Bounds on the causal odds ratio for a binary outcome

The odds ratio is strictly increasing in the treated risk and strictly decreasing in the control risk, so the extreme odds ratios are attained at the corners of the two risk intervals: no search is needed and the bound is exact rather than conservative. The risks are the worst-case bounds on E[y(t)], computed within stratum and averaged.

Usage

Bndlgt(y, D, X)

Arguments

y

Binary outcome, coded 0/1.

D

Binary treatment indicator, coded 0/1.

X

Discrete stratum label, one per unit.

Value

List with lower, upper, width, estimate, p1_lower, p1_upper, p0_lower, p0_upper, n_strata, n. p0_upper, n_strata, n.

Details

Formula: OR = odds(p_1) / odds(p_0), so OR_low = odds(p_1^L) / odds(p_0^U) and OR_high = odds(p_1^U) / odds(p_0^L).

References

Robins, J. M. (2002), for the problem. The risk bounds used are Manski's worst case, equation (2.11) of Molinari, F. (2021), Handbook of Econometrics 7A (arXiv:2004.11751 p. 17); the corner argument is written out in Details.

Examples

set.seed(9)
X <- rep(c("a", "b"), each = 50)
D <- rbinom(100, 1, 0.5)
y <- rbinom(100, 1, 0.3 + 0.2 * D)
Bndlgt(y, D, X)[c("lower", "upper")]
#> $lower
#> [1] 0.1728701
#> 
#> $upper
#> [1] 16.625
#>