PaperlayerView exact revision on arXiv

Source-linked AI summary

Causal Path Analysis from Perturbational and Population-Scale Single-Cell Data with Multiscale Confounding and Measurement Error

Kwangmoon Park, Hongzhe Li

arXiv:2609.16510v1stat.MEstat.APstat.ML

TL;DR

Perturbational and population-scale single-cell studies provide complementary evidence, but target-population causal path analysis must address nontransferable networks, multiscale confounding, and measurement error. The paper constrains the target network with external ancestral relationships and applies two-scale surrogate-variable and errors-in-variables procedures; simulations illustrate that confounding and measurement-error corrections address complementary sources of bias.

  • Problem

    Perturbation studies and population-scale single-cell data offer complementary regulatory and clinical information, but distinct experimental systems and observational data complicate target-population network and path analysis.

    Source: §1 · p. 2

  • Method

    The framework constrains the target-population network with external ancestral relationships, then combines two-scale surrogate-variable analysis with errors-in-variables correction.

    Source: §1 · pp. 3, 5

  • Results

    The simulations illustrate that confounding adjustment and measurement-error correction address complementary sources of bias.

    Source: §8 · p. 31

  • Takeaways & Limitations

    The framework re-estimates target-population direct edges and effects without assuming that the entire perturbational network transfers unchanged.

    Source: §8 · p. 31

    Causal interpretation requires the external ancestral scaffold to contain the true target-population parents and preserve their ordering; the framework also assumes linear models and an outcome downstream of the gene network.

    Source: §8 · p. 31

Abstract

from arXiv · show

Single-cell perturbation experiments provide causal information on gene regulation, whereas population-scale single-cell studies characterize gene expression and phenotypes in human populations. We develop a framework that integrates these complementary data sources for causal path analysis. Rather than assuming that a perturbational gene network transfers directly to the target population, we use externally learned ancestral relationships to constrain the network topology and re-estimate its direct edges and effects from population data. To address latent heterogeneity and measurement error in multiscale single-cell measurements, we develop a surrogate-variable procedure operating at both the cell and subject levels, combined with errors-in-variables correction for network and outcome regressions. We establish theoretical guarantees for confounder recovery and high-dimensional estimation of network and gene-outcome effects. Simulations demonstrate the importance of jointly correcting confounding and measurement error. An application to acute myeloid leukemia identifies distinct regulatory pathways linking transcriptional regulators to blast count.

1 Introduction

Perturbational and population-scale single-cell data offer complementary causal and population evidence, but target-population path analysis faces network-transfer, measurement-error, and multiscale-confounding challenges. The framework uses external ancestral relationships to constrain a network and population data to estimate its direct effects.

1 Introduction

  • Perturbational networks may not transfer directly to primary human cells, while observational population data alone identify gene relationships only up to a Markov equivalence class.The target is to recover pathways from regulators to outcomes, which can involve multiple downstream routes with effects in different directions.Source: §1 · pp. 2–3
  • The framework uses external ancestral relationships to constrain, but not determine, the target-population DAG and re-estimates its direct edges and coefficients.This allows direct-edge presence and regulatory strengths to differ between the experimental system and target population.Source: §1 · p. 3
  • A two-scale surrogate-variable procedure and errors-in-variables correction address latent heterogeneity and measurement error in network and outcome regressions.Cell-level factors help separate cellular heterogeneity from technical noise; subject-level factors address confounding in network and outcome regressions.Source: §1 · p. 4
  • The paper establishes guarantees for confounder recovery and causal-effect estimation and demonstrates the framework in simulations and an acute myeloid leukemia application.Its essential structure is also described for settings with noisy replicated measurements, higher-level outcomes, and external information about causal ordering.Source: §1 · p. 5

1.1 Notation and Preliminaries

  • A DAG represents causal dependence among variables, with a directed edge encoding a direct causal effect and ancestors reachable by directed paths.The notation subsection also specifies vector, matrix, and norm conventions.Source: §1.1 · pp. 5–6

2 Problem formulation and identification

The formulation links cell-level repeated expression measurements to subject-level outcomes through a target-population causal network. External ancestral information constrains the network, while the population data support estimation of its direct edges and path effects.

2.1 Data structure and multiscale measurement model

  • Expression is measured across cells for each subject, while the outcome is recorded at the subject level; the latent state represents gene expression entering the network and outcome model.The model distinguishes observed single-cell measurements from the latent subject-level expression state.Source: §2.1 · p. 6
  • The main task is to estimate the gene-expression and outcome graph from population data while borrowing gene-network topology from Perturb-seq experiments.Observational data alone identify the DAG only up to a Markov equivalence class; target-population data select direct edges from externally identified ancestors and re-estimate their coefficients.Source: §2.1 · p. 7, portability · pp. 9–10
  • Averaging cell measurements reduces but does not eliminate latent cellular heterogeneity and technical measurement error, leaving subject-level summaries vulnerable to confounding and errors-in-variables bias.The cited passage relates this bias to noisy predictors.Source: §2.1 · p. 7

2.2 Target-population causal model and causal estimands

  • The target-population model assumes a linear structural equation network and a linear relationship between latent network variables and the subject-level outcome.The outcome model assumes no reverse causation from outcome to gene expression.Source: §2.2 · pp. 7–8
  • The total causal effect measures a gene's effect on the outcome, while directed paths in the augmented graph specify routes through which that effect can propagate.A directed path runs from a gene through distinct nodes to the outcome, with nonzero network edges and a nonzero final outcome coefficient.Source: §2.2 · pp. 8–9
  • The path-specific causal effect is defined using a path-restricted intervention, and the paper gives closed-form representations for the path-specific and total effects identifiable from the model.The supplied proposition passage introduces the representation for paths beginning at the gene of interest.Source: §2.2 · p. 9

portability

  • The structural transportability condition requires the external ancestral sets to include true target-population parents and preserve upstream–downstream ordering.The population data then select direct edges from those ancestors and re-estimate their coefficients.Source: portability · p. 10

3 Errors-in-variables bias and confounding

Subject-level network and outcome regressions use expression means that remain noisy after cell averaging, creating errors-in-variables bias. Latent cell and subject factors also introduce distinct confounding problems that must be separated from technical error.

3.1 Errors-in-variables bias in estimating the causal effects

  • Averaging cell-level observations produces noisy subject-specific regressors, so estimating network and outcome coefficients is an errors-in-variables problem.The bias arises because the noiseless regressors remain unobserved and the observed means contain error.Source: §3.1 · pp. 10–11
  • Correcting the regression bias requires estimating technical-error covariance, but within-subject variation combines technical error with variation driven by latent cell factors.Without separating these sources, biological heterogeneity may be misattributed to measurement error.Source: §3.1 · p. 11, §3.2 · p. 11

3.2 Unmeasured confounding across scales

  • Subject-level unmeasured factors can affect both the expression network and outcome, and omitting them biases coefficients in both regressions.The passage identifies omitted-variable bias in the estimated network coefficients and outcome effects.Source: §3.2 · p. 11
  • Cell-level hidden factors also affect technical-error covariance estimation, so their within-subject variation must be separated from technical error.This distinction is needed for the errors-in-variables correction.Source: §3.2 · p. 11

4 Surrogate Variable Analysis for Confounders

The section develops subject- and cell-scale surrogate-variable analyses to recover latent confounders in multiscale single-cell data. Their complementary roles support confounder adjustment while separating within-subject biology from technical error.

4.1 Assumptions for two-scale confounder recovery

  • Confounder recovery assumes latent factors retain variation after projection of observed covariates, alongside specified technical- and structural-error conditions.The residualized latent factors must not be collinear with measured covariates.Source: §4.1 · p. 12

4.2 Subject-scale SVA

  • Standard regression of the ancestor genes can be biased by latent confounders, motivating residualization and low-rank SVA.The proposed subject-scale procedure estimates the residualized confounder subspace from the residual matrix.Source: §4.2 · p. 13
  • As N and p grow, subject-scale SVA recovers the confounder subspace when confounding is pervasive across subjects and genes.It residualizes observed covariates and uses a rank-(m+r) truncated SVD; the external ancestor set informs the local SEM.Source: §4.2 · pp. 13–14

4.3 Subject-specific cell-scale SVA

  • As n_i and p grow, cell-scale SVA recovers each subject’s centered cell-factor subspace.This step separates within-subject heterogeneity from technical error and isolates the technical-error covariance needed for EIV correction; subject-scale SVA alone does not make that separation.Source: §4.3 · pp. 14–15

5 EIV bias correction and causal effect estimation

The section shows that measurement error can bias network and outcome regressions even after latent confounder adjustment, then develops EIV-corrected sparse estimators. It establishes estimation-error bounds and consistency results for path-specific and total causal effects under stated conditions.

5.1 EIV formulation and asymptotic bias

  • Even after latent-confounder adjustment, naive network and outcome regressions remain inconsistent because technical-error covariance contaminates the predictor Gram matrix.The EIV bias is analyzed to motivate the subsequent correction.Source: §5.1 · p. 18

5.2 EIV-corrected sparse SEM and outcome regression

  • The correction estimates technical-error covariance after removing cell-level heterogeneity, then applies EIV-corrected sparse regressions to the SEM and outcome models.A CoCoLasso projection addresses loss of positive semidefiniteness after covariance subtraction.Source: §5.2 · pp. 19–20

5.3 Estimation error of the EIV-corrected estimators

  • The estimator error bounds match those of Datta & Zou (2017) under s_max^2 log p ≪ N, a regime that permits p to grow exponentially in N.The paper relates this sparsity regime to having relatively few direct parent genes per local SEM and few genes directly influencing the outcome.Source: §5.3 · p. 23
  • Under the stated regularity conditions, the framework establishes consistency for path-specific and total causal-effect estimates.The path-specific error bound scales with path length; the total-effect bound additionally scales with the number of paths and their maximum length.Source: §5.3 · pp. 23–24

6 Simulation studies

The simulations assess confounder recovery and compare SVA+EIV with methods correcting neither source of bias or only one. SVA+EIV achieves smaller estimation errors, while the component corrections address complementary biases.

6.1 Simulation setup

  • The simulations compare SVA+EIV against Naive, SVA, and EIV across sample sizes, with all four methods using the true ancestor structure.The methods differ by whether they correct confounding, measurement error, or both.Source: §6.1 · pp. 24–25

6.2 Confounder recovery and estimation error comparison

  • Confounder-subspace errors decrease toward zero as sample size N and cell count n_i increase.The authors report this pattern as corroborating their confounder-recovery theorems.Source: §6.2 · p. 25, Figure 2 · p. 26
  • SVA+EIV achieves uniformly smaller DAG-recovery, outcome-regression, and TCE errors than Naive, SVA, and EIV across simulation settings.The SVA–EIV gap persists as sample size increases, indicating remaining measurement-error bias after confounder correction.Source: §6.2 · p. 25
  • With 30% of ancestor nodes perturbed, SVA+EIV still has lower DAG and TCE errors than Naive or EIV.Perturbing 10% of nodes yields comparable DAG error to SVA, and perturbing 20% yields comparable TCE error.Source: §6.2 · p. 26

7 Application to Population-Scale scRNA-seq Data

The AML application uses population-scale single-cell data and Perturb-seq-derived ancestral structure to estimate a target-population regulatory network. TFDP1 has the largest standardized total-effect magnitude among the three transcription factors examined, with distinct paths carrying effects in opposing directions.

7.1 Description of the data

  • The AML cohort comprises 30 bone-marrow samples, 25 genes, and 127–2,256 cells per sample, with blast count as the outcome.Expression was normalized from UMI counts using a Poisson-log-normal fit.Source: §7.1 · p. 27
  • The target-gene set combines ENCODE promoter ChIP-seq enrichment with significant knockdown changes in K562 Perturb-seq data.The external topological information comes from ancestral structure learned from K562 Perturb-seq data.Source: §7.1 · p. 27, §7.2 · p. 28

7.2 Path-Specific Effects of Genes on Blast Count

  • TFDP1’s estimated TCE is 0.28, indicating a 28 percentage-point increase in blast count per unit increase in TFDP1 expression.The estimate is consistent with the positive association between adjusted TFDP1 expression and adjusted blast count.Source: Figure 3 · p. 28, §7.2 · p. 29
  • HSPA8 and PSMD13 are the strongest hubs by total path-specific effect, while a separate TFDP1 → GAPDH → blast-count route has a notable positive effect.The decomposition shows that a positive total effect can arise from multiple pathways with opposing signs.Source: Figure 3 · p. 28, §7.2 · pp. 29–30
  • HSPA8 and GAPDH carry positive path-specific effects and are established druggable targets with small-molecule inhibitors described as suppressing downstream oncogenic activity.The cited inhibitors are VER-155008 for HSPA8 and koningic acid for GAPDH.Source: §7.2 · p. 30

8 Discussion

The framework combines external ancestral information with population-scale single-cell data and jointly addresses multiscale confounding and measurement error. Its causal interpretation has structural, model-form, and outcome-ordering conditions.

8 Discussion

  • The framework uses external ancestral relationships to constrain candidate directions while re-estimating direct edges and effects from population data.Two-scale surrogate variables address latent heterogeneity, and replicated measurements support technical-error correction.Source: §8 · p. 31
  • Simulations show that confounding adjustment and measurement-error correction address complementary biases; correcting either alone leaves substantial estimation error.Their combination improves estimation of the network and gene–outcome effects.Source: §8 · p. 31
  • Causal interpretation assumes the external scaffold contains true target-population parents and preserves their ordering, linear structural and outcome models, and outcomes downstream of expression.The downstream-outcome assumption may be particularly consequential for cross-sectional disease phenotypes; future work could relax these assumptions and add direct uncertainty quantification for path-specific effects.Source: §8 · p. 31
Loading 2609.16510v1…