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Causal Inference in the Closed-Loop: Marginal Structural Models for Sequential Excursion Effects
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Introduces a nonparametric IPW-estimated history-restricted marginal structural model framework for sequential excursion effects in closed-loop (dynamic regime) optogenetics designs with positivity violations, and applies it to a dopamine stimulation learning study.
Problem
Standard analyses of optogenetics experiments discard information and can be biased in closed-loop designs where stimulation depends on animal behavior, creating treatment-confounder feedback and positivity violations; existing excursion-effect methods only handle a one-trial lag.
Approach
Extends history-restricted marginal structural models and excursion effects to dynamic treatment regimes with availability restrictions, defining multi-trial sequential excursion effects estimated by an IPW GEE-style estimator with sandwich-based asymptotic inference.
Key results
- Simulations show the IPW estimator is consistent and HC3 or large-sample sandwich CIs reach ~95% coverage as n or T grows (e.g., HC coverage 0.94-0.95 at T=50, n=30-100).
- In the dopamine application, macro longitudinal GEE finds no significant effects for any individual pose, whereas the sequential excursion HR-MSM finds significant negative single-stimulation effects for 5 of 6 poses.
- The availability-conditional (blip) estimand identifies a significant effect in only one pose, versus more discoveries using sequential excursion effects.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use sequential excursion effects for proximal treatment sequences (Δ>1) rather than macro longitudinal summaries | Closed-loop optogenetics analysis · Six target poses | Significant treatment effects detected | Helped |
| Use availability-conditional Δ=1 estimands instead of sequential excursion effects for longer sequences | Closed-loop optogenetics analysis · Six target poses | Significant treatment effects detected | Hurt |
| Estimate the dose-response over the previous Δ=5 trials rather than only the most recent-trial blip | HR-MSM in the treatment group · Six target poses | Dose-response treatment effect | Helped |
| Use the proposed LS variance estimator in small-n settings rather than HC3 | Sequential excursion effect inference · Simulation, small n and T | 95% CI coverage | Hurt |
| Use the proposed LS variance estimator when n is large | Sequential excursion effect inference · Simulation, large n | 95% CI coverage | No clear effect |
| Increase sample size or number of trials | Proposed IPW estimator · Simulation | Estimator bias | Helped |
| Estimate trial-level sequential effects rather than only pooled outcome summaries | Optogenetic dopamine stimulation analysis · Target-pose outcomes | Detection of causal effects | Helped |
Surprising findings
- Standard macro summaries (GEE on pooled trial counts) show no significant group effects for any pose, even though treatment-confounder feedback hides local stimulation effects.
- Treatment and control groups can show identical average outcomes even when the laser has a large immediate effect, due to treatment-confounder feedback.
Limitations
- Estimands depend on the treatment protocol and marginalize over earlier treatments, so interpretation is tied to the design.
- Computational cost may grow challenging for very large history lengths Delta.
- Inference requires the Donsker condition, excluding some flexible machine learning models such as certain neural networks.
Experimental setup
Datasets: Simulated closed-loop optogenetics data Markowitz et al. dopamine optogenetics pose dataset (shared by original authors)
Benchmarks: simulation study (relative bias, MSE, 95% CI coverage) dopamine optogenetics application
Metrics: relative bias mean squared error 95% CI coverage log odds ratio effect estimates p-values
Baselines: GEE macro longitudinal analysis availability-conditional excursion estimand HC/HC2/HC3 sandwich variance estimators
Builds on: history-restricted marginal structural models excursion effects (availability-conditional estimand) generalized estimating equations inverse probability weighting
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