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multigrain

Overview

multigrain (Multiple Testing using Graphical Approaches; Improve power with Numerical Optimisation) is an R package that finds the optimal graphical multiple testing procedure for your clinical trial.

Confirmatory trials routinely test multiple hypotheses — across endpoints, doses, or subpopulations — and must strongly control the family-wise error rate (FWER). Graphical approaches are a popular framework for this, but choosing the hypothesis weights and transition matrix that make up the graph is typically done by hand.

multigrain automates this: given simulated p-values and a user-defined trial success measure (a function that scores each possible pattern of hypothesis rejections), it searches over hypothesis weights and transition weights to find the graph that maximises expected trial success. The result is a valid graphical test that strongly controls FWER.

The fixed-sample gain-function optimisation workflow implemented by trial_success() and graph_optimise() is described in Spiers et al. (2026), Gain-function optimisation of graphical multiple testing procedures for confirmatory clinical trials (arXiv:2609.19994v1).

Key features

Step Function Purpose
Simulate p-values simulate_pvalues() Draw p-values from a multivariate normal test-statistic model
Define success trial_success() Specify what “trial success” means (compiled to C++ for speed)
Constrain the graph graph_constraint() Fix weights, edges, or testing hierarchies
Optimise graph_optimise() Find the graph that maximises expected trial success
Evaluate calc_power_pvals() Compute local power, disjunctive/conjunctive power, and custom metrics

Installation

Install the released version of {multigrain} from CRAN:

install.packages("multigrain")

Or install the development version from GitHub with:

# install.packages("pak")
pak::pak("GSK-Biostatistics/multigrain")

Quick start

Below is an end-to-end example with four hypotheses: two primary (H1, H2) and two secondary (H3, H4). Secondaries are gated by their corresponding primaries (H3 can only be tested after H1 is rejected; H4 after H2).

1. Simulate p-values

Assume one-sided test statistics are jointly normal. Provide the per-hypothesis nominal power (unadjusted for multiplicity) and a correlation matrix:

library(multigrain)

power_nominal <- c(0.95, 0.90, 0.85, 0.80)
corr_mat <- matrix(
    c(
        1.0, 0.5, 0.4, 0.2,
        0.5, 1.0, 0.2, 0.4,
        0.4, 0.2, 1.0, 0.5,
        0.2, 0.4, 0.5, 1.0
    ),
    nrow = 4, byrow = TRUE
)

set.seed(1)
pvals <- simulate_pvalues(
    power_nominal = power_nominal,
    corr_matrix = corr_mat,
    nsim = 1e5
)

2. Define trial success measures

Use trial_success() to express what “success” means for the trial. The variables r1, r2, r3, r4 are binary indicators — ri = 1 if hypothesis Hi is rejected, 0 otherwise. You can combine them with arithmetic (+, *) and logical (&&, ||) operators.

# Average power: mean proportion of hypotheses rejected
avg_power <- trial_success(0.25 * (r1 + r2 + r3 + r4))

# Disjunctive power: at least one rejection
disjunctive <- trial_success(r1 || r2 || r3 || r4)

# Custom: require a primary rejection, with extra credit for the
# gated secondary (H3 adds value only if H1 is also rejected, etc.)
custom_success <- trial_success(
    0.25 * (2 * (r1 || r2) + r1 * r3 + r2 * r4)
)

3. Constrain the graph (optional)

Use graph_constraint() to encode structural rules — for example, that only primaries receive initial alpha, and that secondaries can only receive alpha recycled from their gating primary:

gc <- graph_constraint(
    hyp_constraint  = c(NA, NA, 0, 0),
    trans_constraint = matrix(
        c(
            0, NA, NA, 0,
            NA, 0, 0, NA,
            0, 1, 0, 0,
            1, 0, 0, 0
        ),
        nrow = 4, byrow = TRUE
    )
)

Here NA means “free to optimise” and a fixed number means “held constant”.

4. Optimise 

g_opt <- graph_optimise(
    pvals = pvals,
    trial_success = custom_success,
    graph_constraint = gc
)

summary(g_opt)
plot(g_opt)

5. Evaluate

Compute multiplicity-adjusted power and any custom trial success measures for the optimised graph:

calc_power_pvals(
    pvals,
    hyp_weight   = g_opt$hyp_weight,
    trans_matrix = g_opt$trans_matrix,
    custom_power = list(
        AvgPower      = avg_power,
        Disjunctive   = disjunctive,
        CustomSuccess = custom_success
    )
)

Documentation

Getting help

Found a bug, or want to request a feature? Please open an issue, including a reprex where relevant.

Contributing

Contributions are welcome. Please open an issue to discuss substantial changes before submitting a pull request.

License

multigrain is released under the LGPL (>= 3) license.

Copyright © GlaxoSmithKline Research & Development Limited.