Causal inference in longitudinal observational health data often requires the accurate estimation of treatment effects on time-to-event outcomes in the presence of time-varying covariates. To tackle this sequential treatment effect estimation problem, we have developed a causal dynamic survival (CDS) model that uses the potential outcomes framework with the recurrent sub-networks with random seed ensembles to estimate the difference in survival curves of its confidence interval. Using simulated survival datasets, the CDS model has shown good causal effect estimation performance across scenarios of sample dimension, event rate, confounding and overlapping. However, increasing the sample size is not effective to alleviate the adverse impact from high level of confounding. In two large clinical cohort studies, our model identified the expected conditional average treatment effect and detected individual effect heterogeneity over time and patient subgroups. CDS provides individualised absolute treatment effect estimations to improve clinical decisions.
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Modern applications of survival analysis increasingly involve time-dependent covariates. In healthcare settings, such covariates provide dynamic patient histories that can be used to assess health risks in realtime by tracking the hazard function. Hazard learning is thus particularly useful in healthcare analytics, and the open-source package BoXHED 1.0 provides the first implementation of a gradient boosted hazard estimator that is fully nonparametric. This paper introduces BoXHED 2.0, a quantum leap over BoXHED 1.0 in several ways. Crucially, BoXHED 2.0 can deal with survival data that goes far beyond right-censoring and it also supports recurring events. To our knowledge, this is the only nonparametric machine learning implementation that is able to do so. Another major improvement is that BoXHED 2.0 is orders of magnitude more scalable, due in part to a novel data preprocessing step that sidesteps the need for explicit quadrature when dealing with time-dependent covariates. BoXHED 2.0 supports the use of GPUs and multicore CPUs, and is available from GitHub: www.github.com/BoXHED.
Spatio-temporal processes in environmental applications are often assumed to follow a Gaussian model, possibly after some transformation. However, heterogeneity in space and time might have a pattern that will not be accommodated by transforming the data. In this scenario, modelling the variance laws is an appealing alternative. This work adds flexibility to the usual Multivariate Dynamic Gaussian model by defining the process as a scale mixture between a Gaussian and log-Gaussian processes. The scale is represented by a process varying smoothly over space and time which is allowed to depend on covariates. State-space equations define the dynamics over time for both mean and variance processes resulting infeasible inference and prediction. Analysis of artificial datasets show that the parameters are identifiable and simpler models are well recovered by the general proposed model. The analyses of two important environmental processes, maximum temperature and maximum ozone, illustrate the effectiveness of our proposal in improving the uncertainty quantification in the prediction of spatio-temporal processes.
This paper develops a general causal inference method for treatment effects models with noisily measured confounders. The key feature is that a large set of noisy measurements are linked with the underlying latent confounders through an unknown, possibly nonlinear factor structure. The main building block is a local principal subspace approximation procedure that combines $K$-nearest neighbors matching and principal component analysis. Estimators of many causal parameters, including average treatment effects and counterfactual distributions, are constructed based on doubly-robust score functions. Large-sample properties of these estimators are established, which only require relatively mild conditions on the principal subspace approximation. The results are illustrated with an empirical application studying the effect of political connections on stock returns of financial firms, and a Monte Carlo experiment. The main technical and methodological results regarding the general local principal subspace approximation method may be of independent interest.
Integrative analyses based on statistically relevant associations between genomics and a wealth of intermediary phenotypes (such as imaging) provide vital insights into their clinical relevance in terms of the disease mechanisms. Estimates for uncertainty in the resulting integrative models are however unreliable unless inference accounts for the selection of these associations with accuracy. In this article, we develop selection-aware Bayesian methods which: (i) counteract the impact of model selection bias through a "selection-aware posterior" in a flexible class of integrative Bayesian models post a selection of promising variables via $\ell_1$-regularized algorithms; (ii) strike an inevitable tradeoff between the quality of model selection and inferential power when the same dataset is used for both selection and uncertainty estimation. Central to our methodological development, a carefully constructed conditional likelihood function deployed with a reparameterization mapping provides notably tractable updates when gradient-based MCMC sampling is used for estimating uncertainties from the selection-aware posterior. Applying our methods to a radiogenomic analysis, we successfully recover several important gene pathways and estimate uncertainties for their associations with patient survival times.
Using observational data to estimate the effect of a treatment is a powerful tool for decision-making when randomized experiments are infeasible or costly. However, observational data often yields biased estimates of treatment effects, since treatment assignment can be confounded by unobserved variables. A remedy is offered by deconfounding methods that adjust for such unobserved confounders. In this paper, we develop the Sequential Deconfounder, a method that enables estimating individualized treatment effects over time in presence of unobserved confounders. This is the first deconfounding method that can be used in a general sequential setting (i.e., with one or more treatments assigned at each timestep). The Sequential Deconfounder uses a novel Gaussian process latent variable model to infer substitutes for the unobserved confounders, which are then used in conjunction with an outcome model to estimate treatment effects over time. We prove that using our method yields unbiased estimates of individualized treatment responses over time. Using simulated and real medical data, we demonstrate the efficacy of our method in deconfounding the estimation of treatment responses over time.
Survival analysis is a critical tool for the modelling of time-to-event data, such as life expectancy after a cancer diagnosis or optimal maintenance scheduling for complex machinery. However, current neural network models provide an imperfect solution for survival analysis as they either restrict the shape of the target probability distribution or restrict the estimation to pre-determined times. As a consequence, current survival neural networks lack the ability to estimate a generic function without prior knowledge of its structure. In this article, we present the metaparametric neural network framework that encompasses existing survival analysis methods and enables their extension to solve the aforementioned issues. This framework allows survival neural networks to satisfy the same independence of generic function estimation from the underlying data structure that characterizes their regression and classification counterparts. Further, we demonstrate the application of the metaparametric framework using both simulated and large real-world datasets and show that it outperforms the current state-of-the-art methods in (i) capturing nonlinearities, and (ii) identifying temporal patterns, leading to more accurate overall estimations whilst placing no restrictions on the underlying function structure.
Deep reinforcement learning (RL) algorithms are predominantly evaluated by comparing their relative performance on a large suite of tasks. Most published results on deep RL benchmarks compare point estimates of aggregate performance such as mean and median scores across tasks, ignoring the statistical uncertainty implied by the use of a finite number of training runs. Beginning with the Arcade Learning Environment (ALE), the shift towards computationally-demanding benchmarks has led to the practice of evaluating only a small number of runs per task, exacerbating the statistical uncertainty in point estimates. In this paper, we argue that reliable evaluation in the few run deep RL regime cannot ignore the uncertainty in results without running the risk of slowing down progress in the field. We illustrate this point using a case study on the Atari 100k benchmark, where we find substantial discrepancies between conclusions drawn from point estimates alone versus a more thorough statistical analysis. With the aim of increasing the field's confidence in reported results with a handful of runs, we advocate for reporting interval estimates of aggregate performance and propose performance profiles to account for the variability in results, as well as present more robust and efficient aggregate metrics, such as interquartile mean scores, to achieve small uncertainty in results. Using such statistical tools, we scrutinize performance evaluations of existing algorithms on other widely used RL benchmarks including the ALE, Procgen, and the DeepMind Control Suite, again revealing discrepancies in prior comparisons. Our findings call for a change in how we evaluate performance in deep RL, for which we present a more rigorous evaluation methodology, accompanied with an open-source library rliable, to prevent unreliable results from stagnating the field.
Synthetic control methods are commonly used to estimate the treatment effect on a single treated unit in panel data settings. A synthetic control (SC) is a weighted average of control units built to match the treated unit's pre-treatment outcome trajectory, with weights typically estimated by regressing pre-treatment outcomes of the treated unit to those of the control units. However, it has been established that such regression estimators can fail to be consistent. In this paper, we introduce a proximal causal inference framework to formalize identification and inference for both the SC weights and the treatment effect on the treated. We show that control units previously perceived as unusable can be repurposed to consistently estimate the SC weights. We also propose to view the difference in the post-treatment outcomes between the treated unit and the SC as a time series, which opens the door to a rich literature on time-series analysis for treatment effect estimation. We further extend the traditional linear model to accommodate general nonlinear models allowing for binary and count outcomes which are understudied in the SC literature. We illustrate our proposed methods with simulation studies and an application to evaluation of the 1990 German Reunification.
The Bayesian paradigm has the potential to solve core issues of deep neural networks such as poor calibration and data inefficiency. Alas, scaling Bayesian inference to large weight spaces often requires restrictive approximations. In this work, we show that it suffices to perform inference over a small subset of model weights in order to obtain accurate predictive posteriors. The other weights are kept as point estimates. This subnetwork inference framework enables us to use expressive, otherwise intractable, posterior approximations over such subsets. In particular, we implement subnetwork linearized Laplace: We first obtain a MAP estimate of all weights and then infer a full-covariance Gaussian posterior over a subnetwork. We propose a subnetwork selection strategy that aims to maximally preserve the model's predictive uncertainty. Empirically, our approach is effective compared to ensembles and less expressive posterior approximations over full networks.
A comprehensive artificial intelligence system needs to not only perceive the environment with different `senses' (e.g., seeing and hearing) but also infer the world's conditional (or even causal) relations and corresponding uncertainty. The past decade has seen major advances in many perception tasks such as visual object recognition and speech recognition using deep learning models. For higher-level inference, however, probabilistic graphical models with their Bayesian nature are still more powerful and flexible. In recent years, Bayesian deep learning has emerged as a unified probabilistic framework to tightly integrate deep learning and Bayesian models. In this general framework, the perception of text or images using deep learning can boost the performance of higher-level inference and in turn, the feedback from the inference process is able to enhance the perception of text or images. This survey provides a comprehensive introduction to Bayesian deep learning and reviews its recent applications on recommender systems, topic models, control, etc. Besides, we also discuss the relationship and differences between Bayesian deep learning and other related topics such as Bayesian treatment of neural networks.
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