Despite the recent progress in the field of causal inference, to date there is no agreed upon methodology to glean treatment effect estimation from observational data. The consequence on clinical practice is that, when lacking results from a randomized trial, medical personnel is left without guidance on what seems to be effective in a real-world scenario. This article proposes a pragmatic methodology to obtain preliminary but robust estimation of treatment effect from observational studies, to provide front-line clinicians with a degree of confidence in their treatment strategy. Our study design is applied to an open problem, the estimation of treatment effect of the proning maneuver on COVID-19 Intensive Care patients.
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In 2019, the World Health Organization identified dengue as one of the top ten global health threats. For the control of dengue, the Applying Wolbachia to Eliminate Dengue (AWED) study group conducted a cluster-randomized trial in Yogyakarta, Indonesia, and used a novel design, called the cluster-randomized test-negative design (CR-TND). This design can yield valid statistical inference with data collected by a passive surveillance system and thus has the advantage of cost-efficiency compared to traditional cluster-randomized trials. We investigate the statistical assumptions and properties of CR-TND under a randomization inference framework, which is known to be robust and efficient for small-sample problems. We find that, when the differential healthcare-seeking behavior comparing intervention and control varies across clusters (in contrast to the setting of Dufault and Jewell, 2020 where the differential healthcare-seeking behavior is constant across clusters), current analysis methods for CR-TND can be biased and have inflated type I error. We propose the log-contrast estimator that can eliminate such bias and improve precision by adjusting for covariates. Furthermore, we extend our methods to handle partial intervention compliance and a stepped-wedge design, both of which appear frequently in cluster-randomized trials. Finally, we demonstrate our results by simulation studies and re-analysis of the AWED study.
As COVID-19 pandemic progresses, severe flu seasons may happen alongside an increase in cases in cases and death of COVID-19, causing severe burdens on health care resources and public safety. A consequence of a twindemic may be a mixture of two different infections in the same person at the same time, "flurona". Admist the raising trend of "flurona", forecasting both influenza outbreaks and COVID-19 waves in a timely manner is more urgent than ever, as accurate joint real-time tracking of the twindemic aids health organizations and policymakers in adequate preparation and decision making. Under the current pandemic, state-of-art influenza and COVID-19 forecasting models carry valuable domain information but face shortcomings under current complex disease dynamics, such as similarities in symptoms and public healthcare seeking patterns of the two diseases. Inspired by the inner-connection between influenza and COVID-19 activities, we propose ARGOX-Joint-Ensemble which allows us to combine historical influenza and COVID-19 disease forecasting models to a new ensemble framework that handles scenarios where flu and COVID co-exist. Our framework is able to emphasize learning from COVID-related or influenza signals, through a winner-takes-all ensemble fashion. Moreover, our experiments demonstrate that our approach is successful in adapting past influenza forecasting models to the current pandemic, while improving upon previous COVID-19 forecasting models, by steadily outperforming alternative benchmark methods, and remaining competitive with publicly available models.
Epidemiologic studies and clinical trials with a survival outcome are often challenged by immortal time (IMT), a period of follow-up during which the survival outcome cannot occur because of the observed later treatment initiation. It has been well recognized that failing to properly accommodate IMT leads to biased estimation and misleading inference. Accordingly, a series of statistical methods have been developed, from the simplest by including or excluding IMT to various weightings and the more recent sequential methods. Our literature review suggests that the existing developments are often "scattered", and there is a lack of comprehensive review and direct comparison. To fill this knowledge gap and better introduce this important topic especially to biomedical researchers, we provide this review to comprehensively describe the available methods, discuss their advantages and disadvantages, and equally important, directly compare their performance via simulation and the analysis of the Stanford heart transplant data. The key observation is that the time-varying treatment modeling and sequential trial methods tend to provide unbiased estimation, while the other methods may result in substantial bias. We also provide an in-depth discussion on the interconnections with causal inference.
We consider continuous-time survival or more general event-history settings, where the aim is to infer the causal effect of a time-dependent treatment process. This is formalised as the effect on the outcome event of a (possibly hypothetical) intervention on the intensity of the treatment process, i.e. a stochastic intervention. To establish whether valid inference about the interventional situation can be drawn from typical observational, i.e. non-experimental, data we propose graphical rules indicating whether the observed information is sufficient to identify the desired causal effect by suitable re-weighting. In analogy to the well-known causal directed acyclic graphs, the corresponding dynamic graphs combine causal semantics with local independence models for multivariate counting processes. Importantly, we highlight that causal inference from censored data requires structural assumptions on the censoring process beyond the usual independent censoring assumption, which can be represented and verified graphically. Our results establish general non-parametric identifiability and do not rely on particular survival models. We illustrate our proposal with a data example on HPV-testing for cervical cancer screening, where the desired effect is estimated by re-weighted cumulative incidence curves.
Because it determines a center-outward ordering of observations in $\mathbb{R}^d$ with $d\geq 2$, the concept of statistical depth permits to define quantiles and ranks for multivariate data and use them for various statistical tasks (e.g. inference, hypothesis testing). Whereas many depth functions have been proposed \textit{ad-hoc} in the literature since the seminal contribution of \cite{Tukey75}, not all of them possess the properties desirable to emulate the notion of quantile function for univariate probability distributions. In this paper, we propose an extension of the \textit{integrated rank-weighted} statistical depth (IRW depth in abbreviated form) originally introduced in \cite{IRW}, modified in order to satisfy the property of \textit{affine-invariance}, fulfilling thus all the four key axioms listed in the nomenclature elaborated by \cite{ZuoS00a}. The variant we propose, referred to as the Affine-Invariant IRW depth (AI-IRW in short), involves the covariance/precision matrices of the (supposedly square integrable) $d$-dimensional random vector $X$ under study, in order to take into account the directions along which $X$ is most variable to assign a depth value to any point $x\in \mathbb{R}^d$. The accuracy of the sampling version of the AI-IRW depth is investigated from a nonasymptotic perspective. Namely, a concentration result for the statistical counterpart of the AI-IRW depth is proved. Beyond the theoretical analysis carried out, applications to anomaly detection are considered and numerical results are displayed, providing strong empirical evidence of the relevance of the depth function we propose here.
Missing data is a systemic problem in practical scenarios that causes noise and bias when estimating treatment effects. This makes treatment effect estimation from data with missingness a particularly tricky endeavour. A key reason for this is that standard assumptions on missingness are rendered insufficient due to the presence of an additional variable, treatment, besides the individual and the outcome. Having a treatment variable introduces additional complexity with respect to why some variables are missing that is not fully explored by previous work. In our work we identify a new missingness mechanism, which we term mixed confounded missingness (MCM), where some missingness determines treatment selection and other missingness is determined by treatment selection. Given MCM, we show that naively imputing all data leads to poor performing treatment effects models, as the act of imputation effectively removes information necessary to provide unbiased estimates. However, no imputation at all also leads to biased estimates, as missingness determined by treatment divides the population in distinct subpopulations, where estimates across these populations will be biased. Our solution is selective imputation, where we use insights from MCM to inform precisely which variables should be imputed and which should not. We empirically demonstrate how various learners benefit from selective imputation compared to other solutions for missing data.
In this paper, we develop a general framework based on the Transformer architecture to address a variety of challenging treatment effect estimation (TEE) problems. Our methods are applicable both when covariates are tabular and when they consist of sequences (e.g., in text), and can handle discrete, continuous, structured, or dosage-associated treatments. While Transformers have already emerged as dominant methods for diverse domains, including natural language and computer vision, our experiments with Transformers as Treatment Effect Estimators (TransTEE) demonstrate that these inductive biases are also effective on the sorts of estimation problems and datasets that arise in research aimed at estimating causal effects. Moreover, we propose a propensity score network that is trained with TransTEE in an adversarial manner to promote independence between covariates and treatments to further address selection bias. Through extensive experiments, we show that TransTEE significantly outperforms competitive baselines with greater parameter efficiency over a wide range of benchmarks and settings.
Causal inference methods can be applied to estimate the effect of a point exposure or treatment on an outcome of interest using data from observational studies. When the outcome of interest is a count, the estimand is often the causal mean ratio, i.e., the ratio of the counterfactual mean count under exposure to the counterfactual mean count under no exposure. This paper considers estimators of the causal mean ratio based on inverse probability of treatment weights, the parametric g-formula, and doubly robust estimation, each of which can account for overdispersion, zero-inflation, and heaping in the measured outcome. Methods are compared in simulations and are applied to data from the Women's Interagency HIV Study to estimate the effect of incarceration in the past six months on two count outcomes in the subsequent six months: the number of sexual partners and the number of cigarettes smoked per day.
The focus of disentanglement approaches has been on identifying independent factors of variation in data. However, the causal variables underlying real-world observations are often not statistically independent. In this work, we bridge the gap to real-world scenarios by analyzing the behavior of the most prominent disentanglement approaches on correlated data in a large-scale empirical study (including 4260 models). We show and quantify that systematically induced correlations in the dataset are being learned and reflected in the latent representations, which has implications for downstream applications of disentanglement such as fairness. We also demonstrate how to resolve these latent correlations, either using weak supervision during training or by post-hoc correcting a pre-trained model with a small number of labels.
Optimal transport distances have found many applications in machine learning for their capacity to compare non-parametric probability distributions. Yet their algorithmic complexity generally prevents their direct use on large scale datasets. Among the possible strategies to alleviate this issue, practitioners can rely on computing estimates of these distances over subsets of data, {\em i.e.} minibatches. While computationally appealing, we highlight in this paper some limits of this strategy, arguing it can lead to undesirable smoothing effects. As an alternative, we suggest that the same minibatch strategy coupled with unbalanced optimal transport can yield more robust behavior. We discuss the associated theoretical properties, such as unbiased estimators, existence of gradients and concentration bounds. Our experimental study shows that in challenging problems associated to domain adaptation, the use of unbalanced optimal transport leads to significantly better results, competing with or surpassing recent baselines.
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