rc_algebraic: Regression Calibration (Algebraic Method)

In vandomed/meuc: Measurement Error and Unmeasured Confounding

Description

Implements the "algebraic" version of regression calibration as described by Rosner et al. (Stat. Med. 1989). For the "conditional expectation" version, see rc_cond_exp.

Usage

rc_algebraic(all_data = NULL, main = NULL, internal = NULL,
  external = NULL, y_var, z_var, d_var = NULL, c_vars = NULL,
  b_vars = NULL, tdm_covariates = NULL, tdm_family = "gaussian",
  mem_covariates = NULL, beta_0_formula = 1, delta_var = TRUE,
  boot_var = FALSE, boots = 100, alpha = 0.05)

Arguments

all_data	Data frame with data for main study and validation study.
main	Data frame with data for the main study.
internal	Data frame with data for internal validation study.
external	Data frame with data for the external validation study.
y_var	Character string specifying name of Y variable.
z_var	Character string specifying name of Z variable.
d_var	Character string specifying name of D variable.
c_vars	Character vector specifying names of C variables.
b_vars	Character vector specifying names of variables in true disease model but not in measurement error model.
tdm_covariates	Character vector specifying variables in true disease model. The Z variable is automatically included whether you include it in tdm_covariates or not.
tdm_family	Character string specifying family of true disease model (see glm).
mem_covariates	Character vector specifying variables in measurement error model.
beta_0_formula	If 1, formula for true disease model intercept is: beta_0.hat = betastar_0.hat - alpha_0.hat beta_Z.hat If 2, formula is: beta_0.hat = betastar_0.hat - alpha_0.hat beta_Z.hat - 1/2 beta_Z.hat^2 sigma_delta^2 Formula 1 yields the same beta_0.hat as the "conditional expectation" view of regression calibration (see rc_cond_exp). When the disease model is logistic regression and the measurement error model is linear regression, formula 1 is appropriate if Y is rare and Z|(D,C) is normal, and formula 2 is appropriate if beta_Z^2 sigma_delta^2 is small (Kuha, Stat. Med. 1994). If neither criteria is met, regression calibration may be unreliable.
delta_var	Logical value for whether to calculate a Delta method variance-covariance matrix.
boot_var	Logical value for whether to calculate a bootstrap variance-covariance matrix.
boots	Numeric value specifying number of bootstrap samples to use.
alpha	Significance level for percentile bootstrap confidence interval.

Details

The true disease model is a GLM:

g[E(Y)] = beta_0 + beta_z Z + beta_c^T C + beta_b^T B

The measurement error model is:

E(Z) = alpha_d D + alpha_c^T C

And the naive disease model is:

g[E(Y)] = beta*_0 + beta*_Z D + beta*_C^T C + beta*_B^T B

The procedure involves fitting the naive disease model using main study data, fitting the measurement error model using validation data, and solving a system of equations to get the regression calibration estimates.

Value

If no variance estimates are requested, a named numeric vector of parameter estimates. If one or more variance estimates are requested, a list that also contains a variance-covariance matrix for each variance estimator.

References

Kuha, J. (1994) "Corrections for exposure measurement error in logistic regression models with an application to nutritional data." Stat. Med. 13(11): 1135-1148.

Lyles, R.H. and Kupper, L.L. (2012) "Approximate and pseudo-likelihood analysis for logistic regression using external validation data to model log exposure." J. Agric. Biol. Environ. Stat. 18(1): 22-38.

Rosner, B., Willett, W. and Spiegelman, D. (1989) "Correction of logistic regression relative risk estimates and confidence intervals for systematic within-person measurement error." Stat. Med. 8(9): 1051-69.

Spiegelman, D., Carroll, R.J. and Kipnis, V. (2001) "Efficient regression calibration for logistic regression in main study/internal validation study designs with an imperfect reference instrument." Stat. Med. 20(1): 139-160.

vandomed/meuc documentation built on May 12, 2019, 6:17 p.m.