ciee function

CIEE: Causal inference based on estimating equations

Functions to perform CIEE under the GLM or AFT setting: ciee obtains point and standard error estimates of all parameter estimates, and p-values for testing the absence of effects; ciee_loop performs ciee in separate analyses of multiple exposure variables with the same outcome measures and factors ond only returns point estimates, standard error estimates and p-values for the exposure variables. Both functions can also compute estimates and p-values from the two traditional regression methods and from the structural equation modeling method.

ciee(setting = "GLM", estimates = c("ee", "mult_reg", "res_reg", "sem"),
  ee_se = c("sandwich"), BS_rep = NULL, Y = NULL, X = NULL, K = NULL,
  L = NULL, C = NULL)

ciee_loop(setting = "GLM", estimates = c("ee", "mult_reg", "res_reg",
  "sem"), ee_se = c("sandwich"), BS_rep = NULL, Y = NULL, X = NULL,
  K = NULL, L = NULL, C = NULL)

Arguments

• setting: String with value "GLM" or "AFT" indicating whether a normally-distributed ("GLM") or censored time-to-event ("AFT") primary outcome Y is analyzed.

• estimates: String vector with possible values "ee", "mult_reg", "res_reg", "sem" indicating which methods are computed. "ee" computes CIEE, "mult_reg"

  the traditional multiple regression method, "res_reg"

  the traditional regression of residuals method, and "sem" the structural equation modeling approach. Multiple methods can be specified.

• ee_se: String with possible values "sandwich", "bootstrap", "naive" indicating how the standard error estimates of the parameter estiamtes are computed for CIEE approach. "sandwich" computes the robust sandwich estimates (default, recommended), "bootstrap" the bootstrap estimates and "naive" the naive unadjusted standard error estimates (not recommended, only for comparison). One method has to be specified.

• BS_rep: Integer indicating the number of bootstrap samples that are drawn (recommended 1000) if bootstrap standard errors are computed.

• Y: Numeric input vector for the primary outcome.

• X: Numeric input vector for the exposure variable if the ciee

  function is used; or numeric input dataframe containing the exposure variables as columns if the ciee_loop function is used.

• K: Numeric input vector for the intermediate outcome.

• L: Numeric input vector for the observed confounding factor.

• C: Numeric input vector for the censoring indicator under the AFT setting (must be coded 0 = censored, 1 = uncensored).

Returns

Object of class ciee, for which the summary function summary.ciee is implemented. ciee returns a list containing the point and standard error estimates of all parameters as well as p-values from hypothesis tests of the absence of effects, for each specified approach. ciee_loop returns a list containing the point and standard error estimates only of the exposure variables as well as p-values from hypothesis tests of the absence of effects, for each specified approach.

Details

For the computation of CIEE, point estimates of the parameters are obtained using the get_estimates function. Robust sandwich (recommended), bootstrap, or naive standard error estimates of the parameter estimates are obtained using the sandwich_se, bootstrap_se

or naive_se function. Large-sample Wald-type tests are performed for testing the absence of effects, using either the robust sandwich or bootstrap standard errors.

Regarding the traditional regression methods, the multiple regression or regression of residual approaches can be computed using the mult_reg and res_reg functions. Finally, the structural equation modeling approachcan be performed using the sem_appl function.

Examples

# Generate data under the GLM setting with default values
maf <- 0.2
n <- 100
dat <- generate_data(n = n, maf = maf)
datX <- data.frame(X = dat$X)
names(datX)[1] <- "X1"
# Add 9 more exposure variables names X2, ..., X10 to X
for (i in 2:10){
  X <- stats::rbinom(n, size = 2, prob = maf)
  datX$X <- X
  names(datX)[i] <- paste("X", i, sep="")
}

# Perform analysis of one exposure variable using all four methods
ciee(Y = dat$Y, X = datX$X1, K = dat$K, L = dat$L)

# Perform analysis of all exposure variables only for CIEE
ciee_loop(estimates = "ee", Y = dat$Y, X = datX, K = dat$K, L = dat$L)