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Monte Carlo Computation of the Parameter \(\delta\) from Parast et al. (2024)

Source: R/compute_delta.R
compute_delta.Rd

This function implements a Monte Carlo approach to estimate the parameter \(\delta\) from Parast et al. (2024) . This parameter represents the difference in treatment effects between the primary and surrogate outcomes, both measured using the Mann-Whitney statistic.

Usage

compute_delta(MC_data)

Arguments

MC_data

A list containing:

  • P_observed: A data frame or matrix with columns "Y" and "S".

  • Z: Treatment assignment vector.

  • n1: Number of treated units.

  • n0: Number of control units.

Value

A list containing:

  • U_Y: Mann-Whitney U statistic for the primary outcome Y computed on P_observed.

  • U_S: Mann-Whitney U statistic for the surrogate S computed on P_observed.

  • delta: The difference U_Y - U_S.

Details

The function processes data from a chosen data generating process, computing the Mann-Whitney U statistic for both the primary outcome \(Y\) and the surrogate \(S\): $$\hat{U}_Y = \frac{1}{n_1 n_0} \sum\limits_{i:Z_i=1} \sum\limits_{j:Z_j=0} I(Y_i > Y_j),$$ $$\hat{U}_S = \frac{1}{n_1 n_0} \sum\limits_{i:Z_i=1} \sum\limits_{j:Z_j=0} I(S_i > S_j).$$ Then, it calculates $$\hat{\delta} = \hat{U}_Y - \hat{U}_S.$$ 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.

References

Parast L, Cai T, Tian L (2024). “A rank-based approach to evaluate a surrogate marker in a small sample setting.” Biometrics, 80(1), ujad035.