# Longitudinal Adaptive Experimental Design for Learning Multiple Target Estimands with Semiparametric Efficient Inference

arXiv: https://arxiv.org/abs/2607.29421 · HTML: https://mlsanity.com/paper/2607.29421/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 48 references that are in the map.
- First posted on arXiv 31 Jul 2026.

## Builds on (most cited first, 9 of 9)

- [Targeting for long-term outcomes](https://mlsanity.com/paper/2010.15835/) (2020)
- [Response-adaptive randomization in clinical trials: from myths to practical considerations](https://mlsanity.com/paper/2005.00564/) (2020)
- [Adaptive Sequential Design for a Single Time-Series](https://mlsanity.com/paper/2102.00102/) (2021)
- [Targeted Maximum Likelihood Based Estimation for Longitudinal Mediation Analysis](https://mlsanity.com/paper/2304.04904/) (2023)
- [Efficient Statistical Estimation for Sequential Adaptive Experiments with Implications for Adaptive Designs](https://mlsanity.com/paper/2508.09135/) (2025)
- [Adaptive Sequential Surveillance with Network and Temporal Dependence](https://mlsanity.com/paper/2212.02422/) (2022)
- [DTR Bandit: Learning to Make Response-Adaptive Decisions With Low Regret](https://mlsanity.com/paper/2005.02791/) (2020)
- [Optimal Adaptive SMART Designs with Binary Outcomes](https://mlsanity.com/paper/2401.03326/) (2023)
- [An Online Meta-Level Adaptive Design Framework with Targeted Learning Inference: Applications to Evaluating and Utilizing Surrogate Outcomes in Adaptive Designs](https://mlsanity.com/paper/2408.02667/) (2024)

## Abstract (arXiv)

Adaptive designs are increasingly used in clinical trials and digital experiments to improve estimation efficiency by updating treatment randomization probabilities as data accumulate. While most existing work focuses on settings with a single-stage treatment, adaptive designs for longitudinal studies with multi-stage, time-varying treatments remain relatively underexplored. In this work, we develop a general semiparametric efficiency framework for designing longitudinal adaptive experiments to optimize the estimation efficiency of a broad class of target estimands of interest. An efficiency-oriented design criterion is proposed to accommodate both single-estimand targets and joint optimization across multiple estimands. We demonstrate that optimal randomization at earlier stages depends on later-stage allocations, yielding a backward-recursive strategy for deriving the oracle design, and propose a longitudinal adaptive design to sequentially learn and target the oracle design using accumulating data. We further develop an adaptive-design-likelihood-based longitudinal targeted maximum likelihood estimator (ADL-LTMLE) for asymptotically normal and semiparametric efficient estimation of statistical estimands from dependent data collected from adaptive experiments, without relying on parametric model assumptions. Applying the framework to time-to-treatment-initiation effects that compare initiating treatment at a given stage with delaying initiation until a subsequent stage, we show that designs optimized for a particular stage-specific effect can substantially compromise estimation efficiency for effects defined at other stages, highlighting the design trade-offs addressed by our framework. Simulation studies show the proposed design and estimation approaches achieve substantial variance reductions relative to non-adaptive designs, with performance close to that of the oracle design.