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Causal inference with MORIE

Source: vignettes/causal-inference.Rmd
causal-inference.Rmd

Overview

This vignette walks through the causal-inference surface of MORIE: ATE, ATT, ATC, augmented IPW (doubly robust), per-unit CATE, group GATE, and sensitivity analysis (the E-value). Each estimator follows the same calling convention — data, treatment, outcome, covariates — so swapping among them is a matter of changing one function name.

A reproducible synthetic example 

library(rmorie)
set.seed(2026)

n <- 800
X1 <- rnorm(n)
X2 <- rnorm(n)
# Confounded treatment assignment
ps    <- plogis(0.5 * X1 - 0.3 * X2)
treat <- as.integer(ps > runif(n))
# True ATE = +1.0
y <- 1.0 * treat + 0.7 * X1 - 0.2 * X2 + rnorm(n, sd = 0.5)

df <- data.frame(y = y, treat = treat, X1 = X1, X2 = X2)

Single-robust ATE / ATT / ATC 

ate <- morie_estimate_ate(df, treatment = "treat", outcome = "y", covariates = c("X1", "X2"))
att <- morie_estimate_att(df, treatment = "treat", outcome = "y", covariates = c("X1", "X2"))
atc <- morie_estimate_atc(df, treatment = "treat", outcome = "y", covariates = c("X1", "X2"))

c(ATE = ate$ate, ATT = att$att, ATC = atc$atc)
#>       ATE       ATT       ATC 
#> 1.0083214 1.0190035 0.9966245
c(ATE = ate$se, ATT = att$se, ATC = atc$se)
#>        ATE        ATT        ATC 
#> 0.06993854 0.07282375 0.08286423

Each result is a list. The point estimate is in a field named after the estimand (ate, att, atc), next to se, ci_lower and ci_upper.

The three quantities estimate slightly different things:

  • ATE (average treatment effect): averaged over the full population.
  • ATT (treated): averaged over the treated subgroup.
  • ATC (controls): averaged over the untreated subgroup.

Under no effect heterogeneity in the covariates, all three converge. Under heterogeneity, they diverge in informative ways.

Doubly robust: augmented IPW

morie_estimate_aipw() is the augmented inverse-probability-weighting estimator. It is consistent if either the propensity model or the outcome model is correctly specified — the doubly-robust guarantee.

aipw <- morie_estimate_aipw(df, treatment = "treat", outcome = "y", covariates = c("X1", "X2"))
aipw$ate
#> [1] 1.010182
aipw$se
#> [1] 0.04052365
c(aipw$ci_lower, aipw$ci_upper)
#> [1] 0.930756 1.089609

Per-unit CATE (T-learner / S-learner) 

cate <- morie_estimate_cate(df, treatment = "treat", outcome = "y", covariates = c("X1", "X2"),
                      meta_learner = "t_learner")
head(cate)
#> [1] 1.0534077 0.9977113 1.0363683 1.0293321 0.9726929 0.9714638

The result is a numeric vector with one conditional average treatment effect per row of df. The true effect in this simulation is constant (+1.0), so the estimates sit close to 1:

length(cate)
#> [1] 800
summary(cate)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>  0.9117  0.9835  1.0041  1.0042  1.0245  1.1058

Group-level GATE 

df$g <- sample(c("A", "B", "C"), nrow(df), replace = TRUE)
gate <- morie_estimate_gate(df, treatment = "treat", outcome = "y",
                      covariates = c("X1", "X2"),
                      group_col = "g")
gate
#>   group       ate         se  ci_lower ci_upper   n
#> 1     B 1.0292613 0.06254227 0.9066784 1.151844 274
#> 2     A 1.0530078 0.07349140 0.9089647 1.197051 265
#> 3     C 0.9384145 0.06603321 0.8089894 1.067840 261

The result is one row per group level with ate, se, and CI.

Sensitivity analysis: the E-value 

# Suppose the observed risk ratio is 2.0; how large would an
# unmeasured confounder need to be to explain it away?
evalue <- morie_e_value(rr = 2.0)
evalue
#> $e_value
#> [1] 3.414214
#> 
#> $e_value_ci
#> [1] NA

The E-value is the minimum strength (on the risk-ratio scale) that an unmeasured confounder would need on both treatment and outcome to fully explain the observed effect. The e_value_ci element is NA here because no confidence limit was supplied; pass rr_lower (the lower 95% limit of the risk ratio) to get the E-value of that limit.

Where to go next

  • morie_mrm_estimate_causal_effect() runs matching, IPW, AIPW and DML on one specification, corrects their p-values for multiple testing, and morie_mrm_report() renders the table; see the native-engines vignette.
  • The mrm-otis-walkthrough vignette runs the ten-estimator ensemble of morie_otis_analyze_a01_mrm() on OTIS-shaped data.
  • The survey-weighted vignette covers sampling, design weights and design effects.