Adust for uncontrolled confounding. — adjust

adjust_uc returns the exposure-outcome odds ratio and confidence interval, adjusted for uncontrolled confounding from a binary confounder.

Usage

adjust_uc(
  data_observed,
  data_validation = NULL,
  u_model_coefs = NULL,
  level = 0.95
)

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 the confounder missing in data_observed.
u_model_coefs: The regression coefficients corresponding to the model: logit(P(U=1)) = α₀ + α₁X + α₂Y + α_2+jC_j, where U is the binary unmeasured confounder, X is the 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.

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).

Details

Bias adjustment can be performed by inputting either a validation dataset or the necessary bias parameters. 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,
  exposure = "X_bi",
  outcome = "Y_bi",
  confounders = c("C1", "C2", "C3")
)

# Using validation data -----------------------------------------------------
df_validation <- data_validation(
  data = df_uc_source,
  true_exposure = "X_bi",
  true_outcome = "Y_bi",
  confounders = c("C1", "C2", "C3", "U")
)

adjust_uc(
  data_observed = df_observed,
  data_validation = df_validation
)
#> $estimate
#> [1] 2.004645
#> 
#> $ci
#> [1] 1.93717 2.07447
#> 

# Using u_model_coefs -------------------------------------------------------
adjust_uc(
  data_observed = df_observed,
  u_model_coefs = c(-0.19, 0.61, 0.70, -0.09, 0.10, -0.15)
)
#> $estimate
#> [1] 2.001891
#> 
#> $ci
#> [1] 1.934495 2.071634
#>