README

RegCalib is an R package for correcting measurement error in continuous exposures and covariates using regression calibration. It provides corrected coefficients, standard errors, p-values, confidence intervals, and variance-covariance matrices for linear and generalized linear outcome models under external validation study design.

Methods

Installation

Function	Method	Supported outcome models	Reference
`RegCalibDF`	Deattenuation factor method	Linear models (`"lm"`) and generalized linear models (`"glm"`)	Rosner, Spiegelman, and Willett (1989, 1990); Spiegelman et al. (1997, 2001)
`RegCalibSub`	Substitution method	Linear models (`"lm"`) and generalized linear models (`"glm"`)	Carroll et al. (2006)

# Install devtools once if needed.
install.packages("devtools")

# Install RegCalib from GitHub.
devtools::install_github("JingyuCui639/RegCalib")

Example: External Validation Study with a Binary Outcome

This example uses the simulated main-study and external-validation datasets included in the package. The outcome variable, case, is binary, so both methods are applied using logistic regression.

Load the package and example data

# Load the RegCalib package.
library(RegCalib)

# Load the simulated main-study dataset included in RegCalib.
data("main_data_sim", package = "RegCalib")

# Display the first six observations in the main-study dataset.
head(main_data_sim)

# Load the simulated external-validation dataset included in RegCalib.
data("valid_data_sim", package = "RegCalib")

# Display the first six observations in the validation dataset.
head(valid_data_sim)

The variable agec is an error-free covariate, and case is the binary outcome.

Deattenuation Factor Method

# Apply the deattenuation factor regression-calibration method.
rcdf <- RegCalibDF(
  # Let RegCalib fit the uncorrected outcome model internally.
  supplyEstimates = FALSE,

  # Supply the main-study data frame.
  ms = main_data_sim,

  # Supply the external-validation data frame.
  vs = valid_data_sim,

  # Identify the surrogate, error-prone variables.
  sur = c("fqtfatinc", "fqcalinc", "fqalcinc"),

  # Identify the corresponding reference variables in the same order.
  exp = c("drtfatinc", "drcalinc", "dralcinc"),

  # Include age category in both the calibration and outcome models.
  covCalib = "agec",

  # Do not include additional error-free covariates only in the outcome model.
  covOutcomePlus = NULL,

  # Identify the binary outcome variable.
  outcome = "case",

  # Fit a generalized linear outcome model.
  method = "glm",

  # Use the binomial family for a binary outcome.
  family = binomial,

  # Use the logit link to fit logistic regression.
  link = "logit",

  # Indicate that the validation study is external.
  external = TRUE,

  # Do not supply separate uncorrected coefficient estimates.
  pointEstimates = NA,

  # Do not supply a separate variance-covariance matrix.
  vcovEstimates = NA
)

# Print the complete result object.
rcdf

# Display the corrected coefficient table.
rcdf$correctedCoefTable

# Display the corrected variance-covariance matrix.
rcdf$correctedVCOV

# Display the uncorrected outcome-model coefficient table for comparison.
rcdf$standardCoefTable

Because the outcome model is logistic regression, the corrected coefficients and confidence limits can be exponentiated to obtain odds ratios:

# Exponentiate the corrected log-odds estimates and confidence limits.
corrected_RC_DF <- exp(
  cbind(
    # Exponentiate the corrected coefficient estimates.
    OR = rcdf$correctedCoefTable[, 1],

    # Exponentiate the lower limits of the 95% confidence intervals.
    "2.5 %" = rcdf$correctedCoefTable[, 5],

    # Exponentiate the upper limits of the 95% confidence intervals.
    "97.5 %" = rcdf$correctedCoefTable[, 6]
  )
)

# Display the corrected odds ratios and 95% confidence intervals.
corrected_RC_DF

Substitution Method

# Apply the substitution regression-calibration method.
rcsub <- RegCalibSub(
  # Supply the main-study data frame.
  ms = main_data_sim,

  # Supply the external-validation data frame.
  vs = valid_data_sim,

  # Identify the surrogate, error-prone variables.
  sur = c("fqtfatinc", "fqcalinc", "fqalcinc"),

  # Identify the corresponding reference variables in the same order.
  exp = c("drtfatinc", "drcalinc", "dralcinc"),

  # Include age category in the calibration models.
  covCalib = "agec",

  # Include age category in the outcome model.
  covOutcome = "agec",

  # Identify the binary outcome variable.
  outcome = "case",

  # Fit a generalized linear outcome model.
  method = "glm",

  # Use the binomial family for a binary outcome.
  family = binomial,

  # Use the logit link to fit logistic regression.
  link = "logit",

  # Indicate that the validation study is external.
  external = TRUE
)

# Print the complete result object.
rcsub

# Display the corrected coefficient table.
rcsub$correctedCoefTable

# Display the corrected variance-covariance matrix.
rcsub$correctedVCOV

The corrected coefficients and confidence limits can again be exponentiated to obtain odds ratios:

# Exponentiate the corrected log-odds estimates and confidence limits.
corrected_RC_SUB <- exp(
  cbind(
    # Exponentiate the corrected coefficient estimates.
    OR = rcsub$correctedCoefTable[, 1],

    # Exponentiate the lower limits of the 95% confidence intervals.
    "2.5 %" = rcsub$correctedCoefTable[, 5],

    # Exponentiate the upper limits of the 95% confidence intervals.
    "97.5 %" = rcsub$correctedCoefTable[, 6]
  )
)

# Display the corrected odds ratios and 95% confidence intervals.
corrected_RC_SUB

Supported Outcome Models

and supply the appropriate family and link. For example, logistic regression uses:

family = binomial
link = "logit"

Dependencies

References

Rosner B, Willett WC, Spiegelman D (1989). Correction of logistic relative risk estimates and confidence intervals for systematic within-person measurement error. Statistics in Medicine 8, 1051–1069.

Rosner B, Spiegelman D, Willett WC (1990). Correction of logistic regression relative risk estimates and confidence intervals for measurement error: the case of multiple covariates measured with error. American Journal of Epidemiology 132, 734–745.

Spiegelman D, McDermott A, Rosner B (1997). The many uses of the regression calibration method for measurement error bias correction in nutritional epidemiology. American Journal of Clinical Nutrition 65, 1179S–1186S.

Spiegelman D, Carroll RJ, Kipnis V (2001). Efficient regression calibration for logistic regression in main study/internal validation study designs with an imperfect reference instrument. Statistics in Medicine 20, 139–160.

Carroll RJ, Ruppert D, Stefanski LA, Crainiceanu CM (2006). Measurement Error in Nonlinear Models: A Modern Perspective, 2nd ed. Chapman & Hall/CRC.

RegCalib