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Construct testing frame and randomisation values

Source: R/construct_test_frame.R
construct_test_frame.Rd

Constructs a data frame of critical values (\(c_1\), \(c_2\)) and randomisation probabilities (\(\gamma_1\), \(\gamma_2\)) for every possible value of the total \(T = 0, \ldots, m + n\), given the null odds ratio, significance level \(\alpha\), and precision. Starting from the \(\alpha/2\) quantiles of the Fisher non-central hypergeometric distribution, a spiral search over \((c_1, c_2)\) is used whenever the initial solution for \((\gamma_1, \gamma_2)\) falls outside \([0, 1]\).

Usage

construct_test_frame(.odds_ratio, .m, .n, .alpha, .precision, .message = FALSE)

Arguments

.odds_ratio

The null hypothesis odds ratio \(\theta_0\). No default.

.m

Number of trials in group 1.

.n

Number of trials in group 2.

.alpha

Nominal significance level \(\alpha\). No default.

.precision

Numerical precision for quantile calculations and BiasedUrn::dFNCHypergeo(). No default.

.message

A logical. Defaults to FALSE. Setting this to TRUE will print progress messages; useful for debugging.

Value

A data frame with m + n + 1 rows, one per possible total \(T = 0, \ldots, m + n\), and columns t (the total), c1 and c2 (lower and upper critical values), d1 and d2 (the \(\alpha/2\) quantiles used as starting points), and gamma1 and gamma2 (the randomisation probabilities at c1 and c2).

See also

modified_fisher_exact_test() for the main user-facing function; optimise_gamma0() which uses this frame to find the optimal gamma0; size_modified() for the resulting test size.

Other modified: local_size_modified(), modified_fisher_exact_test(), optimise_gamma0(), power_modified(), size_modified()

Examples

# Critical values and randomisation probabilities for m = 6, n = 4
# (reproduces Table 1 of van der Meulen et al., 2021):
construct_test_frame(.odds_ratio = 1, .m = 6, .n = 4,
                     .alpha = 0.05, .precision = 1e-3)
#>     t c1 d1    gamma1 c2 d2    gamma2
#> 1   0  0  0 0.0250000  0  1 0.0250000
#> 2   1  0  0 0.0500000  1  2 0.0500000
#> 3   2  0  0 0.1500000  2  3 0.0900000
#> 4   3  0  1 0.6000000  3  4 0.1800000
#> 5   4  1  2 0.1777778  4  4 0.3488889
#> 6   5  2  2 0.0050000  4  5 0.0050000
#> 7   6  2  3 0.3488889  5  6 0.1777778
#> 8   7  3  4 0.1800000  6  6 0.6000000
#> 9   8  4  5 0.0900000  6  6 0.1500000
#> 10  9  5  6 0.0500000  6  6 0.0500000
#> 11 10  6  6 0.0250000  6  6 0.0250000