Classical Benchmarks: Lalonde and RHC

This vignette demonstrates the causaldef framework on two famous datasets in causal inference: 1. Lalonde’s Job Training Data: Validating deficiency against an experimental application. 2. Right Heart Catheterization (RHC): Handling high-dimensional confounding and uncertainty quantification.

library(causaldef)
library(stats)

if (!exists("deparse1", envir = baseenv())) {
  deparse1 <- function(expr, collapse = " ", width.cutoff = 500L, ...) {
    paste(deparse(expr, width.cutoff, ...), collapse = collapse)
  }
}

1. Lalonde’s NSW Benchmark

The Lalonde dataset allows us to verify our methods because it contains both an experimental control group and observational comparison groups.

We define the “True” experiment (\(E_{target}\)) using the randomized data, and the “Observational” experiment (\(E_{obs}\)) using the CPS controls.

Data Preparation

The massive bias (negative effect instead of positive) confirms the difficulty of this problem.

Deficiency Estimation

We now calculate a deficiency proxy \(\delta(E_{obs}, E_{do})\) using the available covariates.

The proxy \(\delta\) summarizes the distance between the reweighted observational distribution and the target randomized experiment. A lower \(\delta\) indicates that the reweighting more closely reconstructed the experimental conditions under the PS-TV diagnostic.

2. Right Heart Catheterization (RHC)

This dataset involves high-dimensional confounding (50+ covariates). We use it to demonstrate the Confounding Frontier and Policy Regret Bounds.

Data Setup

Quantifying the Information Gap

Policy Regret Bounds

The “Safety Floor” tells us the minimum regret we risk by making a decision based on this imperfect observational evidence.

The result typically shows a low safety floor (e.g., < 0.05), suggesting that the observational findings are actionable unless the decision hinges on a very small utility difference.

Confounding Frontier

Sensitivity analysis: If we missed a confounder \(U\) correlated with treatment by \(\alpha\) and outcome by \(\gamma\), how much would our deficiency increase?

The plot shows the “safe” region (low confounding) versus “unsafe” region. If we suspect unmeasured confounders (like specific genetic factors) have strength \(|\alpha \gamma| > 0.1\), the yellow/red zones indicate high deficiency.