multibias (version 1.6.3)

adjust_uc_em_sel: Adust for uncontrolled confounding, exposure misclassification, and selection bias.

Description

adjust_uc_em_sel returns the exposure-outcome odds ratio and confidence interval, adjusted for uncontrolled confounding, exposure misclassificaiton, and selection bias.

Usage

adjust_uc_em_sel(
  data_observed,
  data_validation = NULL,
  u_model_coefs = NULL,
  x_model_coefs = NULL,
  x1u0_model_coefs = NULL,
  x0u1_model_coefs = NULL,
  x1u1_model_coefs = NULL,
  s_model_coefs = NULL,
  level = 0.95
)

Value

A list where the first item is the odds ratio estimate of the effect of the exposure on the outcome and the second item is the confidence interval as the vector: (lower bound, upper bound).

Arguments

data_observed

Object of class data_observed corresponding to the data to perform bias analysis on.

data_validation

Object of class data_validation corresponding to the validation data used to adjust for bias in the observed data. Here, the validation data should have data for the same variables as in the observed data, plus data for: 1) the true and misclassified exposure corresponding to the observed exposure in data_observed, 2) the confounder missing in data_observed, 3) a selection indicator representing whether the observation in data_validation was selected in data_observed.

u_model_coefs

The regression coefficients corresponding to the model: logit(P(U=1)) = α₀ + α₁X + α₂Y, where U is the binary unmeasured confounder, X is the binary true exposure, and Y is the outcome. The number of parameters therefore equals 3.

x_model_coefs

The regression coefficients corresponding to the model: logit(P(X=1)) = δ₀ + δ₁X* + δ₂Y + δ_2+jC_j, where X represents binary true exposure, X* is the binary misclassified exposure, Y is the outcome, C represents the vector of measured confounders (if any), and j corresponds to the number of measured confounders. The number of parameters therefore equals 3 + j.

x1u0_model_coefs

The regression coefficients corresponding to the model: log(P(X=1,U=0)/P(X=0,U=0)) = γ_1,0 + γ_1,1X* + γ_1,2Y + γ_1,2+jC_j, where X is the binary true exposure, U is the binary unmeasured confounder, X* is the binary misclassified exposure, Y is the outcome, C represents the vector of measured confounders (if any), and j corresponds to the number of measured confounders.

x0u1_model_coefs

The regression coefficients corresponding to the model: log(P(X=0,U=1)/P(X=0,U=0)) = γ_2,0 + γ_2,1X* + γ_2,2Y + γ_2,2+jC_j, where X is the binary true exposure, U is the binary unmeasured confounder, X* is the binary misclassified exposure, Y is the outcome, C represents the vector of measured confounders (if any), and j corresponds to the number of measured confounders.

x1u1_model_coefs

The regression coefficients corresponding to the model: log(P(X=1,U=1)/P(X=0,U=0)) = γ_3,0 + γ_3,1X* + γ_3,2Y + γ_3,2+jC_j, where X is the binary true exposure, U is the binary unmeasured confounder, X* is the binary misclassified exposure, Y is the outcome, C represents the vector of measured confounders (if any), and j corresponds to the number of measured confounders.

s_model_coefs

The regression coefficients corresponding to the model: logit(P(S=1)) = β₀ + β₁X* + β₂Y + β_2+jC_2+j, where S represents binary selection, X* is the binary misclassified exposure, Y is the outcome, C represents the vector of measured confounders (if any), and j corresponds to the number of measured confounders. The number of parameters therefore equals 3 + j.

level

Value from 0-1 representing the full range of the confidence interval. Default is 0.95.

Details

Bias adjustment can be performed by inputting either a validation dataset or the necessary bias parameters. Two different options for the bias parameters are availale here: 1) parameters from separate models of U and X (u_model_coefs and x_model_coefs) or 2) parameters from a joint model of U and X (x1u0_model_coefs, x0u1_model_coefs, and x1u1_model_coefs). Both approaches require s_model_coefs.

Values for the bias parameters can be applied as fixed values or as single draws from a probability distribution (ex: rnorm(1, mean = 2, sd = 1)). The latter has the advantage of allowing the researcher to capture the uncertainty in the bias parameter estimates. To incorporate this uncertainty in the estimate and confidence interval, this function should be run in loop across bootstrap samples of the dataframe for analysis. The estimate and confidence interval would then be obtained from the median and quantiles of the distribution of odds ratio estimates.

Examples

df_observed <- data_observed(
  data = df_uc_em_sel,
  exposure = "Xstar",
  outcome = "Y",
  confounders = c("C1", "C2", "C3")
)

# Using validation data -----------------------------------------------------
df_validation <- data_validation(
  data = df_uc_em_sel_source,
  true_exposure = "X",
  true_outcome = "Y",
  confounders = c("C1", "C2", "C3", "U"),
  misclassified_exposure = "Xstar",
  selection = "S"
)

adjust_uc_em_sel(
  data_observed = df_observed,
  data_validation = df_validation
)

# Using u_model_coefs, x_model_coefs, s_model_coefs -------------------------
adjust_uc_em_sel(
  data_observed = df_observed,
  u_model_coefs = c(-0.32, 0.59, 0.69),
  x_model_coefs = c(-2.44, 1.62, 0.72, 0.32, -0.15, 0.85),
  s_model_coefs = c(0.00, 0.26, 0.78, 0.03, -0.02, 0.10)
)

# Using x1u0_model_coefs, x0u1_model_coefs, x1u1_model_coefs, s_model_coefs
adjust_uc_em_sel(
  data_observed = df_observed,
  x1u0_model_coefs = c(-2.78, 1.62, 0.61, 0.36, -0.27, 0.88),
  x0u1_model_coefs = c(-0.17, -0.01, 0.71, -0.08, 0.07, -0.15),
  x1u1_model_coefs = c(-2.36, 1.62, 1.29, 0.25, -0.06, 0.74),
  s_model_coefs = c(0.00, 0.26, 0.78, 0.03, -0.02, 0.10)
)