Fit the Phase-1 multivariate ME calibration model — fit_me

Fits per-equation OLS of each surrogate column on the validation truth: W_j = alpha_0j + alpha_1j * X + e_j, with e ~ N_J(0, Sigma_e). Under shared regressors this is equivalent to seemingly-unrelated regression (SUR) and admits closed-form ML.

Usage

fit_me_calibration(
  validation,
  x_var = "X_true",
  surrogate_pattern = "^W[0-9]+$"
)

Arguments

validation: Validation data frame containing the truth column named in x_var and the surrogate columns matched by surrogate_pattern.
x_var: Name of the truth column. Default "X_true".
surrogate_pattern: Regex used to identify surrogate columns; see extract_surrogate_cols(). Default "^W[0-9]+$".

Value

A list with elements

alpha0 numeric vector of intercepts (length J),
alpha1 numeric vector of slopes (length J),
Sigma_e J x J residual covariance,
W_cols character vector of surrogate column names used,
n_val number of validation rows.

Examples

sim <- generate_aft_data(n = 100, n_val = 200, seed = 1)
fit_me_calibration(sim$validation)
#> $alpha0
#> [1] -0.6927750 -0.6061218 -0.2298794
#> 
#> $alpha1
#> [1] 1.071567 1.067074 1.013832
#> 
#> $Sigma_e
#>           [,1]      [,2]      [,3]
#> [1,] 1.9347981 0.7575053 0.8004875
#> [2,] 0.7575053 2.5947853 1.0883172
#> [3,] 0.8004875 1.0883172 2.8696944
#> 
#> $W_cols
#> [1] "W1" "W2" "W3"
#> 
#> $n_val
#> [1] 200
#>