COCA binary estimator: NOT supported (returns NA)

COCA (Correlated Outcome Control Approach) regresses the negative control W on the outcome Y (W ~ y + X) and recovers the causal effect as a ratio \(-\hat\beta_X / \hat\beta_Y\). That identification argument assumes a linear structural outcome model: the W-Y regression coefficient must be proportional to the confounder-Outcome association on the same scale as the causal effect. With a binary outcome the structural model is nonlinear (logistic), so the linear COCA ratio recovers neither the causal log-odds ratio nor the risk difference. COCA is therefore unsupported for binary outcomes and always returns list(beta=NA, se=NA, pvalue=NA).

Usage

fit_coca_bin(y, X, w, covars = NULL, ...)

Arguments

y

Numeric 0/1 outcome vector (length n).

X

Numeric exposure vector (length n).

w

Numeric NC vector (length n).

covars

Optional data frame of covariates (n rows).

...

Ignored (accepted for signature compatibility).

Value

list(beta = NA, se = NA, pvalue = NA) with an informative "reason" attribute.

Examples

set.seed(1)
dat <- generate_toy_data(n = 200, outcome_type = "binary", seed = 1)
fit_coca_bin(dat$y_bin, dat$X, dat$W[, 1])
#> $beta
#> [1] NA
#> 
#> $se
#> [1] NA
#> 
#> $pvalue
#> [1] NA
#> 
#> attr(,"reason")
#> [1] "COCA regresses W on Y (W ~ y + X) and recovers the effect as a ratio, an identification argument that assumes a linear structural outcome model. With a binary (nonlinear, logistic) outcome the ratio recovers neither the log-OR nor the risk difference. COCA is unsupported for binary outcomes."
# $beta [1] NA (COCA unsupported for binary outcomes)