Mark van der Laan

Ahmed Alaa, Zaid Ahmad, Mark van der Laan

We investigate the problem of machine learning-based (ML) predictive inference on individual treatment effects (ITEs). Previous work has focused primarily on developing ML-based meta-learners that can provide point estimates of the conditional average treatment effect (CATE); these are model-agnostic approaches for combining intermediate nuisance estimates to produce estimates of CATE. In this paper, we develop conformal meta-learners, a general framework for issuing predictive intervals for ITEs by applying the standard conformal prediction (CP) procedure on top of CATE meta-learners. We focus on a broad class of meta-learners based on two-stage pseudo-outcome regression and develop a stochastic ordering framework to study their validity. We show that inference with conformal meta-learners is marginally valid if their (pseudo outcome) conformity scores stochastically dominate oracle conformity scores evaluated on the unobserved ITEs. Additionally, we prove that commonly used CATE meta-learners, such as the doubly-robust learner, satisfy a model- and distribution-free stochastic (or convex) dominance condition, making their conformal inferences valid for practically-relevant levels of target coverage. Whereas existing procedures conduct inference on nuisance parameters (i.e., potential outcomes) via weighted CP, conformal meta-learners enable direct inference on the target parameter (ITE). Numerical experiments show that conformal meta-learners provide valid intervals with competitive efficiency while retaining the favorable point estimation properties of CATE meta-learners.

Alejandro Schuler, Yi Li, Mark van der Laan

Gradient boosting performs exceptionally in most prediction problems and scales well to large datasets. In this paper we prove that a ``lassoed'' gradient boosted tree algorithm with early stopping achieves faster than $n^{-1/4}$ L2 convergence in the large nonparametric space of cadlag functions of bounded sectional variation. This rate is remarkable because it does not depend on the dimension, sparsity, or smoothness. We use simulation and real data to confirm our theory and demonstrate empirical performance and scalability on par with standard boosting. Our convergence proofs are based on a novel, general theorem on early stopping with empirical loss minimizers of nested Donsker classes.

Ahmed Alaa, Rachael V. Phillips, Emre Kıcıman et al.

The validity of medical studies based on real-world clinical data, such as observational studies, depends on critical assumptions necessary for drawing causal conclusions about medical interventions. Many published studies are flawed because they violate these assumptions and entail biases such as residual confounding, selection bias, and misalignment between treatment and measurement times. Although researchers are aware of these pitfalls, they continue to occur because anticipating and addressing them in the context of a specific study can be challenging without a large, often unwieldy, interdisciplinary team with extensive expertise. To address this expertise gap, we explore the use of large language models (LLMs) as co-pilot tools to assist researchers in identifying study design flaws that undermine the validity of causal inferences. We propose a conceptual framework for LLMs as causal co-pilots that encode domain knowledge across various fields, engaging with researchers in natural language interactions to provide contextualized assistance in study design. We provide illustrative examples of how LLMs can function as causal co-pilots, propose a structured framework for their grounding in existing causal inference frameworks, and highlight the unique challenges and opportunities in adapting LLMs for reliable use in epidemiological research.

Toru Shirakawa, Yi Li, Yulun Wu et al.

We propose Deep Longitudinal Targeted Minimum Loss-based Estimation (Deep LTMLE), a novel approach to estimate the counterfactual mean of outcome under dynamic treatment policies in longitudinal problem settings. Our approach utilizes a transformer architecture with heterogeneous type embedding trained using temporal-difference learning. After obtaining an initial estimate using the transformer, following the targeted minimum loss-based likelihood estimation (TMLE) framework, we statistically corrected for the bias commonly associated with machine learning algorithms. Furthermore, our method also facilitates statistical inference by enabling the provision of 95% confidence intervals grounded in asymptotic statistical theory. Simulation results demonstrate our method's superior performance over existing approaches, particularly in complex, long time-horizon scenarios. It remains effective in small-sample, short-duration contexts, matching the performance of asymptotically efficient estimators. To demonstrate our method in practice, we applied our method to estimate counterfactual mean outcomes for standard versus intensive blood pressure management strategies in a real-world cardiovascular epidemiology cohort study.

Yi Li, David Mccoy, Nolan Gunter et al.

Modern deep neural networks are powerful predictive tools yet often lack valid inference for causal parameters, such as treatment effects or entire survival curves. While frameworks like Double Machine Learning (DML) and Targeted Maximum Likelihood Estimation (TMLE) can debias machine-learning fits, existing neural implementations either rely on "targeted losses" that do not guarantee solving the efficient influence function equation or computationally expensive post-hoc "fluctuations" for multi-parameter settings. We propose Targeted Deep Architectures (TDA), a new framework that embeds TMLE directly into the network's parameter space with no restrictions on the backbone architecture. Specifically, TDA partitions model parameters - freezing all but a small "targeting" subset - and iteratively updates them along a targeting gradient, derived from projecting the influence functions onto the span of the gradients of the loss with respect to weights. This procedure yields plug-in estimates that remove first-order bias and produce asymptotically valid confidence intervals. Crucially, TDA easily extends to multi-dimensional causal estimands (e.g., entire survival curves) by merging separate targeting gradients into a single universal targeting update. Theoretically, TDA inherits classical TMLE properties, including double robustness and semiparametric efficiency. Empirically, on the benchmark IHDP dataset (average treatment effects) and simulated survival data with informative censoring, TDA reduces bias and improves coverage relative to both standard neural-network estimators and prior post-hoc approaches. In doing so, TDA establishes a direct, scalable pathway toward rigorous causal inference within modern deep architectures for complex multi-parameter targets.

Laura B. Balzer, Mark van der Laan, James Ayieko et al.

Cluster randomized trials (CRTs) randomly assign an intervention to groups of individuals (e.g., clinics or communities) and measure outcomes on individuals in those groups. While offering many advantages, this experimental design introduces challenges that are only partially addressed by existing analytic approaches. First, outcomes are often missing for some individuals within clusters. Failing to appropriately adjust for differential outcome measurement can result in biased estimates and inference. Second, CRTs often randomize limited numbers of clusters, resulting in chance imbalances on baseline outcome predictors between arms. Failing to adaptively adjust for these imbalances and other predictive covariates can result in efficiency losses. To address these methodological gaps, we propose and evaluate a novel two-stage targeted minimum loss-based estimator (TMLE) to adjust for baseline covariates in a manner that optimizes precision, after controlling for baseline and post-baseline causes of missing outcomes. Finite sample simulations illustrate that our approach can nearly eliminate bias due to differential outcome measurement, while existing CRT estimators yield misleading results and inferences. Application to real data from the SEARCH community randomized trial demonstrates the gains in efficiency afforded through adaptive adjustment for baseline covariates, after controlling for missingness on individual-level outcomes.

Aurélien Bibaut, Antoine Chambaz, Maria Dimakopoulou et al.

Empirical risk minimization (ERM) is the workhorse of machine learning, whether for classification and regression or for off-policy policy learning, but its model-agnostic guarantees can fail when we use adaptively collected data, such as the result of running a contextual bandit algorithm. We study a generic importance sampling weighted ERM algorithm for using adaptively collected data to minimize the average of a loss function over a hypothesis class and provide first-of-their-kind generalization guarantees and fast convergence rates. Our results are based on a new maximal inequality that carefully leverages the importance sampling structure to obtain rates with the right dependence on the exploration rate in the data. For regression, we provide fast rates that leverage the strong convexity of squared-error loss. For policy learning, we provide rate-optimal regret guarantees that close an open gap in the existing literature whenever exploration decays to zero, as is the case for bandit-collected data. An empirical investigation validates our theory.

Aurélien Bibaut, Antoine Chambaz, Maria Dimakopoulou et al.

Contextual bandit algorithms are increasingly replacing non-adaptive A/B tests in e-commerce, healthcare, and policymaking because they can both improve outcomes for study participants and increase the chance of identifying good or even best policies. To support credible inference on novel interventions at the end of the study, nonetheless, we still want to construct valid confidence intervals on average treatment effects, subgroup effects, or value of new policies. The adaptive nature of the data collected by contextual bandit algorithms, however, makes this difficult: standard estimators are no longer asymptotically normally distributed and classic confidence intervals fail to provide correct coverage. While this has been addressed in non-contextual settings by using stabilized estimators, the contextual setting poses unique challenges that we tackle for the first time in this paper. We propose the Contextual Adaptive Doubly Robust (CADR) estimator, the first estimator for policy value that is asymptotically normal under contextual adaptive data collection. The main technical challenge in constructing CADR is designing adaptive and consistent conditional standard deviation estimators for stabilization. Extensive numerical experiments using 57 OpenML datasets demonstrate that confidence intervals based on CADR uniquely provide correct coverage.

Yue You, Mark van der Laan, Philip Collender et al.

We propose a modern method to estimate population size based on capture-recapture designs of K samples. The observed data is formulated as a sample of n i.i.d. K-dimensional vectors of binary indicators, where the k-th component of each vector indicates the subject being caught by the k-th sample, such that only subjects with nonzero capture vectors are observed. The target quantity is the unconditional probability of the vector being nonzero across both observed and unobserved subjects. We cover models assuming a single constraint (identification assumption) on the K-dimensional distribution such that the target quantity is identified and the statistical model is unrestricted. We present solutions for linear and non-linear constraints commonly assumed to identify capture-recapture models, including no K-way interaction in linear and log-linear models, independence or conditional independence. We demonstrate that the choice of constraint has a dramatic impact on the value of the estimand, showing that it is crucial that the constraint is known to hold by design. For the commonly assumed constraint of no K-way interaction in a log-linear model, the statistical target parameter is only defined when each of the $2^K - 1$ observable capture patterns is present, and therefore suffers from the curse of dimensionality. We propose a targeted MLE based on undersmoothed lasso model to smooth across the cells while targeting the fit towards the single valued target parameter of interest. For each identification assumption, we provide simulated inference and confidence intervals to assess the performance on the estimator under correct and incorrect identifying assumptions. We apply the proposed method, alongside existing estimators, to estimate prevalence of a parasitic infection using multi-source surveillance data from a region in southwestern China, under the four identification assumptions.

Cheng Ju, Antoine Chambaz, Mark J. van der Laan

We wish to infer the value of a parameter at a law from which we sample independent observations. The parameter is smooth and we can define two variation-independent features of the law, its $Q$- and $G$-components, such that estimating them consistently at a fast enough product of rates allows to build a confidence interval (CI) with a given asymptotic level from a plain targeted minimum loss estimator (TMLE). Say that the above product is not fast enough and the algorithm for the $G$-component is fine-tuned by a real-valued $h$. A plain TMLE with an $h$ chosen by cross-validation would typically not yield a CI. We construct a collaborative TMLE (C-TMLE) and show under mild conditions that, if there exists an oracle $h$ that makes a bulky remainder term asymptotically Gaussian, then the C-TMLE yields a CI. We illustrate our findings with the inference of the average treatment effect. We conduct a simulation study where the $G$-component is estimated by the LASSO and $h$ is the bound on the coefficients' norms. It sheds light on small sample properties, in the face of low- to high-dimensional baseline covariates, and possibly positivity violation.