CAFbound {SelectionBias}

Counterfactual assumption-free bound

Description

CAFbound() returns a list with the CAF upper and lower bounds. The sensitivity parameters are inserted directly.

Usage

CAFbound(whichEst, M, m, outcome, treatment, selection = NULL)

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".

M

Input value. Sensitivity parameter. Must be between 0 and 1 and larger than m.

m

Input value. Sensitivity parameter. Must be between 0 and 1 and smaller than M.

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 CAF 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
CAFbound(whichEst = "RR_tot", M = Mt, m = mt, outcome = y, treatment = tr,
 selection = sel)

# Example with selection probability.
selprob = mean(sel)
CAFbound(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
CAFbound(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
CAFbound(whichEst = "RD_tot", M = Mt, m = mt, outcome = y, treatment = tr,
 selection = sel)