COCA estimator: Negative-Control Outcome Correction via ratio

Implements the Correlated Outcome Control Approach (COCA). Fits w ~ y + X + covars and recovers the causal effect as \(\hat\beta = -\hat\beta_X / \hat\beta_Y\). Standard errors are obtained via the delta method.

Usage

fit_coca(y, X, w, covars = NULL, ratio_cap = 10, se_cap = 5)

Arguments

y

Numeric primary outcome vector (length n).

X

Numeric exposure vector (length n).

w

Numeric negative-control outcome vector (length n). Recommended: pass rowMeans(W_matrix) for stability.

covars

Optional data frame of additional covariates (n rows).

ratio_cap

Maximum absolute value of the ratio estimate before flagging as unstable and returning NA. Default 10.

se_cap

Maximum SE before flagging as unstable. Default 5.

Value

Named list: beta, se, pvalue. Returns list(beta=NA, se=NA, pvalue=NA) if estimation is unstable (near-zero \(\hat\beta_Y\) or extreme ratio).

Details

The negative-control W should be an outcome that shares the same unmeasured confounders as Y but has no direct causal path from X.

Examples

set.seed(1)
dat <- generate_toy_data(n = 200, seed = 1)
fit_coca(dat$Y[, 1], dat$X, rowMeans(dat$W))
#> $beta
#>          X 
#> 0.07120217 
#> 
#> $se
#> [1] 0.05005562
#> 
#> $pvalue
#>         X 
#> 0.1548925 
#>