GAFbound: Generalized assumption-free bound

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

Generalized assumption-free bound

Description

GAFbound() returns a list with the GAF upper and lower bounds. The sensitivity parameters can be inserted directly or as output from sensitivityparametersM().

Usage

GAFbound(whichEst, sens = NULL, M, m, outcome, treatment, selection = 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.
M	Possible method to input sensitivity parameter. Must be between 0 and 1, larger than m and smaller than max_t P(Y=1|T=t,I_s=1).
m	Possible method to input sensitivity parameter. Must be between 0 and 1, smaller than M and larger than min_t P(Y=1|T=t,I_s=1).
outcome	Input vector. A binary outcome variable. Either the data vector (length>=3) or two conditional outcome probabilities with P(Y=1|T=1,I_s=1) and P(Y=1|T=0,I_s=1) as first and second element.
treatment	Input vector. A binary treatment variable. Either the data vector (length>=3) or two conditional treatment probabilities with P(T=1|I_s=1) and P(T=0|I_s=1) as first and second element.
selection	Input vector or input scalar. A binary selection variable or a selection probability. Can be omitted for subpopulation estimands.

Value

A list containing the upper and lower GAF bounds.

References

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

Examples

# Example with selection indicator variable.
y = c(0, 0, 0, 0, 1, 1, 1, 1)
tr = c(0, 0, 1, 1, 0, 0, 1, 1)
sel = c(0, 1, 0, 1, 0, 1, 0, 1)
Mt = 0.8
mt = 0.2
GAFbound(whichEst = "RR_tot", M = Mt, m = mt, outcome = y, treatment = tr,
 selection = sel)

# Example with selection probability.
selprob = mean(sel)
GAFbound(whichEst = "RR_tot", M = Mt, m = mt, outcome = y[sel==1],
 treatment = tr[sel==1], selection = selprob)

# Example with subpopulation and no selection variable or probability.
Ms = 0.7
ms = 0.1
GAFbound(whichEst = "RR_sub", M = Ms, m = ms, outcome = y, treatment = tr)

# Example with simulated data.
n = 1000
tr = rbinom(n, 1, 0.5)
y = rbinom(n, 1, 0.2 + 0.05 * tr)
sel = rbinom(n, 1, 0.4 + 0.1 * tr + 0.3 * y)
Mt = 0.5
mt = 0.05
GAFbound(whichEst = "RD_tot", M = Mt, m = mt, outcome = y, treatment = tr,
 selection = sel)
 
# 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 = "GAF", 
 Vval = V,  Uval = U, Tcoef = Tr, Ycoef = Y, Scoef = S, Mmodel = "L",
 pY1_T1_S1 = probT1, pY1_T0_S1 = probT0)
 
GAFbound(whichEst = "RR_sub", sens = senspar, outcome = c(probT1, probT0),
 treatment = c(0.01, 0.99))

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