Mark J. 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.

Causal mediation analysis with random interventions has become an area of significant interest for understanding time-varying effects with longitudinal and survival outcomes. To tackle causal and statistical challenges due to the complex longitudinal data structure with time-varying confounders, competing risks, and informative censoring, there exists a general desire to combine machine learning techniques and semiparametric theory. In this manuscript, we focus on targeted maximum likelihood estimation (TMLE) of longitudinal natural direct and indirect effects defined with random interventions. The proposed estimators are multiply robust, locally efficient, and directly estimate and update the conditional densities that factorize data likelihoods. We utilize the highly adaptive lasso (HAL) and projection representations to derive new estimators (HAL-EIC) of the efficient influence curves of longitudinal mediation problems and propose a fast one-step TMLE algorithm using HAL-EIC while preserving the asymptotic properties. The proposed method can be generalized for other longitudinal causal parameters that are smooth functions of data likelihoods, and thereby provides a novel and flexible statistical toolbox.

This paper describes a targeted maximum likelihood estimator (TMLE) for the parameters of longitudinal static and dynamic marginal structural models. We consider a longitudinal data structure consisting of baseline covariates, time-dependent intervention nodes, intermediate time-dependent covariates, and a possibly time-dependent outcome. The intervention nodes at each time point can include a binary treatment as well as a right-censoring indicator. Given a class of dynamic or static interventions, a marginal structural model is used to model the mean of the intervention-specific counterfactual outcome as a function of the intervention, time point, and possibly a subset of baseline covariates. Because the true shape of this function is rarely known, the marginal structural model is used as a working model. The causal quantity of interest is defined as the projection of the true function onto this working model. Iterated conditional expectation double robust estimators for marginal structural model parameters were previously proposed by Robins (2000, 2002) and Bang and Robins (2005). Here we build on this work and present a pooled TMLE for the parameters of marginal structural working models. We compare this pooled estimator to a stratified TMLE (Schnitzer et al. 2014) that is based on estimating the intervention-specific mean separately for each intervention of interest. The performance of the pooled TMLE is compared to the performance of the stratified TMLE and the performance of inverse probability weighted (IPW) estimators using simulations. Concepts are illustrated using an example in which the aim is to estimate the causal effect of delayed switch following immunological failure of first line antiretroviral therapy among HIV-infected patients. Data from the International Epidemiological Databases to Evaluate AIDS, Southern Africa are analyzed to investigate this question using both TML and IPW estimators. Our results demonstrate practical advantages of the pooled TMLE over an IPW estimator for working marginal structural models for survival, as well as cases in which the pooled TMLE is superior to its stratified counterpart.

Introduction: Cardiac surgery is frequently needed in patients with infective endocarditis (IE). Acute kidney injury (AKI) often complicates IE and is associated with poor outcomes. The purpose of the study was to determine the risk factors for post-operative AKI in patients operated on for IE. Methods: A retrospective, non-interventional study of prospectively collected data (2000–2010) included patients with IE and cardiac surgery with cardio-pulmonary bypass. The primary outcome was post-operative AKI, defined as the development of AKI or progression of AKI based on the acute kidney injury network (AKIN) definition. We used ensemble machine learning (“Super Learning”) to develop a predictor of AKI based on potential risk factors, and evaluated its performance using V-fold cross validation. We identified clinically important predictors among a set of risk factors using Targeted Maximum Likelihood Estimation. Results: 202 patients were included, of which 120 (59%) experienced a post-operative AKI. 65 (32.2%) patients presented an AKI before surgery while 91 (45%) presented a progression of AKI in the post-operative period. 20 patients (9.9%) required a renal replacement therapy during the post-operative ICU stay and 30 (14.8%) died during their hospital stay. The following variables were found to be significantly associated with renal function impairment, after adjustment for other risk factors: multiple surgery (OR: 4.16, 95% CI: 2.98-5.80, p<0.001), pre-operative anemia (OR: 1.89, 95% CI: 1.34-2.66, p<0.001), transfusion requirement during surgery (OR: 2.38, 95% CI: 1.55-3.63, p<0.001), and the use of vancomycin (OR: 2.63, 95% CI: 2.07-3.34, p<0.001), aminoglycosides (OR: 1.44, 95% CI: 1.13-1.83, p=0.004) or contrast iodine (OR: 1.70, 95% CI: 1.37-2.12, p<0.001). Post-operative but not pre-operative AKI was associated with hospital mortality. Conclusions: Post-operative AKI following cardiopulmonary bypass for IE results from additive hits to the kidney. We identified several potentially modifiable risk factors such as treatment with vancomycin or aminoglycosides or pre-operative anemia.

It is a challenge to evaluate experimental treatments where it is suspected that the treatment effect may only be strong for certain subpopulations, such as those having a high initial severity of disease, or those having a particular gene variant. Standard randomized controlled trials can have low power in such situations. They also are not optimized to distinguish which subpopulations benefit from a treatment. With the goal of overcoming these limitations, we consider randomized trial designs in which the criteria for patient enrollment may be changed, in a preplanned manner, based on interim analyses. Since such designs allow data-dependent changes to the population enrolled, care must be taken to ensure strong control of the familywise Type I error rate. Our main contribution is a general method for constructing randomized trial designs that allow changes to the population enrolled based on interim data using a prespecified decision rule, for which the asymptotic, familywise Type I error rate is strongly controlled at a specified level α. As a demonstration of our method, we prove new, sharp results for a simple, two-stage enrichment design. We then compare this design to fixed designs, focusing on each design’s ability to determine the overall and subpopulation-specific treatment effects.

Summary Regression models are often used to test for cause‐effect relationships from data collected in randomized trials or experiments. This practice has deservedly come under heavy scrutiny, because commonly used models such as linear and logistic regression will often not capture the actual relationships between variables, and incorrectly specified models potentially lead to incorrect conclusions. In this article, we focus on hypothesis tests of whether the treatment given in a randomized trial has any effect on the mean of the primary outcome, within strata of baseline variables such as age, sex, and health status. Our primary concern is ensuring that such hypothesis tests have correct type I error for large samples. Our main result is that for a surprisingly large class of commonly used regression models, standard regression‐based hypothesis tests (but using robust variance estimators) are guaranteed to have correct type I error for large samples, even when the models are incorrectly specified. To the best of our knowledge, this robustness of such model‐based hypothesis tests to incorrectly specified models was previously unknown for Poisson regression models and for other commonly used models we consider. Our results have practical implications for understanding the reliability of commonly used, model‐based tests for analyzing randomized trials.

We propose a new causal parameter, which is a natural extension of existing approaches to causal inference such as marginal structural models. Modelling approaches are proposed for the difference between a treatment-specific counterfactual population distribution and the actual population distribution of an outcome in the target population of interest. Relevant parameters describe the effect of a hypothetical intervention on such a population and therefore we refer to these models as population intervention models. We focus on intervention models estimating the effect of an intervention in terms of a difference and ratio of means, called risk difference and relative risk if the outcome is binary. We provide a class of inverse-probability-of-treatment-weighted and doubly-robust estimators of the causal parameters in these models. The finite-sample performance of these new estimators is explored in a simulation study.

In this issue of the Journal, Thall et al. present the results of a clinical trial that makes use of sequential randomization, a novel trial design that allows the investigator to study adaptive treatment strategies. Our aim is to complement this groundbreaking work by reviewing the current state of the art of statistical methods available for such analyses. Using the data collected by Thall et al. as an example, we focus on two different approaches for estimating the success rates of different adaptive treatment strategies of interest. By emphasizing the intuitive appeal and straightforward implementation of these methods and illustrating the striking findings to which these methods can lead, we hope to convince the reader that this novel trial design provides a rich source of information that is made readily accessible through current analytical approaches.