multibias (version 1.6.3)

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

Description

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

Usage

adjust_uc_om_sel(
  data_observed,
  data_validation = NULL,
  u_model_coefs = NULL,
  y_model_coefs = NULL,
  u0y1_model_coefs = NULL,
  u1y0_model_coefs = NULL,
  u1y1_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 outcome corresponding to the observed outcome 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 exposure, and Y is the binary true outcome. The number of parameters therefore equals 3.

y_model_coefs

The regression coefficients corresponding to the model: logit(P(Y=1)) = δ₀ + δ₁X + δ₂Y* + δ_2+jC_j, where Y represents binary true outcome, X is the exposure, Y* is the binary misclassified 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.

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 exposure, Y* is the binary misclassified 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.

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 exposure, Y* is the binary misclassified 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.

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 exposure, Y* is the binary misclassified 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.

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 exposure, Y* is the binary misclassified 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 Y (u_model_coefs and y_model_coefs) or 2) parameters from a joint model of U and Y (u1y0_model_coefs, u0y1_model_coefs, and u1y1_model_coefs). Both approaches require s_model_coefs.

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.

Examples

df_observed <- data_observed(
  data = df_uc_om_sel,
  exposure = "X",
  outcome = "Ystar",
  confounders = c("C1", "C2", "C3")
)

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

adjust_uc_om_sel(
  data_observed = df_observed,
  data_validation = df_validation
)

# Using u_model_coefs, y_model_coefs, s_model_coefs -------------------------
adjust_uc_om_sel(
  data_observed = df_observed,
  u_model_coefs = c(-0.32, 0.59, 0.69),
  y_model_coefs = c(-2.85, 0.71, 1.63, 0.40, -0.85, 0.22),
  s_model_coefs = c(0.00, 0.74, 0.19, 0.02, -0.06, 0.02)
)

# Using u1y0_model_coefs, u0y1_model_coefs, u1y1_model_coefs, s_model_coefs
adjust_uc_om_sel(
  data_observed = df_observed,
  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)
)