adjust_multinom_uc_omc_sel {multibias}

Adust for uncontrolled confounding, outcome misclassification, and selection bias.

Description

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

Usage

adjust_multinom_uc_omc_sel(
  data,
  exposure,
  outcome,
  confounders = NULL,
  u0y1_model_coefs,
  u1y0_model_coefs,
  u1y1_model_coefs,
  s_model_coefs,
  level = 0.95
)

Arguments

data

Dataframe for analysis.

exposure

String name of the exposure variable.

outcome

String name of the outcome variable.

confounders

String name(s) of the confounder(s). A maximum of three confounders are allowed.

u0y1_model_coefs

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

u1y0_model_coefs

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

u1y1_model_coefs

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

level

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

Details

This function uses one bias model, a multinomial logistic regression model, to predict the uncontrolled confounder (U) and outcome (Y). If separate bias models for U and Y are desired, use adjust_uc_omc_sel.

Values for the regression coefficients 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.

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).

Examples

adjust_multinom_uc_omc_sel(
  df_uc_omc_sel,
  exposure = "X",
  outcome = "Ystar",
  confounders = c("C1", "C2", "C3"),
  u1y0_model_coefs = c(-0.20, 0.62, 0.01, -0.08, 0.10, -0.15),
  u0y1_model_coefs = c(-3.28, 0.63, 1.65, 0.42, -0.85, 0.26),
  u1y1_model_coefs = c(-2.70, 1.22, 1.64, 0.32, -0.77, 0.09),
  s_model_coefs = c(0.00, 0.74, 0.19, 0.02, -0.06, 0.02)
)