SVbound: Smith and VanderWeele bound

In SelectionBias: Calculates Bounds for the Selection Bias for Binary Treatment and Outcome Variables

Smith and VanderWeele bound

Description

SVbound() returns a list with the SV bound. All sensitivity parameters for the population of interest must be set to numbers, and the rest can be left as NULL. The sensitivity parameters can be inserted directly or as output from sensitivityparametersM().

Usage

SVbound(
  whichEst,
  sens = NULL,
  pY1_T1_S1,
  pY1_T0_S1,
  pT1_S1 = NULL,
  pT0_S1 = NULL,
  RR_UY_T1 = NULL,
  RR_UY_T0 = NULL,
  RR_SU_11 = NULL,
  RR_SU_00 = NULL,
  RR_SU_10 = NULL,
  RR_SU_01 = NULL,
  RR_UY_S1 = NULL,
  RR_TU_1 = NULL,
  RR_TU_0 = NULL
)

Arguments

whichEst	Input string. Defining the causal estimand of interest. Available options are as follows. (1) Risk ratio in the total population: "RR_tot", (2) Risk difference in the total population: "RD_tot", (3) Risk ratio in the subpopulation: "RR_sub", (4) Risk difference in the subpopulation: "RD_sub".
sens	Possible method to input sensitivity parameters. sens can be the output from sensitivityparametersM(), a data.frame with columns 'parameter' and 'value', or a name list with correct names (e.g. "RR_UY_T1", "RR_UY_T0", etc.). If not supplied, parameters can be entered manually as specified below.
pY1_T1_S1	Input value. The probability P(Y=1|T=1,I_S=1). Must be between 0 and 1.
pY1_T0_S1	Input value. The probability P(Y=1|T=0,I_S=1). Must be between 0 and 1.
pT1_S1	Input value. The probability P(T=1|I_S=1). Must be between 0 and 1. Only used for the alternative SV bound for the risk difference in the subpopulation. If a value is given to pT1_S1 and pT0_S1, the alternative bound is used. If they are set to NULL, the original SV bound will be used.
pT0_S1	Input value. The probability P(T=0|I_S=1). Must be between 0 and 1. Only used for the alternative SV bound for the risk difference in the subpopulation. If a value is given to pT1_S1 and pT0_S1, the alternative bound is used. If they are set to NULL, the original SV bound will be used.
RR_UY_T1	Possible method to input sensitivity parameter. The sensitivity parameter RR_UY|T=1. Must be greater than or equal to 1. Used in the bounds for the total population.
RR_UY_T0	Possible method to input sensitivity parameter. The sensitivity parameter RR_UY|T=0. Must be greater than or equal to 1. Used in the bounds for the total population.
RR_SU_11	Possible method to input sensitivity parameter. The sensitivity parameter RR_SU|11. Must be greater than or equal to 1. Used in the bounds for the total population.
RR_SU_00	Possible method to input sensitivity parameter. The sensitivity parameter RR_SU|00. Must be greater than or equal to 1. Used in the bounds for the total population.
RR_SU_10	Possible method to input sensitivity parameter. The sensitivity parameter RR_SU|10. Must be greater than or equal to 1. Used in the bounds for the total population.
RR_SU_01	Possible method to input sensitivity parameter. The sensitivity parameter RR_SU|01. Must be greater than or equal to 1. Used in the bounds for the total population.
RR_UY_S1	Possible method to input sensitivity parameter. The sensitivity parameter RR_UY|S=1. Must be greater than or equal to 1. Used in the bounds for the subpopulation.
RR_TU_1	Possible method to input sensitivity parameter. The sensitivity parameter RR_TU|1. Must be greater than or equal to 1. Used in the bounds for the subpopulation.
RR_TU_0	Possible method to input sensitivity parameter. The sensitivity parameter RR_TU|0. Must be greater than or equal to 1. Used in the bounds for the subpopulation.

Value

A list containing the Smith and VanderWeele lower and upper bounds.

References

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

Zetterstrom S, Sjölander A, Waernbaum I. "Investigations of sharp bounds for causal effects under selection bias." Statistical Methods in Medical Research (2025).

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

Examples

# Example specifying the sensitivity parameters manually. Risk ratio in
# the total population.
SVbound(whichEst = "RR_tot", pY1_T1_S1 = 0.05, pY1_T0_S1 = 0.01,
 RR_UY_T1 = 2, RR_UY_T0 = 2, RR_SU_11 = 1.7, RR_SU_00 = 1.5,
 RR_SU_10 = 2.1, RR_SU_01 = 2.3)
 
# Example specifying the sensitivity parameters manually. Risk difference in
# the total population.
SVbound(whichEst = "RD_tot", pY1_T1_S1 = 0.05, pY1_T0_S1 = 0.01,
 RR_UY_T1 = 2, RR_UY_T0 = 2, RR_SU_11 = 1.7, RR_SU_00 = 1.5,
 RR_SU_10 = 2.1, RR_SU_01 = 2.3)

# Example specifying the sensitivity parameters manually. Risk ratio in
# the subpopulation. 
SVbound(whichEst = "RR_sub", pY1_T1_S1 = 0.05, pY1_T0_S1 = 0.01,
 RR_UY_S1 = 2.71, RR_TU_1 = 1.91, RR_TU_0 = 2.33)

# Example specifying the sensitivity parameters manually. Risk difference in
# the subpopulation.
SVbound(whichEst = "RD_sub", pY1_T1_S1 = 0.05, pY1_T0_S1 = 0.01,
 RR_UY_S1 = 2.71, RR_TU_1 = 1.91, RR_TU_0 = 2.33)
 
# Example specifying the sensitivity parameters manually. 
# Risk difference in the subpopulation with the alternative bound.
SVbound(whichEst = "RD_sub", pY1_T1_S1 = 0.05, pY1_T0_S1 = 0.01, pT1_S1 = 0.6,
pT0_S1 = 0.3, RR_UY_S1 = 2.71, RR_TU_1 = 1.91, RR_TU_0 = 2.33)

# Example specifying the sensitivity parameters from sensitivityparametersM().
# Risk ratio in the subpopulation. 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
senspar = 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)
 
SVbound(whichEst = "RR_sub", sens = senspar, pY1_T1_S1 = probT1, pY1_T0_S1 = probT0)

SelectionBias documentation built on Nov. 5, 2025, 6:48 p.m.