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Publications and source records attributed to Stijn Vansteelandt.
Systematic reviews and meta-analyses of mediation studies are increasingly being implemented in practice. Nonetheless, the methodology for conducting such review and analysis is still in a development phase, with much room for improvement. In this paper, we highlight and discuss challenges that investigators face in mediation systematic reviews and meta-analyses, then propose ways of accommodating these in practice.
Inferring the causal effect of a non-randomly assigned exposure on an outcome requires adjusting for common causes of the exposure and outcome to avoid biased conclusions. Notwithstanding the efforts investigators routinely make to measure and adjust for such common causes (or confounders), some confounders typically remain unmeasured, raising the prospect of biased inference in observational studies. Therefore, it is crucial that investigators can practically assess their substantive conclusions' relative (in)sensitivity to potential unmeasured confounding. In this article, we propose a sensitivity analysis strategy that is informed by the stability of the exposure effect over different, well-chosen subsets of the measured confounders. The proposal entails first approximating the process for recording confounders to learn about how the effect is potentially affected by varying amounts of unmeasured confounding, then extrapolating to the effect had hypothetical unmeasured confounders been additionally adjusted for. A large set of measured confounders can thus be exploited to provide insight into the likely presence of unmeasured confounding bias, albeit under an assumption about how data on the confounders are recorded. The proposal's ability to reveal the true effect and ensure valid inference after extrapolation is empirically compared with existing methods using simulation studies. We demonstrate the procedure using two different publicly available datasets commonly used for causal inference.
Inferring the causal effect of a treatment on an outcome in an observational study requires adjusting for observed baseline confounders to avoid bias. However, adjusting for all observed baseline covariates, when only a subset are confounders of the effect of interest, is known to yield potentially inefficient and unstable estimators of the treatment effect. Furthermore, it raises the risk of finite-sample bias and bias due to model misspecification. For these stated reasons, confounder (or covariate) selection is commonly used to determine a subset of the available covariates that is sufficient for confounding adjustment. In this article, we propose a confounder selection strategy that focuses on stable estimation of the treatment effect. In particular, when the propensity score model already includes covariates that are sufficient to adjust for confounding, then the addition of covariates that are associated with either treatment or outcome alone, but not both, should not systematically change the effect estimator. The proposal, therefore, entails first prioritizing covariates for inclusion in the propensity score model, then using a change-in-estimate approach to select the smallest adjustment set that yields a stable effect estimate. The ability of the proposal to correctly select confounders, and to ensure valid inference of the treatment effect following data-driven covariate selection, is assessed empirically and compared with existing methods using simulation studies. We demonstrate the procedure using three different publicly available datasets commonly used for causal inference.
Decomposing an exposure effect on an outcome into separate natural indirect effects through multiple mediators requires strict assumptions, such as correctly postulating the causal structure of the mediators, and no unmeasured confounding among the mediators. In contrast, interventional indirect effects for multiple mediators can be identified even when - as often - the mediators either have an unknown causal structure, or share unmeasured common causes, or both. Existing estimation methods for interventional indirect effects require calculating each distinct indirect effect in turn. This can quickly become unwieldy or unfeasible, especially when investigating indirect effect measures that may be modified by observed baseline characteristics. In this article, we introduce simplified estimation procedures for such heterogeneous interventional indirect effects using interventional effect models. Interventional effect models are a class of marginal structural models that encode the interventional indirect effects as causal model parameters, thus readily permitting effect modification by baseline covariates using (statistical) interaction terms. The mediators and outcome can be continuous or noncontinuous. We propose two estimation procedures: one using inverse weighting by the counterfactual mediator density or mass functions, and another using Monte Carlo integration. The former has the advantage of not requiring an outcome model, but is susceptible to finite sample biases due to highly variable weights. The latter has the advantage of consistent estimation under a correctly specified (parametric) outcome model, but is susceptible to biases due to extrapolation.
The interpretation of randomised clinical trial results is often complicated by intercurrent events. For instance, rescue medication is sometimes given to patients in response to worsening of their disease, either in addition to the randomised treatment or in its place. The use of such medication complicates the interpretation of the intention-to-treat analysis. In view of this, we propose a novel estimand defined as the intention-to-treat effect that would have been observed, had patients on the active arm been switched to rescue medication if and only if they would have been switched when randomised to control. This enables us to disentangle the treatment effect from the effect of rescue medication on a patient's outcome, while avoiding the strong extrapolations that are typically needed when inferring what the intention-to-treat effect would have been in the absence of rescue medication. We develop an inverse probability weighting method to estimate this estimand under specific untestable assumptions, in view of which we propose a sensitivity analysis. We use the method for the analysis of a clinical trial conducted by Janssen Pharmaceuticals, in which chronically ill patients can switch to rescue medication for ethical reasons. Monte Carlo simulations confirm that the proposed estimator is unbiased in moderate sample sizes.
Motivated by a clinical trial conducted by Janssen Pharmaceuticals in which a flexible dosing regimen is compared to placebo, we evaluate how switchers in the treatment arm (i.e., patients who were switched to the higher dose) would have fared had they been kept on the low dose. This in order to understand whether flexible dosing is potentially beneficial for them. Simply comparing these patients' responses with those of patients who stayed on the low dose is unsatisfactory because the latter patients are usually in a better health condition. Because the available information in the considered trial is too scarce to enable a reliable adjustment, we will instead transport data from a fixed dosing trial that has been conducted concurrently on the same target, albeit not in an identical patient population. In particular, we will propose an estimator which relies on an outcome model and a propensity score model for the association between study and patient characteristics. The proposed estimator is asymptotically unbiased if at least one of both models is correctly specified, and efficient (under the model defined by the restrictions on the propensity score) when both models are correctly specified. We show that the proposed method for using results from an external study is generically applicable in studies where a classical confounding adjustment is not possible due to positivity violation (e.g., studies where switching takes place in a deterministic manner). Monte Carlo simulations and application to the motivating study demonstrate adequate performance.
The analysis of randomized trials with time-to-event endpoints is nearly always plagued by the problem of censoring. As the censoring mechanism is usually unknown, analyses typically employ the assumption of non-informative censoring. While this assumption usually becomes more plausible as more baseline covariates are being adjusted for, such adjustment also raises concerns. Pre-specification of which covariates will be adjusted for (and how) is difficult, thus prompting the use of data-driven variable selection procedures, which may impede valid inferences to be drawn. The adjustment for covariates moreover adds concerns about model misspecification, and the fact that each change in adjustment set, also changes the censoring assumption and the treatment effect estimand. In this paper, we discuss these concerns and propose a simple variable selection strategy that aims to produce a valid test of the null in large samples. The proposal can be implemented using off-the-shelf software for (penalized) Cox regression, and is empirically found to work well in simulation studies and real data analyses.
This proposal is motivated by an analysis of the English Longitudinal Study of Ageing (ELSA), which aims to investigate the role of loneliness in explaining the negative impact of hearing loss on dementia. The methodological challenges that complicate this mediation analysis include the use of a time-to-event endpoint subject to competing risks, as well as the presence of feedback relationships between the mediator and confounders that are both repeatedly measured over time. To account for these challenges, we introduce natural effect proportional (cause-specific) hazard models. These extend marginal structural proportional (cause-specific) hazard models to enable effect decomposition. We show that under certain causal assumptions, the path-specific direct and indirect effects indexing this model are identifiable from the observed data. We next propose an inverse probability weighting approach to estimate these effects. On the ELSA data, this approach reveals little evidence that the total efect of hearing loss on dementia is mediated through the feeling of loneliness, with a non-statistically significant indirect effect equal to 1.012 (hazard ratio (HR) scale; 95% confidence interval (CI) 0.986 to 1.053).
After variable selection, standard inferential procedures for regression parameters may not be uniformly valid; there is no finite-sample size at which a standard test is guaranteed to approximately attain its nominal size. This problem is exacerbated in high-dimensional settings, where variable selection becomes unavoidable. This has prompted a flurry of activity in developing uniformly valid hypothesis tests for a low-dimensional regression parameter (e.g. the causal effect of an exposure A on an outcome Y) in high-dimensional models. So far there has been limited focus on model misspecification, although this is inevitable in high-dimensional settings. We propose tests of the null that are uniformly valid under sparsity conditions weaker than those typically invoked in the literature, assuming working models for the exposure and outcome are both correctly specified. When one of the models is misspecified, by amending the procedure for estimating the nuisance parameters, our tests continue to be valid; hence they are doubly robust. Our proposals are straightforward to implement using existing software for penalized maximum likelihood estimation and do not require sample-splitting. We illustrate them in simulations and an analysis of data obtained from the Ghent University Intensive Care Unit.
Inference for the parameters indexing generalised linear models is routinely based on the assumption that the model is correct and a priori specified. This is unsatisfactory because the chosen model is usually the result of a data-adaptive model selection process, which may induce excess uncertainty that is not usually acknowledged. Moreover, the assumptions encoded in the chosen model rarely represent some a priori known, ground truth, making standard inferences prone to bias, but also failing to give a pure reflection of the information that is contained in the data. Inspired by developments on assumption-free inference for so-called projection parameters, we here propose novel nonparametric definitions of main effect estimands and effect modification estimands. These reduce to standard main effect and effect modification parameters in generalised linear models when these models are correctly specified, but have the advantage that they continue to capture respectively the primary (conditional) association between two variables, or the degree to which two variables interact (in a statistical sense) in their effect on outcome, even when these models are misspecified. We achieve an assumption-lean inference for these estimands (and thus for the underlying regression parameters) by deriving their influence curve under the nonparametric model and invoking flexible data-adaptive (e.g., machine learning) procedures.
With multiple potential mediators on the causal pathway from a treatment to an outcome, we consider the problem of decomposing the effects along multiple possible causal path(s) through each distinct mediator. Under Pearl's path-specific effects framework (Pearl, 2001; Avin et al., 2005), such fine-grained decompositions necessitate stringent assumptions, such as correctly specifying the causal structure among the mediators, and there being no unobserved confounding among the mediators. In contrast, interventional direct and indirect effects for multiple mediators (Vansteelandt and Daniel, 2017) can be identified under much weaker conditions, while providing scientifically relevant causal interpretations. Nonetheless, current estimation approaches require (correctly) specifying a model for the joint mediator distribution, which can be difficult when there is a high-dimensional set of possibly continuous and non-continuous mediators. In this article, we avoid the need to model this distribution, by developing a definition of interventional effects previously suggested by VanderWeele and Tchetgen Tchetgen (2017) for longitudinal mediation. We propose a novel estimation strategy that uses non-parametric estimates of the (counterfactual) mediator distributions. Non-continuous outcomes can be accommodated using non-linear outcome models. Estimation proceeds via Monte Carlo integration. The procedure is illustrated using publicly available genomic data (Huang and Pan, 2016) to assess the causal effect of a microRNA expression on the three-month mortality of brain cancer patients that is potentially mediated by expression values of multiple genes.
Observational longitudinal data on treatments and covariates are increasingly used to investigate treatment effects, but are often subject to time-dependent confounding. Marginal structural models (MSMs), estimated using inverse probability of treatment weighting or the g-formula, are popular for handling this problem. With increasing development of advanced causal inference methods, it is important to be able to assess their performance in different scenarios to guide their application. Simulation studies are a key tool for this, but their use to evaluate causal inference methods has been limited. This paper focuses on the use of simulations for evaluations involving MSMs in studies with a time-to-event outcome. In a simulation, it is important to be able to generate the data in such a way that the correct form of any models to be fitted to those data is known. However, this is not straightforward in the longitudinal setting because it is natural for data to be generated in a sequential conditional manner, whereas MSMs involve fitting marginal rather than conditional hazard models. We provide general results that enable the form of the correctly-specified MSM to be derived based on a conditional data generating procedure, and show how the results can be applied when the conditional hazard model is an Aalen additive hazard or Cox model. Using conditional additive hazard models is advantageous because they imply additive MSMs that can be fitted using standard software. We describe and illustrate a simulation algorithm. Our results will help researchers to effectively evaluate causal inference methods via simulation.
Mediation analysis is concerned with the decomposition of the total effect of an exposure on an outcome into the indirect effect through a given mediator, and the remaining direct effect. This is ideally done using longitudinal measurements of the mediator, as these capture the mediator process more finely. However, longitudinal measurements pose challenges for mediation analysis. This is because the mediators and outcomes measured at a given time-point can act as confounders for the association between mediators and outcomes at a later time-point; these confounders are themselves affected by the prior exposure and outcome. Such post-treatment confounding cannot be dealt with using standard methods (e.g. generalized estimating equations). Analysis is further complicated by the need for so-called cross-world counterfactuals to decompose the total effect. This article addresses these challenges. In particular, we introduce so-called natural effect models, which parameterize the direct and indirect effect of a baseline exposure w.r.t. a longitudinal mediator and outcome. These can be viewed as a generalization of marginal structural models to enable effect decomposition. We introduce inverse probability weighting techniques for fitting these models, adjusting for (measured) time-varying confounding of the mediator-outcome association. Application of this methodology uses data from the Millennium Cohort Study, UK.
Conditional power calculations are frequently used to guide the decision whether or not to stop a trial for futility or to modify planned sample size. These ignore the information in short-term endpoints and baseline covariates, and thereby do not make fully efficient use of the information in the data. We therefore propose an interim decision procedure based on the conditional power approach which exploits the information contained in baseline covariates and short-term outcomes. We will realise this by considering the estimation of the treatment effect at the interim analysis as a missing data problem. This problem is addressed by employing specific prediction models for the long-term endpoint which enable the incorporation of baseline covariates and multiple short-term endpoints. We show that the proposed procedure leads to an efficiency gain and a reduced sample size, without compromising the Type I error rate of the procedure, even when the adopted prediction models are misspecified. In particular, implementing our proposal in the conditional power approach allows earlier decisions relative to standard approaches, whilst controlling the probability of an incorrect decision. This time gain results in a lower expected number of recruited patients in case of stopping for futility, such that fewer patients receive the futile regimen. We explain how these methods can be used in adaptive designs with unblinded sample size reassessment based on the inverse normal $p$-value combination method to control type I error. We support the proposal by Monte Carlo simulations based on data from a real clinical trial.
Eliminating the effect of confounding in observational studies typically involves fitting a model for an outcome adjusted for covariates. When, as often, these covariates are high-dimensional, this necessitates the use of sparse estimators such as the Lasso, or other regularisation approaches. Naiive use of such estimators yields confidence intervals for the conditional treatment effect parameter that are not uniformly valid. Moreover, as the number of covariates grows with sample size, correctly specifying a model for the outcome is non-trivial. In this work, we deal with both of these concerns simultaneously, delivering confidence intervals for conditional treatment effects that are uniformly valid, regardless of whether the outcome model is correct. This is done by incorporating an additional model for the treatment-selection mechanism. When both models are correctly specified, we can weaken the standard conditions on model sparsity. Our procedure extends to multivariate treatment effect parameters and complex longitudinal settings.
The hazard ratio is one of the most commonly reported measures of treatment effect in randomised trials, yet the source of much misinterpretation. This point was made clear by (Hernan, 2010) in commentary, which emphasised that the hazard ratio contrasts populations of treated and untreated individuals who survived a given period of time, populations that will typically fail to be comparable - even in a randomised trial - as a result of different pressures or intensities acting on both populations. The commentary has been very influential, but also a source of surprise and confusion. In this note, we aim to provide more insight into the subtle interpretation of hazard ratios and differences, by investigating in particular what can be learned about treatment effect from the hazard ratio becoming 1 after a certain period of time. Throughout, we will focus on the analysis of randomised experiments, but our results have immediate implications for the interpretation of hazard ratios in observational studies.
Mediation analysis seeks to infer how much of the effect of an exposure on an outcome can be attributed to specific pathways via intermediate variables or mediators. This requires identification of so-called path-specific effects. These express how a change in exposure affects those intermediate variables (along certain pathways), and how the resulting changes in those variables in turn affect the outcome (along subsequent pathways). However, unlike identification of total effects, adjustment for confounding is insufficient for identification of path-specific effects because their magnitude is also determined by the extent to which individuals who experience large exposure effects on the mediator, tend to experience relatively small or large mediator effects on the outcome. This chapter therefore provides an accessible review of identification strategies under general nonparametric structural equation models (with possibly unmeasured variables), which rule out certain such dependencies. In particular, it is shown which path-specific effects can be identified under such models, and how this can be done.
Time-to-event analyses are often plagued by both -- possibly unmeasured -- confounding and competing risks. To deal with the former, the use of instrumental variables for effect estimation is rapidly gaining ground. We show how to make use of such variables in competing risk analyses. In particular, we show how to infer the effect of an arbitrary exposure on cause-specific hazard functions under a semi-parametric model that imposes relatively weak restrictions on the observed data distribution. The proposed approach is flexible accommodating exposures and instrumental variables of arbitrary type, and enables covariate adjustment. It makes use of closed-form estimators that can be recursively calculated, and is shown to perform well in simulation studies. We also demonstrates its use in an application on the effect of mammography screening on the risk of dying from breast cancer