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Incremental Causal Effect for Time to Treatment Initialization

ICLR 2025 · Probabilistic and scientific modeling › Treatment effects · approach: Latent-variable causal inference · 0 citations (OpenAlex)

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Defines incremental causal effects for time to treatment initiation by multiplying the treatment hazard, shows identification without positivity via IPW, and gives a Cox-based IPW estimator with bootstrap inference, illustrated on a rheumatoid arthritis methotrexate study.

Problem

Causal effects of time to treatment initiation (e.g., screening, vaccination, HIV treatment start) are usually framed as 'when to treat' under static or dynamic regimes that require positivity, which often fails in practice. The paper asks how the outcome changes if the hazard of treatment initiatio

Approach

Define the incremental causal effect by shifting the treatment hazard by a positive factor theta(t,l) (hazard-ratio intervention), identify it from observed data under consistency and sequential randomization only (no positivity), and estimate it with a plug-in IPW estimator that accommodates any hazard estimator (e.g., Cox model) with root-n asymptotics and multiplier bootstrap inference.

Key results

• In simulations with n=5000, the IPW estimator has near-zero bias and 95% coverage between 94.3% and 95.7% across theta values from 1/3 to 3.
• On the methotrexate data, doubling the MTX initiation hazard gives psi(2)=1.87 tender joints (95% CI 1.81-1.93) versus 1.90 observed, a 1.23% decrease.
• Multiplying the hazard five-fold gives psi(5)=1.79 (95% CI 1.71-1.88), a 5.42% decrease in tender joints at one year.

Measured effects reported in the paper

Limitations

• Efficiency is not attained; the IPW estimator is not semiparametrically efficient and augmentation is left to future work.
• Identification requires no unmeasured confounding (sequential randomization) and correct hazard model specification for the Cox-based nuisance estimate.
• Analysis is limited to a single binary-outcome-free setting with a point outcome at fixed time tau and no time-varying confounders or survival outcomes.

Experimental setup

Datasets: simulated data rheumatoid arthritis methotrexate cohort (1010 patients after exclusions from 1240)

Benchmarks: simulation study (bias, SEE, SD, 95% coverage) rheumatoid arthritis methotrexate data

Metrics: bias percent bias empirical standard error average estimated standard error 95% coverage probability

Baselines: static interventions pre-specified dynamic regimes marginal structural linear model with IPW least squares proximal recursive least squares

Builds on: incremental causal effects (Kennedy 2019) Cox proportional hazards model inverse probability weighting multiplier bootstrap

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