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Stijn Vansteelandt

Publications and source records attributed to Stijn Vansteelandt.

At least 37 records · Page 2Linked to original sources
arXiv2024

The Real Deal Behind the Artificial Appeal: Inferential Utility of Tabular Synthetic Data

Recent advances in generative models facilitate the creation of synthetic data to be made available for research in privacy-sensitive contexts. However, the analysis of synthetic data raises a unique set of methodological challenges. In this work, we highlight the importance of inferential utility and provide empirical evidence against naive inference from synthetic data, whereby synthetic data are treated as if they were actually observed. Before publishing synthetic data, it is essential to develop statistical inference tools for such data. By means of a simulation study, we show that the rate of false-positive findings (type 1 error) will be unacceptably high, even when the estimates are unbiased. Despite the use of a previously proposed correction factor, this problem persists for deep generative models, in part due to slower convergence of estimators and resulting underestimation of the true standard error. We further demonstrate our findings through a case study.

cs.LG↗
arXiv2024

On Weighted Orthogonal Learners for Heterogeneous Treatment Effects

Motivated by applications in personalized medicine and individualized policymaking, there is a growing interest in techniques for quantifying treatment effect heterogeneity in terms of the conditional average treatment effect (CATE). Some of the most prominent methods for CATE estimation developed in recent years are T-Learner, DR-Learner and R-Learner. The latter two were designed to improve on the former by being Neyman-orthogonal. However, the relations between them remain unclear, and likewise the literature remains vague on whether these learners converge to a useful quantity or (functional) estimand when the underlying optimization procedure is restricted to a class of functions that does not include the CATE. In this article, we provide insight into these questions by discussing DR-Learner and R-Learner as special cases of a general class of weighted Neyman-orthogonal learners for the CATE, for which we moreover derive oracle bounds. Our results shed light on how one may construct Neyman-orthogonal learners with desirable properties, on when DR-Learner may be preferred over R-Learner (and vice versa), and on novel learners that may sometimes be preferable to either of these. Theoretical findings are confirmed using results from simulation studies on synthetic data, as well as an application in critical care medicine.

stat.ME↗
arXiv2024

Assumption-Lean Quantile Regression

Quantile regression is a powerful tool for detecting exposure-outcome associations given covariates across different parts of the outcome's distribution, but has two major limitations when the aim is to infer the effect of an exposure. Firstly, the exposure coefficient estimator may not converge to a meaningful quantity when the model is misspecified, and secondly, variable selection methods may induce bias and excess uncertainty, rendering inferences biased and overly optimistic. In this paper, we address these issues via partially linear quantile regression models which parametrize the conditional association of interest, but do not restrict the association with other covariates in the model. We propose consistent estimators for the unknown model parameter by mapping it onto a nonparametric main effect estimand that captures the (conditional) association of interest even when the quantile model is misspecified. This estimand is estimated using the efficient influence function under the nonparametric model, allowing for the incorporation of data-adaptive procedures such as variable selection and machine learning. Our approach provides a flexible and reliable method for detecting associations that is robust to model misspecification and excess uncertainty induced by variable selection methods. The proposal is illustrated using simulation studies and data on annual health care costs associated with excess body weight.

stat.ME↗
arXiv2024

Optimally weighted average derivative effects

Weighted average derivative effects (WADEs) are nonparametric estimands with uses in economics and causal inference. Debiased WADE estimators typically require learning the conditional mean outcome as well as a Riesz representer (RR) that characterises the requisite debiasing corrections. RR estimators for WADEs often rely on kernel estimators, introducing complicated bandwidth-dependant biases. In our work we propose a new class of RRs that are isomorphic to the class of WADEs and we derive the WADE weight that is optimal, in the sense of having minimum nonparametric efficiency bound. Our optimal WADE estimators require estimating conditional expectations only (e.g. using machine learning), thus overcoming the limitations of kernel estimators. Moreover, we connect our optimal WADE to projection parameters in partially linear models. We ascribe a causal interpretation to WADE and projection parameters in terms of so-called incremental effects. We propose efficient estimators for two WADE estimands in our class, which we evaluate in a numerical experiment and use to determine the effect of Warfarin dose on blood clotting function.

stat.ME↗
arXiv2023

Handling time-dependent exposures and confounders when estimating attributable fractions -- bridging the gap between multistate and counterfactual modeling

The population-attributable fraction (PAF) expresses the proportion of events that can be ascribed to a certain exposure in a certain population. It can be strongly time-dependent because either exposure incidence or excess risk may change over time. Competing events may moreover hinder the outcome of interest from being observed. Occurrence of either of these events may, in turn, prevent the exposure of interest. Estimation approaches therefore need to carefully account for the timing of events in such highly dynamic settings. The use of multistate models has been widely encouraged to eliminate preventable yet common types of time-dependent bias. Even so, it has been pointed out that proposed multistate modeling approaches for PAF estimation fail to fully eliminate such bias. In addition, assessing whether patients die from rather than with a certain exposure not only requires adequate modeling of the timing of events but also of their confounding factors. While proposed multistate modeling approaches for confounding adjustment may adequately accommodate baseline imbalances, unlike g-methods, these proposals are not generally equipped to handle time-dependent confounding. However, the connection between multistate modeling and g-methods (e.g. inverse probability of censoring weighting) for PAF estimation is not readily apparent. In this paper, we provide a weighting-based characterization of both approaches to illustrate this connection, to pinpoint current shortcomings of multistate modeling, and to enhance intuition into simple modifications to overcome these. R code is made available to foster the uptake of g-methods for PAF estimation.

stat.ME↗
arXiv2023

Orthogonal prediction of counterfactual outcomes

Orthogonal meta-learners, such as DR-learner, R-learner and IF-learner, are increasingly used to estimate conditional average treatment effects. They improve convergence rates relative to na\"ıve meta-learners (e.g., T-, S- and X-learner) through de-biasing procedures that involve applying standard learners to specifically transformed outcome data. This leads them to disregard the possibly constrained outcome space, which can be particularly problematic for dichotomous outcomes: these typically get transformed to values that are no longer constrained to the unit interval, making it difficult for standard learners to guarantee predictions within the unit interval. To address this, we construct orthogonal meta-learners for the prediction of counterfactual outcomes which respect the outcome space. As such, the obtained i-learner or imputation-learner is more generally expected to outperform existing learners, even when the outcome is unconstrained, as we confirm empirically in simulation studies and an analysis of critical care data. Our development also sheds broader light onto the construction of orthogonal learners for other estimands.

stat.ME↗
arXiv2023

Inverse probability of treatment weighting with generalized linear outcome models for doubly robust estimation

There are now many options for doubly robust estimation; however, there is a concerning trend in the applied literature to believe that the combination of a propensity score and an adjusted outcome model automatically results in a doubly robust estimator and/or to misuse more complex established doubly robust estimators. A simple alternative, canonical link generalized linear models (GLM) fit via inverse probability of treatment (propensity score) weighted maximum likelihood estimation followed by standardization (the g-formula) for the average causal effect, is a doubly robust estimation method. Our aim is for the reader not just to be able to use this method, which we refer to as IPTW GLM, for doubly robust estimation, but to fully understand why it has the doubly robust property. For this reason, we define clearly, and in multiple ways, all concepts needed to understand the method and why it is doubly robust. In addition, we want to make very clear that the mere combination of propensity score weighting and an adjusted outcome model does not generally result in a doubly robust estimator. Finally, we hope to dispel the misconception that one can adjust for residual confounding remaining after propensity score weighting by adjusting in the outcome model for what remains `unbalanced' even when using doubly robust estimators. We provide R code for our simulations and real open-source data examples that can be followed step-by-step to use and hopefully understand the IPTW GLM method. We also compare to a much better-known but still simple doubly robust estimator.

stat.ME↗
arXiv2023

Adjusting for time-varying treatment switches in randomized clinical trials: the danger of extrapolation and how to avoid it

When choosing estimands and estimators in randomized clinical trials, caution is warranted as intercurrent events, such as - due to patients who switch treatment after disease progression, are often extreme. Statistical analyses may then easily lure one into making large implicit extrapolations, which often go unnoticed. We will illustrate this problem of implicit extrapolations using a real oncology case study, with a right-censored time-to-event endpoint, in which patients can cross over from the control to the experimental treatment after disease progression, for ethical reasons. We resolve this by developing an estimator for the survival risk ratio contrasting the survival probabilities at each time t if all patients would take experimental treatment with the survival probabilities at those times t if all patients would take control treatment up to time t, using randomization as an instrumental variable to avoid reliance on no unmeasured confounders assumptions. This doubly robust estimator can handle time-varying treatment switches and right-censored survival times. Insight into the rationale behind the estimator is provided and the approach is demonstrated by re-analyzing the oncology trial.

stat.AP↗
arXiv2022

Structural mean models for instrumented difference-in-differences

In the standard difference-in-differences research design, the parallel trends assumption may be violated when the relationship between the exposure trend and the outcome trend is confounded by unmeasured confounders. Progress can be made if there is an exogenous variable that (i) does not directly influence the change in outcome means (i.e. the outcome trend) except through influencing the change in exposure means (i.e. the exposure trend), and (ii) is not related to the unmeasured exposure - outcome confounders on the trend scale. Such exogenous variable is called an instrument for difference-in-differences. For continuous outcomes that lend themselves to linear modelling, so-called instrumented difference-in-differences methods have been proposed. In this paper, we will suggest novel multiplicative structural mean models for instrumented difference-in-differences, which allow one to identify and estimate the average treatment effect on count and rare binary outcomes, in the whole population or among the treated, when a valid instrument for difference-in-differences is available. We discuss the identifiability of these models, then develop efficient semi-parametric estimation approaches that allow the use of flexible, data-adaptive or machine learning methods to estimate the nuisance parameters. We apply our proposal on health care data to investigate the risk of moderate to severe weight gain under sulfonylurea treatment compared to metformin treatment, among new users of antihyperglycemic drugs.

stat.ME↗
arXiv2022

On Estimation and Cross-validation of Dynamic Treatment Regimes with Competing Risks

The optimal moment to start renal replacement therapy in a patient with acute kidney injury (AKI) remains a challenging problem in intensive care nephrology. Multiple randomised controlled trials have tried to answer this question, but these can, by definition, only analyse a limited number of treatment initiation strategies. In view of this, we use routinely collected observational data from the Ghent University Hospital intensive care units (ICUs) to investigate different pre-specified timing strategies for renal replacement therapy initiation based on time-updated levels of serum potassium, pH and fluid balance in critically ill patients with AKI with the aim to minimize 30-day ICU mortality. For this purpose, we apply statistical techniques for evaluating the impact of specific dynamic treatment regimes in the presence of ICU discharge as a competing event. We discuss two approaches, a non-parametric one - using an inverse probability weighted Aalen-Johansen estimator - and a semiparametric one - using dynamic-regime marginal structural models. Furthermore, we suggest an easy to implement cross-validation technique that can be used for the out-of-sample performance assessment of the optimal dynamic treatment regime. Our work illustrates the potential of data-driven medical decision support based on routinely collected observational data.

stat.AP↗
arXiv2022

A statistical test to reject the structural interpretation of a latent factor model

Factor analysis is often used to assess whether a single univariate latent variable is sufficient to explain most of the covariance among a set of indicators for some underlying construct. When evidence suggests that a single factor is adequate, research often proceeds by using a univariate summary of the indicators in subsequent research. Implicit in such practices is the assumption that it is the underlying latent, rather than the indicators, that is causally efficacious. The assumption that the indicators do not have effects on anything subsequent, and that they are themselves only affected by antecedents through the underlying latent is a strong assumption, effectively imposing a structural interpretation on the latent factor model. In this paper, we show that this structural assumption has empirically testable implications, even though the latent variable itself is unobserved. We develop a statistical test to potentially reject the structural interpretation of a latent factor model. We apply this test to data concerning associations between the Satisfaction-with-Life-Scale and subsequent all-cause mortality, which provides strong evidence against a structural interpretation for a univariate latent underlying the scale. Discussion is given to the implications of this result for the development, evaluation, and use of measures and for the use of factor analysis itself.

stat.ME↗
arXiv2022

IV estimation of causal hazard ratio

Cox's proportional hazards model is one of the most popular statistical models to evaluate associations of exposure with a censored failure time outcome. When confounding factors are not fully observed, the exposure hazard ratio estimated using a Cox model is subject to unmeasured confounding bias. To address this, we propose a novel approach for the identification and estimation of the causal hazard ratio in the presence of unmeasured confounding factors. Our approach is based on a binary instrumental variable, and an additional no-interaction assumption in a first stage regression of the treatment on the IV and unmeasured confounders. We propose, to the best of our knowledge, the first consistent estimator of the (population) causal hazard ratio within an instrumental variable framework. A version of our estimator admits a closed-form representation. We derive the asymptotic distribution of our estimator, and provide a consistent estimator for its asymptotic variance. Our approach is illustrated via simulation studies and a data application.

stat.ME↗
arXiv2021

Demystifying statistical learning based on efficient influence functions

Evaluation of treatment effects and more general estimands is typically achieved via parametric modelling, which is unsatisfactory since model misspecification is likely. Data-adaptive model building (e.g. statistical/machine learning) is commonly employed to reduce the risk of misspecification. Naive use of such methods, however, delivers estimators whose bias may shrink too slowly with sample size for inferential methods to perform well, including those based on the bootstrap. Bias arises because standard data-adaptive methods are tuned towards minimal prediction error as opposed to e.g. minimal MSE in the estimator. This may cause excess variability that is difficult to acknowledge, due to the complexity of such strategies. Building on results from non-parametric statistics, targeted learning and debiased machine learning overcome these problems by constructing estimators using the estimand's efficient influence function under the non-parametric model. These increasingly popular methodologies typically assume that the efficient influence function is given, or that the reader is familiar with its derivation. In this paper, we focus on derivation of the efficient influence function and explain how it may be used to construct statistical/machine-learning-based estimators. We discuss the requisite conditions for these estimators to perform well and use diverse examples to convey the broad applicability of the theory.

math.ST↗
arXiv2021

Ensuring valid inference for hazard ratios after variable selection

The problem of how to best select variables for confounding adjustment forms one of the key challenges in the evaluation of exposure effects in observational studies, and has been the subject of vigorous recent activity in causal inference. A major drawback of routine procedures is that there is no finite sample size at which they are guaranteed to deliver exposure effect estimators and associated confidence intervals with adequate performance. In this work, we will consider this problem when inferring conditional causal hazard ratios from observational studies under the assumption of no unmeasured confounding. The major complication that we face with survival data is that the key confounding variables may not be those that explain the censoring mechanism. In this paper, we overcome this problem using a novel and simple procedure that can be implemented using off-the-shelf software for penalized Cox regression. In particular, we will propose tests of the null hypothesis that the exposure has no effect on the considered survival endpoint, which are uniformly valid under standard sparsity conditions. Simulation results show that the proposed methods yield valid inferences even when covariates are high-dimensional.

stat.ME↗
arXiv2021

Causal inference in survival analysis using longitudinal observational data: Sequential trials and marginal structural models

Longitudinal observational patient data can be used to investigate the causal effects of time-varying treatments on time-to-event outcomes. Several methods have been developed for controlling for the time-dependent confounding that typically occurs. The most commonly used is inverse probability weighted estimation of marginal structural models (MSM-IPTW). An alternative, the sequential trials approach, is increasingly popular, in particular in combination with the target trial emulation framework. This approach involves creating a sequence of `trials' from new time origins, restricting to individuals as yet untreated and meeting other eligibility criteria, and comparing treatment initiators and non-initiators. Individuals are censored when they deviate from their treatment status at the start of each `trial' (initiator/non-initiator) and this is addressed using inverse probability of censoring weights. The analysis is based on data combined across trials. We show that the sequential trials approach can estimate the parameter of a particular MSM, and compare it to a MSM-IPTW with respect to the estimands being identified, the assumptions needed and how data are used differently. We show how both approaches can estimate the same marginal risk differences. The two approaches are compared using a simulation study. The sequential trials approach, which tends to involve less extreme weights than MSM-IPTW, results in greater efficiency for estimating the marginal risk difference at most follow-up times, but this can, in certain scenarios, be reversed at late time points. We apply the methods to longitudinal observational data from the UK Cystic Fibrosis Registry to estimate the effect of dornase alfa on survival.

stat.ME↗
arXiv2021

A novel approach for identifying and addressing case-mix heterogeneity in individual participant data meta-analysis

Case-mix heterogeneity across studies complicates meta-analyses. As a result of this, treatments that are equally effective on patient subgroups may appear to have different effectiveness on patient populations with different case mix. It is therefore important that meta-analyses be explicit for what patient population they describe the treatment effect. To achieve this, we develop a new approach for meta-analysis of randomized clinical trials, which use individual patient data (IPD) from all trials to infer the treatment effect for the patient population in a given trial, based on direct standardization using either outcome regression (OCR) or inverse probability weighting (IPW). Accompanying random-effect meta-analysis models are developed. The new approach enables disentangling heterogeneity due to case mix from that due to beyond case-mix reasons.

stat.AP↗
arXiv2021

Robust Inference for Mediated Effects in Partially Linear Models

We consider mediated effects of an exposure, X on an outcome, Y, via a mediator, M, under no unmeasured confounding assumptions in the setting where models for the conditional expectation of the mediator and outcome are partially linear. We propose G-estimators for the direct and indirect effect and demonstrate consistent asymptotic normality for indirect effects when models for the conditional means of M, or X and Y are correctly specified, and for direct effects, when models for the conditional means of Y, or X and M are correct. This marks an improvement, in this particular setting, over previous `triple' robust methods, which do not assume partially linear mean models. Testing of the no-mediation hypothesis is inherently problematic due to the composite nature of the test (either X has no effect on M or M no effect on Y), leading to low power when both effect sizes are small. We use Generalized Methods of Moments (GMM) results to construct a new score testing framework, which includes as special cases the no-mediation and the no-direct-effect hypotheses. The proposed tests rely on an orthogonal estimation strategy for estimating nuisance parameters. Simulations show that the GMM based tests perform better in terms of power and small sample performance compared with traditional tests in the partially linear setting, with drastic improvement under model misspecification. New methods are illustrated in a mediation analysis of data from the COPERS trial, a randomized trial investigating the effect of a non-pharmacological intervention of patients suffering from chronic pain. An accompanying R package implementing these methods can be found at github.com/ohines/plmed.

stat.ME↗