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Compute the correlation matrix for group sequential test statistics

Source: R/gs_corr.R
gs_corr.Rd

In a group sequential design, test statistics \(Z_1, \ldots, Z_K\) at analyses with information fractions \(t_1, \ldots, t_K\) follow the canonical joint distribution with correlation $$\text{Cor}(Z_i, Z_j) = \sqrt{t_i / t_j}, \quad i \le j.$$

This correlation structure arises from the independent increments property of the score process. It depends only on the information fractions, not on the specific test or endpoint.

Usage

gs_corr(info_frac)

Arguments

info_frac

A numeric vector of information fractions at each analysis. Must be positive and monotonically non-decreasing.

Value

A symmetric correlation matrix of dimension \(K \times K\), where \(K\) is the length of info_frac. The diagonal entries are all 1.

See also

gs_boundaries() which uses this correlation matrix for computing group sequential boundaries.

Examples

# Three equally spaced analyses
gs_corr(c(1 / 3, 2 / 3, 1))
#>           [,1]      [,2]      [,3]
#> [1,] 1.0000000 0.7071068 0.5773503
#> [2,] 0.7071068 1.0000000 0.8164966
#> [3,] 0.5773503 0.8164966 1.0000000

# Two analyses at 50% and 100%
gs_corr(c(0.5, 1))
#>           [,1]      [,2]
#> [1,] 1.0000000 0.7071068
#> [2,] 0.7071068 1.0000000