_sided

Logical, default TRUE. If TRUE, a one-sided test is assumed. If FALSE, a two-sided test is used, with a warning about power interpretation for positive effect sizes.

Value

a named list containing computation settings and results, including:

  • power_joint_any - power for joint endpoints and any additional endpoint

  • power_joint_one - power for joint endpoints and a specific endpoint (specified by ind_index)

  • power_joint - power for the joint endpoint test

  • power_ind - power for the specific endpoint (specified by ind_index)

  • n1 - sample size for the first treatment group

  • n2 - sample size for the second treatment group

  • alpha - significance level

  • method - the O'Brien test method used

  • one_sided - logical indicating if the test is one-sided

Examples

# Generate GST power for 3 endpoints (joint + any)
obrien_plus(
  n1 = 25,
  n2 = 30,
  es_ind = c(1, 0.5, 0.5),
  cor_mtx = cor_cs(0.25, m = 3),
  ind_index = NULL,
  method = "ols",
  alpha = 0.05,
  one_sided = TRUE
  )
#> $power_joint_any
#> [1] 0.9609566
#> 
#> $power_joint_one
#> [1] NA
#> 
#> $power_joint
#> [1] 0.9634129
#> 
#> $power_ind
#> [1] NA
#> 
#> $n1
#> [1] 25
#> 
#> $n2
#> [1] 30
#> 
#> $alpha
#> [1] 0.05
#> 
#> $method
#> [1] "ols"
#> 
#> $one_sided
#> [1] TRUE
#> 

# Generate GST power for 4 endpoints (joint + 3rd endpoint)
obrien_plus(
  n1 = 28,
  n2 = 40,
  es_ind = c(1, 0.25, 0.75, 0.5),
  cor_mtx = cor_cs(0.35, m = 4),
  ind_index = 3,
  method = "ols",
  alpha = 0.05,
  one_sided = TRUE
  )
#> $power_joint_any
#> [1] 0.968545
#> 
#> $power_joint_one
#> [1] 0.9027638
#> 
#> $power_joint
#> [1] 0.9686713
#> 
#> $power_ind
#> [1] 0.9142672
#> 
#> $n1
#> [1] 28
#> 
#> $n2
#> [1] 40
#> 
#> $alpha
#> [1] 0.05
#> 
#> $method
#> [1] "ols"
#> 
#> $one_sided
#> [1] TRUE
#>