bias_params {multibias}R Documentation

Represent bias parameters

Description

bias_params is one of two different options to represent bias assumptions for bias adjustment. The multibias_adjust() function will apply the assumptions from these models and use them to adjust for biases in the observed data. It takes one input, a list, where each item in the list corresponds to the necessary models for bias adjustment. See below for bias models.

For each of the following bias models, the variables are defined:

Uncontrolled confounding
logit(P(U=1)) = α0 + α1X + α2Y + α2+jCj
Exposure misclassification
logit(P(X=1)) = δ0 + δ1X* + δ2Y + δ2+jCj
Outcome misclassification
logit(P(Y=1)) = δ0 + δ1X + δ2Y* + δ2+jCj
Selection bias
logit(P(S=1)) = β0 + β1X + β2Y
Uncontrolled Confounding & Exposure Misclassification (Option 1)
logit(P(U=1)) = α0 + α1X + α2Y
logit(P(X=1)) = δ0 + δ1X* + δ2Y + δ2+jCj
Uncontrolled Confounding & Exposure Misclassification (Option 2)
log(P(X=1,U=0)/P(X=0,U=0)) = γ1,0 + γ1,1X* + γ1,2Y + γ1,2+jCj
log(P(X=0,U=1)/P(X=0,U=0)) = γ2,0 + γ2,1X* + γ2,2Y + γ2,2+jCj
log(P(X=1,U=1)/P(X=0,U=0)) = γ3,0 + γ3,1X* + γ3,2Y + γ3,2+jCj
Uncontrolled Confounding & Outcome Misclassification (Option 1)
logit(P(U=1)) = α0 + α1X + α2Y
logit(P(Y=1)) = δ0 + δ1X + δ2Y* + δ2+jCj
Uncontrolled Confounding & Outcome Misclassification (Option 2)
log(P(U=1,Y=0)/P(U=0,Y=0)) = γ1,0 + γ1,1X + γ1,2Y* + γ1,2+jCj
log(P(U=0,Y=1)/P(U=0,Y=0)) = γ2,0 + γ2,1X + γ2,2Y* + γ2,2+jCj
log(P(U=1,Y=1)/P(U=0,Y=0)) = γ3,0 + γ3,1X + γ3,2Y* + γ3,2+jCj
Uncontrolled Confounding & Selection Bias
logit(P(U=1)) = α0 + α1X + α2Y + α2+jCj
logit(P(S=1)) = β0 + β1X + β2Y
Exposure Misclassification & Outcome Misclassification (Option 1)
logit(P(X=1)) = δ0 + δ1X* + δ2Y* + δ2+jCj
logit(P(Y=1)) = β0 + β1X + β2Y* + β2+jCj
Exposure Misclassification & Outcome Misclassification (Option 2)
log(P(X=1,Y=0) / P(X=0,Y=0)) = γ1,0 + γ1,1X* + γ1,2Y* + γ1,2+jCj
log(P(X=0,Y=1) / P(X=0,Y=0)) = γ2,0 + γ2,1X* + γ2,2Y* + γ2,2+jCj
log(P(X=1,Y=1) / P(X=0,Y=0)) = γ3,0 + γ3,1X* + γ3,2Y* + γ3,2+jCj
Exposure Misclassification & Selection Bias
logit(P(X=1)) = δ0 + δ1X* + δ2Y + δ2+jCj
logit(P(S=1)) = β0 + β1X* + β2Y + β2+jCj
Outcome Misclassification & Selection Bias
logit(P(Y=1)) = δ0 + δ1X + δ2Y* + δ2+jCj
logit(P(S=1)) = β0 + β1X + β2Y* + β2+jCj
Uncontrolled Confounding, Exposure Misclassification, and Selection Bias (Option 1)
logit(P(U=1)) = α0 + α1X + α2Y
logit(P(X=1)) = δ0 + δ1X* + δ2Y + δ2+jCj
logit(P(S=1)) = β0 + β1X* + β2Y + β2+jCj
Uncontrolled Confounding, Exposure Misclassification, and Selection Bias (Option 2)
log(P(X=1,U=0)/P(X=0,U=0)) = γ1,0 + γ1,1X* + γ1,2Y + γ1,2+jCj
log(P(X=0,U=1)/P(X=0,U=0)) = γ2,0 + γ2,1X* + γ2,2Y + γ2,2+jCj
log(P(X=1,U=1)/P(X=0,U=0)) = γ3,0 + γ3,1X* + γ3,2Y + γ3,2+jCj
logit(P(S=1)) = β0 + β1X* + β2Y + β2+jCj
Uncontrolled Confounding, Outcome Misclassification, and Selection Bias (Option 1)
logit(P(U=1)) = α0 + α1X + α2Y
logit(P(Y=1)) = δ0 + δ1X + δ2Y* + δ2+jCj
logit(P(S=1)) = β0 + β1X + β2Y* + β2+jCj
Uncontrolled Confounding, Outcome Misclassification, and Selection Bias (Option 2)
log(P(U=1,Y=0)/P(U=0,Y=0)) = γ1,0 + γ1,1X + γ1,2Y* + γ1,2+jCj
log(P(U=0,Y=1)/P(U=0,Y=0)) = γ2,0 + γ2,1X + γ2,2Y* + γ2,2+jCj
log(P(U=1,Y=1)/P(U=0,Y=0)) = γ3,0 + γ3,1X + γ3,2Y* + γ3,2+jCj
logit(P(S=1)) = β0 + β1X + β2Y* + β2+jCj

Usage

bias_params(coef_list)

Arguments

coef_list

List of coefficient values from the above options of models. Each item of the list is an equation. The left side of the equation identifies the model (i.e., "u" for the model predicting the uncontrolled confounder). For the multinomial models, specify the value here based on the numerator (i.e., "x1u0", "x0u1", "x1u1" for the three multinomial models in Uncontrolled Confounding & Exposure Misclassification, Option 2) The right side of the equation is the vector of values corresponding to the model coefficients (from left to right).

Examples

list_for_uc <- list(
  u = c(-0.19, 0.61, 0.70, -0.09, 0.10, -0.15)
)

bp_uc <- bias_params(coef_list = list_for_uc)

list_for_em_om <- list(
  x1y0 = c(-2.18, 1.63, 0.23, 0.36),
  x0y1 = c(-3.17, 0.22, 1.60, 0.40),
  x1y1 = c(-4.76, 1.82, 1.83, 0.72)
)

bp_em_om <- bias_params(coef_list = list_for_em_om)


[Package multibias version 1.7.2 Index]