sensitivityparametersM {SelectionBias}

Sensitivity parameters for the Smith and VanderWeele bound and the GAF bound

Description

sensitivityparametersM() returns a list with the sensitivity parameters and an indicator if bias is negative and the treatment coding is reversed for an assumed model.

Usage

sensitivityparametersM(
  whichEst,
  whichBound,
  Vval,
  Uval,
  Tcoef,
  Ycoef,
  Scoef,
  Mmodel,
  pY1_T1_S1,
  pY1_T0_S1
)

Arguments

whichEst

Input string. Defining the causal estimand of interest. Available options are as follows. (1) Relative risk in the total population: "RR_tot", (2) Risk difference in the total population: "RD_tot", (3) Relative risk in the subpopulation: "RR_sub", (4) Risk difference in the subpopulation: "RD_sub".

whichBound

Input string. Defining the bound of interest. Available options are as follows. (1) SV bound: "SV", (2) GAF bound: "GAF".

Vval

Input matrix. The first column is the values of the categories of V. The second column is the probabilities of the categories of V. If V is continuous, use a fine grid of values and probabilities.

Uval

Input matrix. The first column is the values of the categories of U. The second column is the probabilities of the categories of U. If U is continuous, use a fine grid of values and probabilities.

Tcoef

Input vector. Two numerical elements. The first element is the intercept in the model for the treatment. The second element is the slope in the model for the treatment.

Ycoef

Input vector. Three numerical elements. The first element is the intercept in the model for the outcome. The second element is the slope for T in the model for the outcome. The third element is the slope for U in the model for the outcome.

Scoef

Input matrix. Numerical matrix of size K by 4, where K is the number of selection variables. Each row is the coefficients for one selection variable. The first column is the intercepts in the models for the selection variables. The second column is the slopes for V in the models for the selection variables. The third column is the slopes for U in the models for the selection variables. The fourth column is the slopes for T in the models for the selection variables.

Mmodel

Input string. Defining the models for the variables in the M structure. If "P", the probit model is used. If "L", the logit model is

pY1_T1_S1

Input scalar. The observed probability P(Y=1|T=1,I_S=1).

pY1_T0_S1

Input scalar. The observed probability P(Y=1|T=0,I_S=1). used.

Value

A list containing the sensitivity parameters and, for the SV bound, an indicator if the treatment has been reversed.

References

Smith, Louisa H., and Tyler J. VanderWeele. "Bounding bias due to selection." Epidemiology (Cambridge, Mass.) 30.4 (2019): 509.

Zetterstrom, Stina and Waernbaum, Ingeborg. "Selection bias and multiple inclusion criteria in observational studies" Epidemiologic Methods 11, no. 1 (2022): 20220108.

Zetterstrom, Stina. "Bounds for selection bias using outcome probabilities" Epidemiologic Methods 13, no. 1 (2024): 20230033

Examples

# Examples with no selection bias.
V = matrix(c(1, 0, 0.1, 0.9), ncol = 2)
U = matrix(c(1, 0, 0.1, 0.9), ncol = 2)
Tr = c(0, 1)
Y = c(0, 0, 1)
S = matrix(c(1, 0, 0, 0, 1, 0, 0, 0), nrow = 2, byrow = TRUE)
probT1 = 0.534
probT0 = 0.534
sensitivityparametersM(whichEst = "RR_tot", whichBound = "SV", Vval = V,
 Uval = U, Tcoef = Tr, Ycoef = Y, Scoef = S, Mmodel = "P",
 pY1_T1_S1 = probT1, pY1_T0_S1 = probT0)

sensitivityparametersM(whichEst = "RR_tot", whichBound = "GAF", Vval = V,
 Uval = U, Tcoef = Tr, Ycoef = Y, Scoef = S, Mmodel = "P",
 pY1_T1_S1 = probT1, pY1_T0_S1 = probT0)


# Examples with selection bias. DGP from the zika example.
V = matrix(c(1, 0, 0.85, 0.15), ncol = 2)
U = matrix(c(1, 0, 0.5, 0.5), ncol = 2)
Tr = c(-6.2, 1.75)
Y = c(-5.2, 5.0, -1.0)
S = matrix(c(1.2, 2.2, 0.0, 0.5, 2.0, -2.75, -4.0, 0.0), ncol = 4)
probT1 = 0.286
probT0 = 0.004
sensitivityparametersM(whichEst = "RR_sub", whichBound = "SV", Vval = V,
 Uval = U, Tcoef = Tr, Ycoef = Y, Scoef = S, Mmodel = "L",
 pY1_T1_S1 = probT1, pY1_T0_S1 = probT0)

sensitivityparametersM(whichEst = "RR_sub", whichBound = "GAF", Vval = V,
 Uval = U, Tcoef = Tr, Ycoef = Y, Scoef = S, Mmodel = "L",
 pY1_T1_S1 = probT1, pY1_T0_S1 = probT0)