Causal inference in high dimensions: A marriage between Bayesian modeling and good frequentist properties

Using joint models for longitudinal and time-to-event data to investigate the causal effect of salvage therapy after prostatectomy

Prostate cancer patients who undergo prostatectomy are closely monitored for recurrence and metastasis using routine prostate-specific antigen measurements. When prostate-specific antigen levels rise, salvage therapies are recommended in order to decrease the risk of metastasis. However, due to the side effects of these therapies and to avoid over-treatment, it is important to understand which patients and when to initiate these salvage therapies. In this work, we use the University of Michigan Prostatectomy Registry Data to tackle this question. Due to the observational nature of this data, we face the challenge that prostate-specific antigen is simultaneously a time-varying confounder and an intermediate variable for salvage therapy. We define different causal salvage therapy effects defined conditionally on different specifications of the longitudinal prostate-specific antigen history. We then illustrate how these effects can be estimated using the framework of joint models for longitudinal and time-to-event data. All proposed methodology is implemented in the freely-available R package JMbayes2.

Improved inference for doubly robust estimators of heterogeneous treatment effects

We propose a doubly robust approach to characterizing treatment effect heterogeneity in observational studies. We develop a frequentist inferential procedure that utilizes posterior distributions for both the propensity score and outcome regression models to provide valid inference on the conditional average treatment effect even when high-dimensional or nonparametric models are used. We show that our approach leads to conservative inference in finite samples or under model misspecification and provides a consistent variance estimator when both models are correctly specified. In simulations, we illustrate the utility of these results in difficult settings such as high-dimensional covariate spaces or highly flexible models for the propensity score and outcome regression. Lastly, we analyze environmental exposure data from NHANES to identify how the effects of these exposures vary by subject-level characteristics.

Bayesian causal inference: a critical review

This paper provides a critical review of the Bayesian perspective of causal inference based on the potential outcomes framework. We review the causal estimands, assignment mechanism, the general structure of Bayesian inference of causal effects and sensitivity analysis. We highlight issues that are unique to Bayesian causal inference, including the role of the propensity score, the definition of identifiability, the choice of priors in both low- and high-dimensional regimes. We point out the central role of covariate overlap and more generally the design stage in Bayesian causal inference. We extend the discussion to two complex assignment mechanisms: instrumental variable and time-varying treatments. We identify the strengths and weaknesses of the Bayesian approach to causal inference. Throughout, we illustrate the key concepts via examples. This article is part of the theme issue 'Bayesian inference: challenges, perspectives, and prospects'.

Estimating a Causal Exposure Response Function with a Continuous Error-Prone Exposure: A Study of Fine Particulate Matter and All-Cause Mortality

Numerous studies have examined the associations between long-term exposure to fine particulate matter (PM2.5) and adverse health outcomes. Recently, many of these studies have begun to employ high-resolution predicted PM2.5 concentrations, which are subject to measurement error. Previous approaches for exposure measurement error correction have either been applied in non-causal settings or have only considered a categorical exposure. Moreover, most procedures have failed to account for uncertainty induced by error correction when fitting an exposure-response function (ERF). To remedy these deficiencies, we develop a multiple imputation framework that combines regression calibration and Bayesian techniques to estimate a causal ERF. We demonstrate how the output of the measurement error correction steps can be seamlessly integrated into a Bayesian additive regression trees (BART) estimator of the causal ERF. We also demonstrate how locally-weighted smoothing of the posterior samples from BART can be used to create a more accurate ERF estimate. Our proposed approach also properly propagates the exposure measurement error uncertainty to yield accurate standard error estimates. We assess the robustness of our proposed approach in an extensive simulation study. We then apply our methodology to estimate the effects of PM2.5 on all-cause mortality among Medicare enrollees in New England from 2000-2012.

A reference-free R-learner for treatment recommendation

Assigning optimal treatments to individual patients based on their characteristics is the ultimate goal of precision medicine. Deriving evidence-based recommendations from observational data while considering the causal treatment effects and patient heterogeneity is a challenging task, especially in situations of multiple treatment options. Herein, we propose a reference-free R-learner based on a simplex algorithm for treatment recommendation. We showed through extensive simulation that the proposed method produced accurate recommendations that corresponded to optimal treatment outcomes, regardless of the reference group. We used the method to analyze data from the Systolic Blood Pressure Intervention Trial (SPRINT) and achieved recommendations consistent with the current clinical guidelines.

Evaluation of propensity score methods for causal inference with high-dimensional covariates

In recent work, researchers have paid considerable attention to the estimation of causal effects in observational studies with a large number of covariates, which makes the unconfoundedness assumption plausible. In this paper, we review propensity score (PS) methods developed in high-dimensional settings and broadly group them into model-based methods that extend models for prediction to causal inference and balance-based methods that combine covariate balancing constraints. We conducted systematic simulation experiments to evaluate these two types of methods, and studied whether the use of balancing constraints further improved estimation performance. Our comparison methods were post-double-selection (PDS), double-index PS (DiPS), outcome-adaptive LASSO (OAL), group LASSO and doubly robust estimation (GLiDeR), high-dimensional covariate balancing PS (hdCBPS), regularized calibrated estimators (RCAL) and approximate residual balancing method (balanceHD). For the four model-based methods, simulation studies showed that GLiDeR was the most stable approach, with high estimation accuracy and precision, followed by PDS, OAL and DiPS. For balance-based methods, hdCBPS performed similarly to GLiDeR in terms of accuracy, and outperformed balanceHD and RCAL. These findings imply that PS methods do not benefit appreciably from covariate balancing constraints in high-dimensional settings. In conclusion, we recommend the preferential use of GLiDeR and hdCBPS approaches for estimating causal effects in high-dimensional settings; however, further studies on the construction of valid confidence intervals are required.

Simulation-based estimators of analytically intractable causal effects

In causal inference problems, one is often tasked with estimating causal effects which are analytically intractable functionals of the data-generating mechanism. Relevant settings include estimating intention-to-treat effects in longitudinal problems with missing data or computing direct and indirect effects in mediation analysis. One approach to computing these effects is to use the g-formula implemented via Monte Carlo integration; when simulation-based methods such as the nonparametric bootstrap or Markov chain Monte Carlo are used for inference, Monte Carlo integration must be nested within an already computationally intensive algorithm. We develop a widely-applicable approach to accelerating this Monte Carlo integration step which greatly reduces the computational burden of existing g-computation algorithms. We refer to our method as accelerated g-computation (AGC). The algorithms we present are similar in spirit to multiple imputation, but require removing within-imputation variance from the standard error rather than adding it. We illustrate the use of AGC on a mediation analysis problem using a beta regression model and in a longitudinal clinical trial subject to nonignorable missingness using a Bayesian additive regression trees model.