Unified Regression Calibration Wrapper (Internal Reliability Study)

A single formula interface for regression calibration in internal reliability studies. The user simply specifies `link = "linear"`, `"logistic"`, or `"log"`, and the wrapper selects the appropriate model: * `"linear"` → Gaussian (identity link) * `"logistic"` → Binomial (logit link) * `"log"` → Poisson (log link)

Usage

RC_InReliab(
  formula,
  main_data,
  link = c("linear", "logistic", "log"),
  return_details = FALSE
)

Arguments

formula: A formula or character string such as `Y ~ sbp(sbp2, sbp3) + chol(chol2, chol3) + age + weight`. Terms of the form `var(rep1, rep2, ...)` are treated as error-prone exposures with replicates in `main_data`; other terms are treated as covariates W.
main_data: Data frame holding the outcome, replicate error-prone exposures, and any covariates.
link: Character; one of `"linear"`, `"logistic"`, or `"log"`.
return_details: Logical; if `TRUE`, return parsed, prepared, and RC internals.

Value

A list with: * `uncorrected`: naive regression estimates * `corrected` : sandwich-corrected regression calibration estimates * optional `details` if `return_details = TRUE`

Examples

set.seed(123)
add_err <- function(v, sd = sqrt(0.4)) v + rnorm(length(v), 0, sd)

## --- Example 1: Internal 1Z 0W ---
x <- rnorm(3000)
z <- rbind(
  cbind(add_err(x[1:1500]), NA, NA, NA),
  cbind(add_err(x[1501:2000]), add_err(x[1501:2000]), NA, NA),
  cbind(add_err(x[2001:2400]), add_err(x[2001:2400]), add_err(x[2001:2400]), NA),
  cbind(add_err(x[2401:3000]), add_err(x[2401:3000]),
        add_err(x[2401:3000]), add_err(x[2401:3000]))
)
colnames(z) <- paste0("z_", 1:4)
Y <- rbinom(3000, 1, plogis(-2.65 + log(1.5) * x))
main_data <- data.frame(Y, z)
res1 <- RC_InReliab(Y ~ myz(z_1, z_2, z_3, z_4),
                    main_data = main_data,
                    link = "logistic")
res1$corrected
#>               Estimate Std. Error    z value     Pr(>|z|)        OR     CI.low
#> (Intercept) -2.7171752 0.07701872 -35.279412 2.000000e+00 0.0660611 0.05680495
#> myz          0.3411573 0.08265864   4.127304 3.670418e-05 1.4065745 1.19619582
#>                CI.high
#> (Intercept) 0.07682551
#> myz         1.65395313

## --- Example 2: Internal 1Z 1W ---
x  <- rnorm(3000)
W1 <- rnorm(3000)
z <- rbind(
  cbind(add_err(x[1:1500]), NA, NA, NA),
  cbind(add_err(x[1501:2000]), add_err(x[1501:2000]), NA, NA),
  cbind(add_err(x[2001:2400]), add_err(x[2001:2400]), add_err(x[2001:2400]), NA),
  cbind(add_err(x[2401:3000]), add_err(x[2401:3000]),
        add_err(x[2401:3000]), add_err(x[2401:3000]))
)
colnames(z) <- paste0("z_", 1:4)
Y <- rbinom(3000, 1, plogis(-2.65 + log(1.5) * x + 0.5 * W1))
main_data <- data.frame(Y, z, W1)
res2 <- RC_InReliab(Y ~ myz(z_1, z_2, z_3, z_4) + W1,
                    main_data = main_data,
                    link = "logistic")
res2$corrected
#>               Estimate Std. Error    z value     Pr(>|z|)         OR     CI.low
#> (Intercept) -2.5679464 0.07450904 -34.464900 2.000000e+00 0.07669288 0.06627224
#> myz          0.4930941 0.07141417   6.904709 5.030643e-12 1.63737454 1.42350522
#> W1           0.4994671 0.06588726   7.580633 3.438739e-14 1.64784292 1.44820967
#>                CI.high
#> (Intercept) 0.08875205
#> myz         1.88337587
#> W1          1.87499527

## --- Example 3: Internal 2Z 0W ---
x <- mgcv::rmvn(3000, c(0,0), matrix(c(1,0.3,0.3,1), 2))
z1 <- rbind(
  cbind(add_err(x[1:1500, 1]), NA, NA, NA),
  cbind(add_err(x[1501:2000, 1]), add_err(x[1501:2000, 1]), NA, NA),
  cbind(add_err(x[2001:2400, 1]), add_err(x[2001:2400, 1]), add_err(x[2001:2400, 1]), NA),
  cbind(add_err(x[2401:3000, 1]), add_err(x[2401:3000, 1]),
        add_err(x[2401:3000, 1]), add_err(x[2401:3000, 1]))
)
colnames(z1) <- paste0("z1_", 1:4)
z2 <- rbind(
  cbind(add_err(x[1:1500, 2]), NA, NA, NA),
  cbind(add_err(x[1501:2000, 2]), add_err(x[1501:2000, 2]), NA, NA),
  cbind(add_err(x[2001:2400, 2]), add_err(x[2001:2400, 2]), add_err(x[2001:2400, 2]), NA),
  cbind(add_err(x[2401:3000, 2]), add_err(x[2401:3000, 2]),
        add_err(x[2401:3000, 2]), add_err(x[2401:3000, 2]))
)
colnames(z2) <- paste0("z2_", 1:4)
Y <- rbinom(3000, 1, plogis(-2.65 + log(1.5) * rowSums(x)))
main_data <- data.frame(Y, z1, z2)
res3 <- RC_InReliab(
  Y ~ myz1(z1_1, z1_2, z1_3, z1_4) + myz2(z2_1, z2_2, z2_3, z2_4),
  main_data = main_data,
  link = "logistic")
res3$corrected
#>               Estimate Std. Error    z value     Pr(>|z|)         OR     CI.low
#> (Intercept) -2.6495693 0.07952853 -33.315959 2.000000e+00 0.07068165 0.06047984
#> myz1         0.4285456 0.08305847   5.159566 2.475230e-07 1.53502342 1.30441027
#> myz2         0.4835185 0.09087986   5.320414 1.035313e-07 1.62177059 1.35715958
#>                CI.high
#> (Intercept) 0.08260431
#> myz1        1.80640779
#> myz2        1.93797389