Package 'multibias'

Title: Simultaneous Multi-Bias Adjustment
Description: Quantify the causal effect of a binary exposure on a binary outcome with adjustment for multiple biases. The functions can simultaneously adjust for any combination of uncontrolled confounding, exposure/outcome misclassification, and selection bias. The underlying method generalizes the concept of combining inverse probability of selection weighting with predictive value weighting. Simultaneous multi-bias analysis can be used to enhance the validity and transparency of real-world evidence obtained from observational, longitudinal studies. Based on the work from Paul Brendel, Aracelis Torres, and Onyebuchi Arah (2023) <doi:10.1093/ije/dyad001>.
Authors: Paul Brendel [aut, cre, cph]
Maintainer: Paul Brendel <[email protected]>
License: MIT + file LICENSE
Version: 1.6
Built: 2024-10-27 12:33:18 UTC
Source: CRAN

Help Index

Adust for exposure misclassification.

Description

adjust_em returns the exposure-outcome odds ratio and confidence interval, adjusted for exposure misclassificaiton.

Usage

adjust_em(
  data_observed,
  data_validation = NULL,
  x_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 true and misclassified exposure corresponding to the observed exposure in data_observed.
x_model_coefs

The regression coefficients corresponding to the model: logit(P(X=1)) = δ0 + δ1X* + δ2Y + δ2+jCj, where X represents the 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 is therefore 3 + j.
level

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

Details

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

df_observed <- data_observed(
  data = df_em,
  exposure = "Xstar",
  outcome = "Y",
  confounders = "C1"
)

# Using validation data -----------------------------------------------------
df_validation <- data_validation(
  data = df_em_source,
  true_exposure = "X",
  true_outcome = "Y",
  confounders = "C1",
  misclassified_exposure = "Xstar"
)

adjust_em(
  data_observed = df_observed,
  data_validation = df_validation
)

# Using x_model_coefs -------------------------------------------------------
adjust_em(
  data_observed = df_observed,
  x_model_coefs = c(-2.10, 1.62, 0.63, 0.35)
)

Adust for exposure misclassification and outcome misclassification.

Description

adjust_em_om returns the exposure-outcome odds ratio and confidence interval, adjusted for exposure misclassification and outcome misclassification. Two different options for the bias parameters are available here: 1) parameters from separate models of X and Y (x_model_coefs and y_model_coefs) or 2) parameters from a joint model of X and Y (x1y0_model_coefs, x0y1_model_coefs, and x1y1_model_coefs).

Usage

adjust_em_om(
  data_observed,
  x_model_coefs = NULL,
  y_model_coefs = NULL,
  x1y0_model_coefs = NULL,
  x0y1_model_coefs = NULL,
  x1y1_model_coefs = NULL,
  level = 0.95
)

Arguments

data_observed

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

The regression coefficients corresponding to the model: logit(P(X=1)) = δ0 + δ1X* + δ2Y* + δ2+jCj, where X represents the binary true exposure, X* is the binary misclassified 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 is therefore 3 + j.
y_model_coefs

The regression coefficients corresponding to the model: logit(P(Y=1)) = β0 + β1X + β2Y* + β2+jCj, where Y represents the binary true exposure, X is the binary 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 is therefore 3 + j.
x1y0_model_coefs

The regression coefficients corresponding to the model: log(P(X=1,Y=0) / P(X=0,Y=0)) = γ1,0 + γ1,1X* + γ1,2Y* + γ1,2+jCj, where X is the binary true exposure, Y is the binary true outcome, X* is the binary misclassified 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.
x0y1_model_coefs

The regression coefficients corresponding to the model: log(P(X=0,Y=1) / P(X=0,Y=0)) = γ2,0 + γ2,1X* + γ2,2Y* + γ2,2+jCj, where X is the binary true exposure, Y is the binary true outcome, X* is the binary misclassified 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.
x1y1_model_coefs

The regression coefficients corresponding to the model: log(P(X=1,Y=1) / P(X=0,Y=0)) = γ3,0 + γ3,1X* + γ3,2Y* + γ3,2+jCj, where X is the binary true exposure, Y is the binary true outcome, X* is the binary misclassified 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.
level

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

Details

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

df <- data_observed(
  data = df_em_om,
  exposure = "Xstar",
  outcome = "Ystar",
  confounders = "C1"
)

# Using x_model_coefs and y_model_coefs -------------------------------------
adjust_em_om(
  df,
  x_model_coefs = c(-2.15, 1.64, 0.35, 0.38),
  y_model_coefs = c(-3.10, 0.63, 1.60, 0.39)
)

# Using x1y0_model_coefs, x0y1_model_coefs, and x1y1_model_coefs ------------
adjust_em_om(
  df,
  x1y0_model_coefs = c(-2.18, 1.63, 0.23, 0.36),
  x0y1_model_coefs = c(-3.17, 0.22, 1.60, 0.40),
  x1y1_model_coefs = c(-4.76, 1.82, 1.83, 0.72)
)

Adust for exposure misclassification and selection bias.

Description

adjust_em_sel returns the exposure-outcome odds ratio and confidence interval, adjusted for exposure misclassification and selection bias.

Usage

adjust_em_sel(data_observed, x_model_coefs, s_model_coefs, level = 0.95)

Arguments

data_observed

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

The regression coefficients corresponding to the model: logit(P(X=1)) = δ0 + δ1X* + δ2Y + δ2+jCj, where X represents the 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 is therefore 3 + j.
s_model_coefs

The regression coefficients corresponding to the model: logit(P(S=1)) = β0 + β1X* + β2Y + β2+jCj, 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 is therefore 3 + j.
level

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

Details

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

df <- data_observed(
  data = df_em_sel,
  exposure = "Xstar",
  outcome = "Y",
  confounders = "C1"
)
adjust_em_sel(
  df,
  x_model_coefs = c(-2.78, 1.62, 0.58, 0.34),
  s_model_coefs = c(0.04, 0.18, 0.92, 0.05)
)

Adust for outcome misclassification.

Description

adjust_om returns the exposure-outcome odds ratio and confidence interval, adjusted for outcome misclassificaiton.

Usage

adjust_om(
  data_observed,
  data_validation = NULL,
  y_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 true and misclassified outcome corresponding to the observed outcome in data_observed.
y_model_coefs

The regression coefficients corresponding to the model: logit(P(Y=1)) = δ0 + δ1X + δ2Y* + δ2+jCj, where Y represents 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 is therefore 3 + j.
level

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

Details

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

df_observed <- data_observed(
  data = df_om,
  exposure = "X",
  outcome = "Ystar",
  confounders = "C1"
)
# Using validation data -----------------------------------------------------
df_validation <- data_validation(
  data = df_om_source,
  true_exposure = "X",
  true_outcome = "Y",
  confounders = "C1",
  misclassified_outcome = "Ystar"
)

adjust_om(
  data_observed = df_observed,
  data_validation = df_validation
)

# Using y_model_coefs -------------------------------------------------------
adjust_om(
  data_observed = df_observed,
  y_model_coefs = c(-3.1, 0.6, 1.6, 0.4)
)

Adust for outcome misclassification and selection bias.

Description

adjust_om_sel returns the exposure-outcome odds ratio and confidence interval, adjusted for outcome misclassification and selection bias.

Usage

adjust_om_sel(data_observed, y_model_coefs, s_model_coefs, level = 0.95)

Arguments

data_observed

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

The regression coefficients corresponding to the model: logit(P(Y=1)) = δ0 + δ1X + δ2Y* + δ2+jCj, where Y represents 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 is therefore 3 + j.
s_model_coefs

The regression coefficients corresponding to the model: logit(P(S=1)) = β0 + β1X + β2Y* + β2+jCj, 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 is therefore 3 + j.
level

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

Details

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

df <- data_observed(
  data = df_om_sel,
  exposure = "X",
  outcome = "Ystar",
  confounders = "C1"
)
adjust_om_sel(
  df,
  y_model_coefs = c(-3.24, 0.58, 1.59, 0.45),
  s_model_coefs = c(0.03, 0.92, 0.12, 0.05)
)

Adust for selection bias.

Description

adjust_sel returns the exposure-outcome odds ratio and confidence interval, adjusted for selection bias.

Usage

adjust_sel(
  data_observed,
  data_validation = NULL,
  s_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 selection indicator representing whether the observation was selected in data_observed.
s_model_coefs

The regression coefficients corresponding to the model: logit(P(S=1)) = β0 + β1X + β2Y, where S represents binary selection, X is the exposure, and Y is the outcome. The number of parameters is therefore 3.
level

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

Details

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

df_observed <- data_observed(
  data = df_sel,
  exposure = "X",
  outcome = "Y",
  confounders = "C1"
)

# Using validation data -----------------------------------------------------
df_validation <- data_validation(
  data = df_sel_source,
  true_exposure = "X",
  true_outcome = "Y",
  confounders = "C1",
  selection = "S"
)

adjust_sel(
  data_observed = df_observed,
  data_validation = df_validation
)

# Using s_model_coefs -------------------------------------------------------
adjust_sel(
  data_observed = df_observed,
  s_model_coefs = c(0, 0.9, 0.9)
)

Adust for uncontrolled confounding.

Description

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 + α2+jCj, 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.

Details

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

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
)

# 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)
)

Adust for uncontrolled confounding and exposure misclassification.

Description

adjust_uc_em returns the exposure-outcome odds ratio and confidence interval, adjusted for uncontrolled confounding and exposure misclassificaiton. Two different options for the bias parameters are available 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).

Usage

adjust_uc_em(
  data_observed,
  u_model_coefs = NULL,
  x_model_coefs = NULL,
  x1u0_model_coefs = NULL,
  x0u1_model_coefs = NULL,
  x1u1_model_coefs = NULL,
  level = 0.95
)

Arguments

data_observed

Object of class data_observed corresponding to the data to perform bias analysis on.
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 + δ2+jCj, where X represents the binary true exposure, X* is the binary misclassified exposure, Y is the outcome, and 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)) = γ1,0 + γ1,1X* + γ1,2Y + γ1,2+jCj, 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)) = γ2,0 + γ2,1X* + γ2,2Y + γ2,2+jCj, 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)) = γ3,0 + γ3,1X* + γ3,2Y + γ3,2+jCj, 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.
level

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

Details

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

df <- data_observed(
  data = df_uc_em,
  exposure = "Xstar",
  outcome = "Y",
  confounders = "C1"
)
# Using u_model_coefs and x_model_coefs -------------------------------------
adjust_uc_em(
  df,
  u_model_coefs = c(-0.23, 0.63, 0.66),
  x_model_coefs = c(-2.47, 1.62, 0.73, 0.32)
)

# Using x1u0_model_coefs, x0u1_model_coefs, x1u1_model_coefs ----------------
adjust_uc_em(
  df,
  x1u0_model_coefs = c(-2.82, 1.62, 0.68, -0.06),
  x0u1_model_coefs = c(-0.20, 0.00, 0.68, -0.05),
  x1u1_model_coefs = c(-2.36, 1.62, 1.29, 0.27)
)

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. 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.

Usage

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

Arguments

data_observed

Object of class data_observed corresponding to the data to perform bias analysis on.
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 + δ2+jCj, 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)) = γ1,0 + γ1,1X* + γ1,2Y + γ1,2+jCj, 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)) = γ2,0 + γ2,1X* + γ2,2Y + γ2,2+jCj, 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)) = γ3,0 + γ3,1X* + γ3,2Y + γ3,2+jCj, 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 + β2+jC2+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

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

df <- data_observed(
  data = df_uc_em_sel,
  exposure = "Xstar",
  outcome = "Y",
  confounders = c("C1", "C2", "C3")
)
# Using u_model_coefs, x_model_coefs, s_model_coefs -------------------------
adjust_uc_em_sel(
  df,
  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(
  df,
  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)
)

Adust for uncontrolled confounding and outcome misclassification.

Description

adjust_uc_om returns the exposure-outcome odds ratio and confidence interval, adjusted for uncontrolled confounding and outcome misclassificaiton. Two different options for the bias parameters are available 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).

Usage

adjust_uc_om(
  data_observed,
  u_model_coefs = NULL,
  y_model_coefs = NULL,
  u1y0_model_coefs = NULL,
  u0y1_model_coefs = NULL,
  u1y1_model_coefs = NULL,
  level = 0.95
)

Arguments

data_observed

Object of class data_observed corresponding to the data to perform bias analysis on.
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, 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* + δ2+jCj, 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.
u1y0_model_coefs

The regression coefficients corresponding to the model: log(P(U=1,Y=0)/P(U=0,Y=0)) = γ1,0 + γ1,1X + γ1,2Y* + γ1,2+jCj, 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.
u0y1_model_coefs

The regression coefficients corresponding to the model: log(P(U=0,Y=1)/P(U=0,Y=0)) = γ2,0 + γ2,1X + γ2,2Y* + γ2,2+jCj, 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.
u1y1_model_coefs

The regression coefficients corresponding to the model: log(P(U=1,Y=1)/P(U=0,Y=0)) = γ3,0 + γ3,1X + γ3,2Y* + γ3,2+jCj, 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.
level

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

Details

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

df <- data_observed(
  data = df_uc_om,
  exposure = "X",
  outcome = "Ystar",
  confounders = "C1"
)
# Using u_model_coefs and y_model_coefs -------------------------------------
adjust_uc_om(
  df,
  u_model_coefs = c(-0.22, 0.61, 0.70),
  y_model_coefs = c(-2.85, 0.73, 1.60, 0.38)
)

# Using u1y0_model_coefs, u0y1_model_coefs, u1y1_model_coefs ----------------
adjust_uc_om(
  df,
  u1y0_model_coefs = c(-0.19, 0.61, 0.00, -0.07),
  u0y1_model_coefs = c(-3.21, 0.60, 1.60, 0.36),
  u1y1_model_coefs = c(-2.72, 1.24, 1.59, 0.34)
)

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. 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.

Usage

adjust_uc_om_sel(
  data_observed,
  u_model_coefs = NULL,
  y_model_coefs = NULL,
  u0y1_model_coefs = NULL,
  u1y0_model_coefs = NULL,
  u1y1_model_coefs = NULL,
  s_model_coefs,
  level = 0.95
)

Arguments

data_observed

Object of class data_observed corresponding to the data to perform bias analysis on.
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* + δ2+jCj, 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)) = γ2,0 + γ2,1X + γ2,2Y* + γ2,2+jCj, 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)) = γ1,0 + γ1,1X + γ1,2Y* + γ1,2+jCj, 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)) = γ3,0 + γ3,1X + γ3,2Y* + γ3,2+jCj, 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* + β2+jC2+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

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

df <- data_observed(
  data = df_uc_om_sel,
  exposure = "X",
  outcome = "Ystar",
  confounders = c("C1", "C2", "C3")
)
# Using u_model_coefs, y_model_coefs, s_model_coefs -------------------------
adjust_uc_om_sel(
  df,
  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(
  df,
  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)
)

Adust for uncontrolled confounding and selection bias.

Description

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

Usage

adjust_uc_sel(data_observed, u_model_coefs, s_model_coefs, level = 0.95)

Arguments

data_observed

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

The regression coefficients corresponding to the model: logit(P(U=1)) = α0 + α1X + α2Y + α2+jCj, 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.
s_model_coefs

The regression coefficients corresponding to the model: logit(P(S=1)) = β0 + β1X + β2Y, where S represents binary selection, X is the exposure, and Y is the outcome. The number of parameters therefore equals 3.
level

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

Details

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

df <- data_observed(
  data = df_uc_sel,
  exposure = "X",
  outcome = "Y",
  confounders = c("C1", "C2", "C3")
)
adjust_uc_sel(
  df,
  u_model_coefs = c(-0.19, 0.61, 0.72, -0.09, 0.10, -0.15),
  s_model_coefs = c(-0.01, 0.92, 0.94)
)

Represent observed causal data

Description

data_observed combines the observed dataframe with specific identification of the columns corresponding to the exposure, outcome, and confounders. It is an essential input of all adjust functions.

Usage

data_observed(data, exposure, outcome, confounders = NULL)

Arguments

data

Dataframe for bias analysis.
exposure

String name of the column in data corresponding to the exposure variable.
outcome

String name of the column in data corresponding to the outcome variable.
confounders

String name(s) of the column(s) in data corresponding to the confounding variable(s).

Examples

df <- data_observed(
  data = df_sel,
  exposure = "X",
  outcome = "Y",
  confounders = c("C1", "C2", "C3")
)

Represent validation causal data

Description

data_validation combines the validation dataframe with specific identification of the appropriate columns for bias adjustment, including: true exposure, true outcome, confounders, misclassified exposure, misclassified outcome, and selection. The purpose of validation data is to use an external data source to transport the necessary causal relationships that are missing in the observed data.

Usage

data_validation(
  data,
  true_exposure,
  true_outcome,
  confounders = NULL,
  misclassified_exposure = NULL,
  misclassified_outcome = NULL,
  selection = NULL
)

Arguments

data

Dataframe of validation data
true_exposure

String name of the column in data corresponding to the true exposure.
true_outcome

String name of the column in data corresponding to the true outcome.
confounders

String name(s) of the column(s) in data corresponding to the confounding variable(s).
misclassified_exposure

String name of the column in data corresponding to the misclassified exposure.
misclassified_outcome

String name of the column in data corresponding to the misclassified outcome.
selection

String name of the column in data corresponding to the selection indicator.

Examples

df <- data_validation(
  data = df_sel_source,
  true_exposure = "X",
  true_outcome = "Y",
  confounders = c("C1", "C2", "C3"),
  selection = "S"
)

Simulated data with exposure misclassification

Description

Data containing one source of bias, three known confounders, and 100,000 observations. This data is obtained from df_emc_source by removing the column X. The resulting data corresponds to what a researcher would see in the real-world: a misclassified exposure, Xstar, and no data on the true exposure. As seen in df_emc_source, the true, unbiased exposure-outcome odds ratio = 2.

Usage

df_em

Format

A dataframe with 100,000 rows and 5 columns:

Xstar

misclassified exposure, 1 = present and 0 = absent

Y

outcome, 1 = present and 0 = absent

C1

1st confounder, 1 = present and 0 = absent

C2

2nd confounder, 1 = present and 0 = absent

C3

3rd confounder, 1 = present and 0 = absent

Simulated data with exposure misclassification and outcome misclassification

Description

Data containing two sources of bias, three known confounders, and 100,000 observations. This data is obtained from df_emc_omc_source by removing the columns X and Y. The resulting data corresponds to what a researcher would see in the real-world: a misclassified exposure, Xstar, and a misclassified outcome, Ystar. As seen in df_em_om_source, the true, unbiased exposure-outcome odds ratio = 2.

Usage

df_em_om

Format

A dataframe with 100,000 rows and 5 columns:

Xstar

misclassified exposure, 1 = present and 0 = absent

Ystar

misclassified outcome, 1 = present and 0 = absent

C1

1st confounder, 1 = present and 0 = absent

C2

2nd confounder, 1 = present and 0 = absent

C3

3rd confounder, 1 = present and 0 = absent

Data source for df_em_om

Description

Data with complete information on the two sources of bias, three known confounders, and 100,000 observations. This data is used to derive df_em_om and can be used to obtain bias parameters for purposes of validating the simultaneous multi-bias adjustment method with df_em_om. With this source data, the fitted regression logit(P(Y=1)) = α0 + α1X + α2C1 + α3C2 + α4C3 shows that the true, unbiased exposure-outcome odds ratio = 2.

Usage

df_em_om_source

Format

A dataframe with 100,000 rows and 7 columns:

X

true exposure, 1 = present and 0 = absent

Y

outcome, 1 = present and 0 = absent

C1

1st confounder, 1 = present and 0 = absent

C2

2nd confounder, 1 = present and 0 = absent

C3

3rd confounder, 1 = present and 0 = absent

Xstar

misclassified exposure, 1 = present and 0 = absent

Ystar

misclassified outcome, 1 = present and 0 = absent

Simulated data with exposure misclassification and selection bias

Description

Data containing two sources of bias, three known confounders, and 100,000 observations. This data is obtained by sampling with replacement with probability = S from df_em_sel_source then removing the columns X and S. The resulting data corresponds to what a researcher would see in the real-world: a misclassified exposure, Xstar, and missing data for those not selected into the study (S=0). As seen in df_em_sel_source, the true, unbiased exposure-outcome odds ratio = 2.

Usage

df_em_sel

Format

A dataframe with 100,000 rows and 5 columns:

Xstar

misclassified exposure, 1 = present and 0 = absent

Y

outcome, 1 = present and 0 = absent

C1

1st confounder, 1 = present and 0 = absent

C2

2nd confounder, 1 = present and 0 = absent

C3

3rd confounder, 1 = present and 0 = absent

Data source for df_em_sel

Description

Data with complete information on the two sources of bias, three known confounders, and 100,000 observations. This data is used to derive df_em_sel and can be used to obtain bias parameters for purposes of validating the simultaneous multi-bias adjustment method with df_em_sel. With this source data, the fitted regression logit(P(Y=1)) = α0 + α1X + α2C1 + α3C2 + α4C3 shows that the true, unbiased exposure-outcome odds ratio = 2.

Usage

df_em_sel_source

Format

A dataframe with 100,000 rows and 7 columns:

X

true exposure, 1 = present and 0 = absent

Y

outcome, 1 = present and 0 = absent

C1

1st confounder, 1 = present and 0 = absent

C2

2nd confounder, 1 = present and 0 = absent

C3

3rd confounder, 1 = present and 0 = absent

Xstar

misclassified exposure, 1 = present and 0 = absent

S

selection, 1 = selected into the study and 0 = not selected into the study

Data source for df_em

Description

Data with complete information on one sources of bias, three known confounders, and 100,000 observations. This data is used to derive df_em and can be used to obtain bias parameters for purposes of validating the simultaneous multi-bias adjustment method with df_em. With this source data, the fitted regression logit(P(Y=1)) = α0 + α1X + α2C1 + α3C2 + α4C3 shows that the true, unbiased exposure-outcome odds ratio = 2.

Usage

df_em_source

Format

A dataframe with 100,000 rows and 6 columns:

X

exposure, 1 = present and 0 = absent

Y

true outcome, 1 = present and 0 = absent

C1

1st confounder, 1 = present and 0 = absent

C2

2nd confounder, 1 = present and 0 = absent

C3

3rd confounder, 1 = present and 0 = absent

Xstar

misclassified exposure, 1 = present and 0 = absent

Simulated data with outcome misclassification

Description

Data containing one source of bias, three known confounders, and 100,000 observations. This data is obtained from df_om_source by removing the column Y. The resulting data corresponds to what a researcher would see in the real-world: a misclassified outcome, Ystar, and no data on the true outcome. As seen in df_om_source, the true, unbiased exposure-outcome odds ratio = 2.

Usage

df_om

Format

A dataframe with 100,000 rows and 5 columns:

X

exposure, 1 = present and 0 = absent

Ystar

misclassified outcome, 1 = present and 0 = absent

C1

1st confounder, 1 = present and 0 = absent

C2

2nd confounder, 1 = present and 0 = absent

C3

3rd confounder, 1 = present and 0 = absent

Simulated data with outcome misclassification and selection bias

Description

Data containing two sources of bias, a known confounder, and 100,000 observations. This data is obtained by sampling with replacement with probability = S from df_om_sel_source then removing the columns Y and S. The resulting data corresponds to what a researcher would see in the real-world: a misclassified outcome, Ystar, and missing data for those not selected into the study (S=0). As seen in df_om_sel_source, the true, unbiased exposure-outcome odds ratio = 2.

Usage

df_om_sel

Format

A dataframe with 100,000 rows and 5 columns:

X

exposure, 1 = present and 0 = absent

Ystar

misclassified outcome, 1 = present and 0 = absent

C1

1st confounder, 1 = present and 0 = absent

C2

2nd confounder, 1 = present and 0 = absent

C3

3rd confounder, 1 = present and 0 = absent

Data source for df_om_sel

Description

Data with complete information on the two sources of bias, a known confounder, and 100,000 observations. This data is used to derive df_om_sel and can be used to obtain bias parameters for purposes of validating the simultaneous multi-bias adjustment method with df_om_sel. With this source data, the fitted regression logit(P(Y=1)) = α0 + α1X + α2C1 + α3C2 + α4C3 shows that the true, unbiased exposure-outcome odds ratio = 2.

Usage

df_om_sel_source

Format

A dataframe with 100,000 rows and 7 columns:

X

exposure, 1 = present and 0 = absent

Y

true outcome, 1 = present and 0 = absent

C1

1st confounder, 1 = present and 0 = absent

C2

2nd confounder, 1 = present and 0 = absent

C3

3rd confounder, 1 = present and 0 = absent

Ystar

misclassified outcome, 1 = present and 0 = absent

S

selection, 1 = selected into the study and 0 = not selected into the study

Data source for df_om

Description

Data with complete information on one sources of bias, three known confounders, and 100,000 observations. This data is used to derive df_om and can be used to obtain bias parameters for purposes of validating the simultaneous multi-bias adjustment method with df_om. With this source data, the fitted regression logit(P(Y=1)) = α0 + α1X + α2C1 + α3C2 + α4C3 shows that the true, unbiased exposure-outcome odds ratio = 2.

Usage

df_om_source

Format

A dataframe with 100,000 rows and 6 columns:

X

exposure, 1 = present and 0 = absent

Y

true outcome, 1 = present and 0 = absent

C1

1st confounder, 1 = present and 0 = absent

C2

2nd confounder, 1 = present and 0 = absent

C3

3rd confounder, 1 = present and 0 = absent

Ystar

misclassified outcome, 1 = present and 0 = absent

Simulated data with selection bias

Description

Data containing one source of bias, three known confounders, and 100,000 observations. This data is obtained by sampling with replacement with probability = S from df_sel_source then removing the S column. The resulting data corresponds to what a researcher would see in the real-world: missing data for those not selected into the study (S=0). As seen in df_sel_source, the true, unbiased exposure-outcome odds ratio = 2.

Usage

df_sel

Format

A dataframe with 100,000 rows and 5 columns:

X

exposure, 1 = present and 0 = absent

Y

outcome, 1 = present and 0 = absent

C1

1st confounder, 1 = present and 0 = absent

C2

2nd confounder, 1 = present and 0 = absent

C3

3rd confounder, 1 = present and 0 = absent

Data source for df_sel

Description

Data with complete information on study selection, three known confounders, and 100,000 observations. This data is used to derive df_sel and can be used to obtain bias parameters for purposes of validating the simultaneous multi-bias adjustment method with df_sel. With this source data, the fitted regression logit(P(Y=1)) = α0 + α1X + α2C1 + α3C2 + α4C3 shows that the true, unbiased exposure-outcome odds ratio = 2.

Usage

df_sel_source

Format

A dataframe with 100,000 rows and 6 columns:

X

true exposure, 1 = present and 0 = absent

Y

outcome, 1 = present and 0 = absent

C1

1st confounder, 1 = present and 0 = absent

C2

2nd confounder, 1 = present and 0 = absent

C3

3rd confounder, 1 = present and 0 = absent

S

selection, 1 = selected into the study and 0 = not selected into the study

Simulated data with uncontrolled confounding

Description

Data containing one source of bias, three known confounders, and 100,000 observations. This data is obtained from df_uc_source by removing the column U. The resulting data corresponds to what a researcher would see in the real-world: information on known confounders (C1, C2, and C3), but not for confounder U. As seen in df_uc_source, the true, unbiased exposure-outcome effect estimate = 2.

Usage

df_uc

Format

A dataframe with 100,000 rows and 7 columns:

X_bi

binary exposure, 1 = present and 0 = absent

X_cont

continuous exposure

Y_bi

binary outcome corresponding to exposure X_bi, 1 = present and 0 = absent

Y_cont

continuous outcome corresponding to exposure X_cont

C1

1st confounder, 1 = present and 0 = absent

C2

2nd confounder, 1 = present and 0 = absent

C3

3rd confounder, 1 = present and 0 = absent

Simulated data with uncontrolled confounding and exposure misclassification

Description

Data containing two sources of bias, three known confounders, and 100,000 observations. This data is obtained from df_uc_em_source by removing the columns X and U. The resulting data corresponds to what a researcher would see in the real-world: a misclassified exposure, Xstar, and missing data on a confounder U. As seen in df_uc_em_source, the true, unbiased exposure-outcome odds ratio = 2.

Usage

df_uc_em

Format

A dataframe with 100,000 rows and 5 columns:

Xstar

misclassified exposure, 1 = present and 0 = absent

Y

outcome, 1 = present and 0 = absent

C1

1st confounder, 1 = present and 0 = absent

C2

2nd confounder, 1 = present and 0 = absent

C3

3rd confounder, 1 = present and 0 = absent

Simulated data with uncontrolled confounding, exposure misclassification, and selection bias

Description

Data containing three sources of bias, three known confounders, and 100,000 observations. This data is obtained by sampling with replacement with probability = S from df_uc_em_sel_source then removing the columns X, U, and S. The resulting data corresponds to what a researcher would see in the real-world: a misclassified exposure, Xstar; missing data on a confounder U; and missing data for those not selected into the study (S=0). As seen in df_uc_em_sel_source, the true, unbiased exposure-outcome odds ratio = 2.

Usage

df_uc_em_sel

Format

A dataframe with 100,000 rows and 5 columns:

Xstar

misclassified exposure, 1 = present and 0 = absent

Y

outcome, 1 = present and 0 = absent

C1

1st confounder, 1 = present and 0 = absent

C2

2nd confounder, 1 = present and 0 = absent

C3

3rd confounder, 1 = present and 0 = absent

Data source for df_uc_em_sel

Description

Data with complete information on the three sources of bias, three known confounders, and 100,000 observations. This data is used to derive df_uc_em_sel and can be used to obtain bias parameters for purposes of validating the simultaneous multi-bias adjustment method with df_uc_em_sel. With this source data, the fitted regression logit(P(Y=1)) = α0 + α1X + α2C1 + α3C2 + α4C3 + α5U shows that the true, unbiased exposure-outcome odds ratio = 2.

Usage

df_uc_em_sel_source

Format

A dataframe with 100,000 rows and 8 columns:

X

true exposure, 1 = present and 0 = absent

Y

outcome, 1 = present and 0 = absent

C1

1st confounder, 1 = present and 0 = absent

C2

2nd confounder, 1 = present and 0 = absent

C3

3rd confounder, 1 = present and 0 = absent

U

unmeasured confounder, 1 = present and 0 = absent

Xstar

misclassified exposure, 1 = present and 0 = absent

S

selection, 1 = selected into the study and 0 = not selected into the study

Data source for df_uc_em

Description

Data with complete information on the two sources of bias, a known confounder, and 100,000 observations. This data is used to derive df_uc_em and can be used to obtain bias parameters for purposes of validating the simultaneous multi-bias adjustment method with df_uc_em. With this source data, the fitted regression logit(P(Y=1)) = α0 + α1X + α2C1 + α3U shows that the true, unbiased exposure-outcome odds ratio = 2.

Usage

df_uc_em_source

Format

A dataframe with 100,000 rows and 7 columns:

X

true exposure, 1 = present and 0 = absent

Y

outcome, 1 = present and 0 = absent

C1

1st confounder, 1 = present and 0 = absent

C2

2nd confounder, 1 = present and 0 = absent

C3

3rd confounder, 1 = present and 0 = absent

U

unmeasured confounder, 1 = present and 0 = absent

Xstar

misclassified exposure, 1 = present and 0 = absent

Simulated data with uncontrolled confounding and outcome misclassification

Description

Data containing two sources of bias, three known confounders, and 100,000 observations. This data is obtained from df_uc_om_source by removing the columns Y and U. The resulting data corresponds to what a researcher would see in the real-world: a misclassified outcome, Ystar, and missing data on the binary confounder U. As seen in df_uc_omc_source, the true, unbiased exposure-outcome odds ratio = 2.

Usage

df_uc_om

Format

A dataframe with 100,000 rows and 5 columns:

X

exposure, 1 = present and 0 = absent

Ystar

misclassified outcome, 1 = present and 0 = absent

C1

1st confounder, 1 = present and 0 = absent

C2

2nd confounder, 1 = present and 0 = absent

C3

3rd confounder, 1 = present and 0 = absent

Simulated data with uncontrolled confounding, outcome misclassification, and selection bias

Description

Data containing three sources of bias, three known confounders, and 100,000 observations. This data is obtained by sampling with replacement with probability = S from df_uc_om_sel_source then removing the columns Y, U, and S. The resulting data corresponds to what a researcher would see in the real-world: a misclassified outcome, Ystar; missing data on a confounder U; and missing data for those not selected into the study (S=0). As seen in df_uc_om_sel_source, the true, unbiased exposure-outcome odds ratio = 2.

Usage

df_uc_om_sel

Format

A dataframe with 100,000 rows and 5 columns:

X

exposure, 1 = present and 0 = absent

Ystar

misclassified outcome, 1 = present and 0 = absent

C1

1st confounder, 1 = present and 0 = absent

C2

2nd confounder, 1 = present and 0 = absent

C3

3rd confounder, 1 = present and 0 = absent

Data source for df_uc_om_sel

Description

Data with complete information on the three sources of bias, three known confounders, and 100,000 observations. This data is used to derive df_uc_om_sel and can be used to obtain bias parameters for purposes of validating the simultaneous multi-bias adjustment method with df_uc_om_sel. With this source data, the fitted regression logit(P(Y=1)) = α0 + α1X + α2C1 + α3C2 + α4C3 + α5U shows that the true, unbiased exposure-outcome odds ratio = 2.

Usage

df_uc_om_sel_source

Format

A dataframe with 100,000 rows and 8 columns:

X

exposure, 1 = present and 0 = absent

Y

true outcome, 1 = present and 0 = absent

C1

1st confounder, 1 = present and 0 = absent

C2

2nd confounder, 1 = present and 0 = absent

C3

3rd confounder, 1 = present and 0 = absent

U

unmeasured confounder, 1 = present and 0 = absent

Ystar

misclassified outcome, 1 = present and 0 = absent

S

selection, 1 = selected into the study and 0 = not selected into the study

Data source for df_uc_om

Description

Data with complete information on the two sources of bias, three known confounders, and 100,000 observations. This data is used to derive df_uc_om and can be used to obtain bias parameters for purposes of validating the simultaneous multi-bias adjustment method with df_uc_om. With this source data, the fitted regression logit(P(Y=1)) = α0 + α1X + α2C1 + α3U shows that the true, unbiased exposure-outcome odds ratio = 2.

Usage

df_uc_om_source

Format

A dataframe with 100,000 rows and 7 columns:

X

exposure, 1 = present and 0 = absent

Y

outcome, 1 = present and 0 = absent

C1

1st confounder, 1 = present and 0 = absent

C2

2nd confounder, 1 = present and 0 = absent

C3

3rd confounder, 1 = present and 0 = absent

U

unmeasured confounder, 1 = present and 0 = absent

Ystar

misclassified outcome, 1 = present and 0 = absent

Simulated data with uncontrolled confounding and selection bias

Description

Data containing two sources of bias, three known confounders, and 100,000 observations. This data is obtained by sampling with replacement with probability = S from df_uc_sel_source then removing the columns U and S. The resulting data corresponds to what a researcher would see in the real-world: missing data on confounder U; and missing data for those not selected into the study (S=0). As seen in df_uc_sel_source, the true, unbiased exposure-outcome odds ratio = 2.

Usage

df_uc_sel

Format

A dataframe with 100,000 rows and 5 columns:

X

exposure, 1 = present and 0 = absent

Y

outcome, 1 = present and 0 = absent

C1

1st confounder, 1 = present and 0 = absent

C2

2nd confounder, 1 = present and 0 = absent

C3

3rd confounder, 1 = present and 0 = absent

Data source for df_uc_sel

Description

Data with complete information on the two sources of bias, a known confounder, and 100,000 observations. This data is used to derive df_uc_sel and can be used to obtain bias parameters for purposes of validating the simultaneous multi-bias adjustment method with df_uc_sel. With this source data, the fitted regression logit(P(Y=1)) = α0 + α1X + α2C1 + α3C2 + α4C3 + α5U shows that the true, unbiased exposure-outcome odds ratio = 2.

Usage

df_uc_sel_source

Format

A dataframe with 100,000 rows and 7 columns:

X

true exposure, 1 = present and 0 = absent

Y

outcome, 1 = present and 0 = absent

C1

1st confounder, 1 = present and 0 = absent

C2

2nd confounder, 1 = present and 0 = absent

C3

3rd confounder, 1 = present and 0 = absent

U

unmeasured confounder, 1 = present and 0 = absent

S

selection, 1 = selected into the study and 0 = not selected into the study

Data source for df_uc

Description

Data with complete information on one source of bias, three known confounders, and 100,000 observations. This data is used to derive df_uc and can be used to obtain bias parameters for purposes of validating the simultaneous multi-bias adjustment method with df_uc. With this source data, the fitted regression g(P(Y=1)) = α0 + α1X + α2C1 + α3C2 + α4C3 + α5U shows that the true, unbiased exposure-outcome effect estimate = 2 when:

  1. g = logit, Y = Y_bi, and X = X_bi or

  2. g = identity, Y = Y_cont, X = X_cont.

Usage

df_uc_source

Format

A dataframe with 100,000 rows and 8 columns:

X_bi

binary exposure, 1 = present and 0 = absent

X_cont

continuous exposure

Y_bi

binary outcome corresponding to exposure X_bi, 1 = present and 0 = absent

Y_cont

continuous outcome corresponding to exposure X_cont

C1

1st confounder, 1 = present and 0 = absent

C2

2nd confounder, 1 = present and 0 = absent

C3

3rd confounder, 1 = present and 0 = absent

U

uncontrolled confounder, 1 = present and 0 = absent

Evans County dataset

Description

Data from a cohort study in which white males in Evans County were followed for 7 years, with coronary heart disease as the outcome of interest.

Usage

evans

Format

A dataframe with 609 rows and 9 columns:

ID

subject identifiction

CHD

outcome variable; 1 = coronary heart disease

AGE

age (in years)

CHL

cholesterol, mg/dl

SMK

1 = subject has ever smoked

ECG

1 = presence of electrocardiogram abnormality

DBP

diastolic blood pressure, mmHg

SBP

systolic blood pressure, mmHg

HPT

1 = SBP greater than or equal to 160 or DBP greater than or equal to 95

Source

http://web1.sph.emory.edu/dkleinb/logreg3.htm#data