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IV2SLS2 mediation estimator: 2-stage MR with instruments for both X and M

Source: R/mediation.R
fit_iv2sls_mediation2.Rd

Uses TWO genetic instruments: G for the exposure X and Gm for the mediator M. This is the key extension: by instrumenting both endogenous variables, NDE and NIE become point-identified even under mediator-outcome (M-O) confounding, resolving the identification failure that limits the single-instrument estimators.

Usage

fit_iv2sls_mediation2(
  y,
  X,
  M,
  g,
  gm,
  covars = NULL,
  min_f = 10,
  W1 = NULL,
  W2 = NULL,
  w = NULL
)

Arguments

y

Numeric outcome vector (length n).

X

Numeric exposure vector (length n).

M

Numeric mediator vector (length n).

g

Numeric instrument for X (length n).

gm

Numeric instrument for M (length n).

covars

Optional data frame of additional covariates (n rows).

min_f

Minimum acceptable partial F-statistic for each excluded instrument. Default 10.

W1

Optional negative-control panel (vector length n or matrix n x q) proxying the exposure-mediator confounder (X->M path); added to stage 1 only. Default NULL (stage 1 unaugmented).

W2

Optional negative-control panel (vector length n or matrix n x q) proxying the mediator-outcome confounder (M->Y path); added to stages 2 and 3. Default NULL (stages 2–3 unaugmented).

w

Defunct. The pooled single-panel argument was removed because conditioning on a pooled panel in all three stages opens a collider path under multi-confounder designs. Use W1 and/or W2 instead.

Value

Named list: NDE, NDE_se, NDE_p, NIE, NIE_se, NIE_p. Returns all-NA if either first-stage partial F is below min_f.

Details

The motivating design uses two distinct genetic instruments: a mediator instrument (e.g. a cis-eQTL) instruments the mediator (M), while a separate exposure instrument (e.g. a polygenic score) instruments the exposure (X). The mediator set must be restricted to features for which a mediator instrument is available.

Strategy (sequential 2SLS, three OLS stages), with optional path-specific negative-control (NC) augmentation:

  1. X ~ G (+ W1) + covars -> X_hat (purge U1 from X). Weak-IV check: partial F for G >= min_f.

  2. M ~ X_hat + Gm (+ W2) + covars -> M_hat, alpha_M = coef on X_hat. Weak-IV check: partial F for Gm >= min_f.

  3. Y ~ X_hat + M_hat (+ W2) + covars -> NDE = beta_X_hat, beta_M = coef on M_hat.

NIE = alpha_M * beta_M (delta-method SE).

Path-specific NC augmentation (optional). W1 proxies the exposure-mediator confounder (U1, the X->M path) and is added to stage 1 only; W2 proxies the mediator-outcome confounder (U2, the M->Y path) and is added to stages 2 and 3. Either panel may be omitted: with W1 = NULL stage 1 is unaugmented, with W2 = NULL stages 2–3 are unaugmented, and with both NULL the estimator reduces to plain two-instrument 2-stage MR. Conditioning on a pooled panel (W1 + W2) / 2 in all three stages is a collider under multi-confounder designs (the pooled panel is a common child of the independent confounders U1 and U2) and is therefore not supported: if W1 and W2 are identical they are treated as absent (pure MR). Pass the two path-specific panels separately to obtain the coverage-improves-accuracy behaviour.

Path-specific augmentation is only defined when W1 and W2 proxy distinct confounders. When the two panels are distinct-noise proxies of the same latent composite (the single-confounder / shared-loading design), their column spaces are near-collinear and stage-1 W1 would inject the shared M->Y confounder into X_hat. The estimator detects this (leading-PC correlation between the panels) and falls back to plain two-instrument 2-stage MR, exactly as for an identical pooled panel. Genuinely distinct panels are unaffected.

Including X_hat in the M first-stage (stage 2) is essential: M structurally depends on X, so the X -> M path must be captured for alpha_M and the NIE to be correctly estimated. Gm provides the exogenous variation that identifies the M -> Y effect net of U1 confounding.

The sequential 2SLS implementation matches the pattern of fit_iv2sls_mediation (three separate OLS stages). Standard errors in the outcome stage do not account for the two-stage estimation of M_hat, consistent with the existing estimators; the simulation benchmarks bias, not SE accuracy. A unit test cross-validates this estimator's NDE and beta_M against AER::ivreg on the just-identified system (Y ~ X + M | G + Gm, pure-MR form).

References

Rudolph, K. E., et al. (2024). Natural direct and indirect effects with an instrumental variable. Biometrics.

Examples

set.seed(1)
dat <- generate_toy_data(n = 500, mo_confounding = 0.8,
phi = 0.8, lambda_XM = c(1, 0), lambda_MY = c(0, 1),
omega_1 = 0.7, omega_2 = 0.7, seed = 1)
fit_iv2sls_mediation2(dat$Y[, 1], dat$X, dat$M, dat$G[, 1], dat$Gm,
W1 = dat$W1, W2 = dat$W2)
#> $NDE
#> [1] 0.1074552
#> 
#> $NDE_se
#> [1] 0.01497136
#> 
#> $NDE_p
#> [1] 2.738294e-12
#> 
#> $NIE
#> [1] 0.1524762
#> 
#> $NIE_se
#> [1] 0.008039873
#> 
#> $NIE_p
#> [1] 3.320173e-80
#> 
#> $alpha_M
#> [1] 0.5039503
#> 
#> $alpha_se
#> [1] 0.01205152
#> 
#> $beta_M
#> [1] 0.302562
#> 
#> $beta_M_se
#> [1] 0.01421859
#>