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Bayesian Test from Carlotti and Parast (2026)

Source: R/Bayesian_test.R
Bayesian_test.Rd

This function performs a Bayesian test for surrogate evaluation based on the imputation-based methodology of Carlotti and Parast (2026) . It calculates credible intervals, the \(\eta\) threshold used, and determines if the surrogate is valid. This function is generally not intended to be called directly by the user and is instead used internally within BSET_no_X and BSET_X.

Usage

Bayesian_test(
  P_MCMC,
  alpha = 0.05,
  V_S_star,
  theta_true = NULL,
  V_Y_true = NULL
)

Arguments

P_MCMC

A three-dimensional array of potential outcomes obtained via MCMC sampling with dimensions [n_subjects, variables, n_samples]. The variables should correspond to \((Y_1, S_1, Y_0, S_0)\).

alpha

Numeric. Significance level for the credible interval (default is 0.05).

V_S_star

Numeric. The value of \(v_S\) that satisfies the power constraint for the surrogate validation test.

theta_true

Numeric (optional). The true value of \(\eta\), used to calculate frequentist coverage during simulations.

V_Y_true

Numeric (optional). The true value of \(V_Y\), used to calculate the surrogate validation threshold \(\eta\) during simulations. If not provided, it will be estimated from the MCMC samples.

Value

A list containing:

  • V_Y_MCMC: Posterior draws for \(V_Y\).

  • V_S_MCMC: Posterior draws for \(V_S\).

  • theta_MCMC: Posterior draws for \(\theta = V_Y - V_S\).

  • CI: The calculated credible interval for \(\theta\).

  • threshold: The \(\eta\) threshold value used in the test.

  • coverage: Logical indicating if theta_true falls within the CI (if theta_true is provided).

  • power: Logical indicating if the upper bound of CI is below threshold, which indicates that the test identifies the surrogate as valid.

References

Carlotti P, Parast L (2026). “A Bayesian Critique of Rank-Based Methods for Surrogate Marker Evaluation.” arXiv preprint arXiv:2603.14381.