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Local size of the MFET

Source: R/local_size_modified.R
local_size_modified.Rd

Computes the unconditional rejection probability (local size) of the MFET at nuisance parameter \(p_0\), where \(p_1 = p_0 / (p_0 + \theta_0 (1 - p_0))\). Called repeatedly by size_modified() during numerical optimisation over \(p_0\) to find the maximum size. Computed as the bilinear form \(p_u^\top R \, p_v\), where \(R\) is the rejection matrix from .build_rejection_matrix() and \(p_u\), \(p_v\) are the binomial probability vectors of the two groups.

Usage

local_size_modified(
  nuisance,
  .gamma0,
  .odds_ratio,
  .m,
  .n,
  .df,
  .alpha,
  .precision,
  .rejection_matrix = NULL
)

Arguments

nuisance

The nuisance parameter \(p_0\): success probability in group 1 under \(H_0\). Must be in \([0, 1]\).

.gamma0

The \(\gamma_0\) threshold: boundary values in the test frame are rejected only when their randomisation probability exceeds this value. Typically the output of optimise_gamma0().

.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.

.df

Test frame (data frame) generated by construct_test_frame(), containing critical values \(c_1\), \(c_2\) and randomisation probabilities \(\gamma_1\), \(\gamma_2\) for every possible total \(T\).

.alpha

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

.precision

Numerical precision. No default.

.rejection_matrix

Optional prebuilt rejection matrix from .build_rejection_matrix(). Defaults to NULL, in which case the matrix is built internally from .df and .gamma0. Supply a prebuilt matrix when calling repeatedly with the same test frame and \(\gamma_0\) (as size_modified() does across its zoom grid) to avoid rebuilding it on every call. If supplied, it must correspond to the same .df and .gamma0 passed alongside it; this is not checked.

Value

A single numeric value: the local size (unconditional rejection probability) of the MFET at the given nuisance parameter, in \([0, 1]\).

See also

local_size_asymptotic(), local_size_probability(), local_size_randomised() for the local size under alternative tests at the same nuisance parameter value; size_modified() for the modified local size maximised over the nuisance parameter; power_modified() for the power of the modified Fisher exact test; modified_fisher_exact_test() for the main user-facing function.

Other size: local_size_asymptotic(), local_size_probability(), local_size_randomised(), size_modified()

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

Examples

df <- construct_test_frame(.odds_ratio = 1, .m = 6, .n = 4,
                           .alpha = 0.05, .precision = 1e-3)
# Local size at nuisance parameter p0 = 0.5, with gamma0 = 0.05:
local_size_modified(nuisance = 0.5, .gamma0 = 0.05, .odds_ratio = 1,
                .m = 6, .n = 4, .df = df, .alpha = 0.05, .precision = 1e-3)
#> [1] 0.1777344