Sensitivity Analysis and Confounding Inference

Introduction

This vignette shows how iconic stress-tests a causal estimate by replaying the analysis on synthetic data that preserve the observed feature texture while sweeping the strength of unmeasured confounding and instrument exogeneity violations.

Installation

iconic is being submitted to Bioconductor. Once accepted, install the release version with:

if (!requireNamespace("BiocManager", quietly = TRUE))
    install.packages("BiocManager")
BiocManager::install("iconic")

The development version is available from GitHub:

BiocManager::install("sbresnahan/iconic")

What sensitivity analysis does

Even after diagnosis declares an estimator eligible, its validity rests on the assumption that the genetic instrument is exogenous — that the instrument-confounder correlations $\rho_{G1}$ and $\rho_{G2}$ are zero. These correlations cannot be estimated from data (the confounders are unobserved), so iconic_sensitivity() sweeps them over a plausible grid and reports how each estimator’s bias degrades.

The output reports, for each estimator:

Maximum absolute bias across the sensitivity surface.
Tipping points: the first $\rho_{G2}$ at $\rho_{G1} = 0$ where $|\text{bias}| > 0.10$ .
Texture source: whether the synthetic data used the generative texture model (GAN + copula) or the parametric benchmark generator.

A minimal example

We simulate a small mediation panel, train a texture model briefly, and run the sensitivity sweep.

dat <- generate_toy_data(
  n = 200, n_features = 10, seed = 1,
  phi = 0.8, omega_1 = 0.7, omega_2 = 0.7
)

idat <- iconic_data(
  X = dat$X, Y = dat$Y, M = dat$M,
  G = dat$G, Gm = dat$Gm,
  W1 = dat$W1, W2 = dat$W2,
  covariates = dat$synthetic_data
)

# Train a texture model briefly and attach it to the iconic_data object.
input <- load_real_input_data(
  X_matrix = matrix(dat$X, nrow = 1),
  Y_matrix = t(dat$Y), M_matrix = t(dat$M),
  W_matrix = t(dat$W), covariates_df = dat$synthetic_data
)

idat$trained_gan <- train_gan_on_real_data(
  input$gan_training_data,
  feature_correlations = input$feature_correlations,
  feature_texture = input$feature_texture,
  epochs = 5, seed = 1, verbose = FALSE
)

The sensitivity-sweep chunks in this vignette are skipped because torch is not available. Install torch with install.packages("torch") and run torch::install_torch() to run them.

sens <- iconic_sensitivity(idat, n_iter = 3)
sens

Inferring confounding from the data

infer_confounding() estimates the held-fixed confounding parameters from your data, supplying a confounding = "inferred" mode for iconic_sensitivity() and iconic_prospect().

diag <- iconic_diagnose(idat)
est <- iconic_estimate(idat, diagnosis = diag)
conf <- infer_confounding(idat, diag, est)
conf

#> <iconic_confounding>
#>  conf_strength    0.409 (UNADJ-IV2SLS gap (NDE))
#>  mo_confounding   0.025 (IV2SLS-IV2SLS2 NIE gap)
#>  omega_1          0.485 (sqrt(R^2) of W on Y residualized on X+C)
#>  warning: composite: coverage x confounder strength, not pure coverage
#>  omega_2          0.484 (sqrt(R^2) of W on Y residualized on X+C)
#>  warning: composite: coverage x confounder strength, not pure coverage
#>  k                1 [CI: 1, 2] (parallel analysis (Horn, 1965))
#> 
#>  Unavailable: rho_G1, rho_G2

The inferred parameters include:

Confounding strength ( $\delta$ ): from the gap between unadjusted OLS and IV2SLS estimates.
Mediator-outcome confounding ( $\delta_{mo}$ ): from the gap between IV2SLS and IV2SLS2 natural indirect effects.
Negative-control coverage ( $\omega_1$ , $\omega_2$ ): from the $R^2$ of each NC feature regressed on the outcome residual.
Number of latent confounders ( $k$ ): via parallel analysis on the residualized outcome correlation matrix.

Parameters that cannot be inferred (the instrument-confounder correlations $\rho_{G1}$ , $\rho_{G2}$ ) fall back to defaults with a warning and are always swept.

Inferred vs. default confounding

sens_inf <- iconic_sensitivity(idat, n_iter = 3, confounding = "inferred")
sens_inf

The confounding = "default" mode uses fixed defaults ( $\delta_{mo} = 0.8$ , $\omega_1 = \omega_2 = 0.7$ , $\phi = 0.8$ ) and is the recommended starting point. The confounding = "inferred" mode calibrates to your data but uses estimator validity (e.g., that IV2SLS is unbiased) to set up a benchmark whose purpose is to test estimator validity — so inferred values should be read as best-case calibrations under the stated assumptions.

Session information

sessionInfo()

#> R version 4.6.1 (2026-06-24)
#> Platform: x86_64-pc-linux-gnu
#> Running under: Ubuntu 24.04.4 LTS
#> 
#> Matrix products: default
#> BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 
#> LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so;  LAPACK version 3.12.0
#> 
#> locale:
#>  [1] LC_CTYPE=C.UTF-8       LC_NUMERIC=C           LC_TIME=C.UTF-8       
#>  [4] LC_COLLATE=C.UTF-8     LC_MONETARY=C.UTF-8    LC_MESSAGES=C.UTF-8   
#>  [7] LC_PAPER=C.UTF-8       LC_NAME=C              LC_ADDRESS=C          
#> [10] LC_TELEPHONE=C         LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C   
#> 
#> time zone: UTC
#> tzcode source: system (glibc)
#> 
#> attached base packages:
#> [1] stats     graphics  grDevices utils     datasets  methods   base     
#> 
#> other attached packages:
#> [1] iconic_0.99.2    BiocStyle_2.40.0
#> 
#> loaded via a namespace (and not attached):
#>  [1] cli_3.6.6           knitr_1.51          rlang_1.3.0        
#>  [4] xfun_0.60           processx_3.9.0      otel_0.2.0         
#>  [7] torch_0.17.0        coro_1.1.0          textshaping_1.0.5  
#> [10] jsonlite_2.0.0      bit_4.6.0           htmltools_0.5.9    
#> [13] ps_1.9.3            ragg_1.5.2          sass_0.4.10        
#> [16] rmarkdown_2.31      evaluate_1.0.5      jquerylib_0.1.4    
#> [19] fastmap_1.2.0       yaml_2.3.12         lifecycle_1.0.5    
#> [22] bookdown_0.47       BiocManager_1.30.27 compiler_4.6.1     
#> [25] fs_2.1.0            Rcpp_1.1.2          systemfonts_1.3.2  
#> [28] digest_0.6.39       R6_2.6.1            magrittr_2.0.5     
#> [31] callr_3.8.0         bslib_0.12.0        withr_3.0.3        
#> [34] bit64_4.8.2         tools_4.6.1         pkgdown_2.2.1      
#> [37] cachem_1.1.0        desc_1.4.3

Sean T. Bresnahan and Charis Xiong

2026-08-18