A practical introduction to Bayesian estimation of causal effects: Parametric and nonparametric approaches

Estimating causal effects from panel data with dynamic multivariate panel models

Panel data are ubiquitous in scientific fields such as social sciences. Various modeling approaches have been presented for observational causal inference based on such data. Existing approaches typically impose restrictive assumptions on the data-generating process such as Gaussian responses or time-invariant effects, or they can only consider short-term causal effects. To surmount these restrictions, we present the dynamic multivariate panel model (DMPM) that supports time-varying, time-invariant, and individual-specific effects, multiple responses across a wide variety of distributions, and arbitrary dependency structures of lagged responses of any order. We formally demonstrate how DMPM facilitates causal inference within the structural causal modeling framework and we take a Bayesian approach for the estimation of the posterior distributions of the model parameters and causal effects of interest. We demonstrate the use of DMPM by applying the approach to both real and synthetic data.

Covariate adjustment in Bayesian adaptive randomized controlled trials

In conventional randomized controlled trials, adjustment for baseline values of covariates known to be at least moderately associated with the outcome increases the power of the trial. Recent work has shown a particular benefit for more flexible frequentist designs, such as information adaptive and adaptive multi-arm designs. However, covariate adjustment has not been characterized within the more flexible Bayesian adaptive designs, despite their growing popularity. We focus on a subclass of these which allow for early stopping at an interim analysis given evidence of treatment superiority. We consider both collapsible and non-collapsible estimands and show how to obtain posterior samples of marginal estimands from adjusted analyses. We describe several estimands for three common outcome types. We perform a simulation study to assess the impact of covariate adjustment using a variety of adjustment models in several different scenarios. This is followed by a real-world application of the compared approaches to a COVID-19 trial with a binary endpoint. For all scenarios, it is shown that covariate adjustment increases power and the probability of stopping the trials early, and decreases the expected sample sizes as compared to unadjusted analyses.

Bayesian inference for a principal stratum estimand on recurrent events truncated by death

Recurrent events are often important endpoints in randomized clinical trials. For example, the number of recurrent disease-related hospitalizations may be considered as a clinically meaningful endpoint in cardiovascular studies. In some settings, the recurrent event process may be terminated by an event such as death, which makes it more challenging to define and estimate a causal treatment effect on recurrent event endpoints. In this paper, we focus on the principal stratum estimand, where the treatment effect of interest on recurrent events is defined among subjects who would be alive regardless of the assigned treatment. For the estimation of the principal stratum effect in randomized clinical trials, we propose a Bayesian approach based on a joint model of the recurrent event and death processes with a frailty term accounting for within-subject correlation. We also present Bayesian posterior predictive check procedures for assessing the model fit. The proposed approaches are demonstrated in the randomized Phase III chronic heart failure trial PARAGON-HF (NCT01920711).

BayesGmed: An R-package for Bayesian causal mediation analysis

BACKGROUND

The past decade has seen an explosion of research in causal mediation analysis. However, most analytic tools developed so far rely on frequentist methods which may not be robust in the case of small sample sizes. In this paper, we propose a Bayesian approach for causal mediation analysis based on Bayesian g-formula, which will overcome the limitations of the frequentist methods.

METHODS

We created BayesGmed, an R-package for fitting Bayesian mediation models in R. The application of the methodology (and software tool) is demonstrated by a secondary analysis of data collected as part of the MUSICIAN study, a randomised controlled trial of remotely delivered cognitive behavioural therapy (tCBT) for people with chronic pain. We tested the hypothesis that the effect of tCBT would be mediated by improvements in active coping, passive coping, fear of movement and sleep problems. We then demonstrate the use of informative priors to conduct probabilistic sensitivity analysis around violations of causal identification assumptions.

RESULT

The analysis of MUSICIAN data shows that tCBT has better-improved patients' self-perceived change in health status compared to treatment as usual (TAU). The adjusted log-odds of tCBT compared to TAU range from 1.491 (95% CI: 0.452-2.612) when adjusted for sleep problems to 2.264 (95% CI: 1.063-3.610) when adjusted for fear of movement. Higher scores of fear of movement (log-odds, -0.141 [95% CI: -0.245, -0.048]), passive coping (log-odds, -0.217 [95% CI: -0.351, -0.104]), and sleep problem (log-odds, -0.179 [95% CI: -0.291, -0.078]) leads to lower odds of a positive self-perceived change in health status. The result of BayesGmed, however, shows that none of the mediated effects are statistically significant. We compared BayesGmed with the mediation R- package, and the results were comparable. Finally, our sensitivity analysis using the BayesGmed tool shows that the direct and total effect of tCBT persists even for a large departure in the assumption of no unmeasured confounding.

CONCLUSION

This paper comprehensively overviews causal mediation analysis and provides an open-source software package to fit Bayesian causal mediation models.

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'.

Socio-economic and ethnic disparities in childhood cancer survival, Yorkshire, UK

BACKGROUND

Establishing the existence of health inequalities remains a high research and policy agenda item in the United Kingdom. We describe ethnic and socio-economic differences in paediatric cancer survival, focusing specifically on the extent to which disparities have changed over a 20-year period.

METHODS

Cancer registration data for 2674 children (0-14 years) in Yorkshire were analysed. Five-year survival estimates by ethnic group (south Asian/non-south Asian) and Townsend deprivation fifths (I-V) were compared over time (1997-2016) for leukaemia, lymphoma, central nervous system (CNS) and other solid tumours. Hazard ratios (HR: 95% CI) from adjusted Cox models quantified the joint effect of ethnicity and deprivation on mortality risk over time, framed through causal interpretation of the deprivation coefficient.

RESULTS

Increasing deprivation was associated with significantly higher risk of death for children with leukaemia (1.11 (1.03-1.20)) and all cancers between 1997 and 2001. While we observed a trend towards reducing differences in survival over time in this group, a contrasting trend was observed for CNS tumours whereby sizeable variation in outcome remained for cases diagnosed until 2012. South Asian children with lymphoma had a 15% reduced chance of surviving at least 5 years compared to non-south Asian, across the study period.

DISCUSSION

Even in the United Kingdom, with a universally accessible healthcare system, socio-economic and ethnic disparities in childhood cancer survival exist. Findings should inform where resources should be directed to provide all children with an equitable survival outcome following a cancer diagnosis.

Oxygenation thresholds for invasive ventilation in hypoxemic respiratory failure: a target trial emulation in two cohorts

BACKGROUND

The optimal thresholds for the initiation of invasive ventilation in patients with hypoxemic respiratory failure are unknown. Using the saturation-to-inspired oxygen ratio (SF), we compared lower versus higher hypoxemia severity thresholds for initiating invasive ventilation.

METHODS

This target trial emulation included patients from the Medical Information Mart for Intensive Care (MIMIC-IV, 2008-2019) and the Amsterdam University Medical Centers (AmsterdamUMCdb, 2003-2016) databases admitted to intensive care and receiving inspired oxygen fraction ≥ 0.4 via non-rebreather mask, noninvasive ventilation, or high-flow nasal cannula. We compared the effect of using invasive ventilation initiation thresholds of SF < 110, < 98, and < 88 on 28-day mortality. MIMIC-IV was used for the primary analysis and AmsterdamUMCdb for the secondary analysis. We obtained posterior means and 95% credible intervals (CrI) with nonparametric Bayesian G-computation.

RESULTS

We studied 3,357 patients in the primary analysis. For invasive ventilation initiation thresholds SF < 110, SF < 98, and SF < 88, the predicted 28-day probabilities of invasive ventilation were 72%, 47%, and 19%. Predicted 28-day mortality was lowest with threshold SF < 110 (22.2%, CrI 19.2 to 25.0), compared to SF < 98 (absolute risk increase 1.6%, CrI 0.6 to 2.6) or SF < 88 (absolute risk increase 3.5%, CrI 1.4 to 5.4). In the secondary analysis (1,279 patients), the predicted 28-day probability of invasive ventilation was 50% for initiation threshold SF < 110, 28% for SF < 98, and 19% for SF < 88. In contrast with the primary analysis, predicted mortality was highest with threshold SF < 110 (14.6%, CrI 7.7 to 22.3), compared to SF < 98 (absolute risk decrease 0.5%, CrI 0.0 to 0.9) or SF < 88 (absolute risk decrease 1.9%, CrI 0.9 to 2.8).

CONCLUSION

Initiating invasive ventilation at lower hypoxemia severity will increase the rate of invasive ventilation, but this can either increase or decrease the expected mortality, with the direction of effect likely depending on baseline mortality risk and clinical context.

An introduction to causal inference for pharmacometricians

As formal causal inference begins to play a greater role in disciplines that intersect with pharmacometrics, such as biostatistics, epidemiology, and artificial intelligence/machine learning, pharmacometricians may increasingly benefit from a basic fluency in foundational causal inference concepts. This tutorial seeks to orient pharmacometricians to three such fundamental concepts: potential outcomes, g-formula, and directed acyclic graphs (DAGs).

A Causal Framework for Making Individualized Treatment Decisions in Oncology

Simple Summary

Physicians routinely make individualized treatment decisions by accounting for the joint effects of patient prognostic covariates and treatments on clinical outcomes. Ideally, this is performed using historical randomized clinical trial (RCT) data. Randomization ensures that unbiased estimates of causal treatment effect parameters can be obtained from the historical RCT data and used to predict each new patient’s outcome based on the joint effect of their baseline covariates and each treatment being considered. However, this process becomes problematic if a patient seen in the clinic is very different from the patients who were enrolled in the RCT. That is, if a new patient does not satisfy the entry criteria of the RCT, then the patient does not belong to the population represented by the patients who were studied in the RCT. In such settings, it still may be possible to utilize the RCT data to help choose a new patient’s treatment. This may be achieved by combining the RCT data with data from other clinical trials, or possibly preclinical experiments, and using the combined dataset to predict the patient’s expected outcome for each treatment being considered. In such settings, combining data from multiple sources in a way that is statistically reliable is not entirely straightforward, and correctly identifying and estimating the effects of treatments and patient covariates on clinical outcomes can be complex. Causal diagrams provide a rational basis to guide this process. The first step is to construct a causal diagram that reflects the plausible relationships between treatment variables, patient covariates, and clinical outcomes. If the diagram is correct, it can be used to determine what additional data may be needed, how to combine data from multiple sources, how to formulate a statistical model for clinical outcomes as a function of treatment and covariates, and how to compute an unbiased treatment effect estimate for each new patient. We use adjuvant therapy of renal cell carcinoma to illustrate how causal diagrams may be used to guide these steps.

Abstract

We discuss how causal diagrams can be used by clinicians to make better individualized treatment decisions. Causal diagrams can distinguish between settings where clinical decisions can rely on a conventional additive regression model fit to data from a historical randomized clinical trial (RCT) to estimate treatment effects and settings where a different approach is needed. This may be because a new patient does not meet the RCT’s entry criteria, or a treatment’s effect is modified by biomarkers or other variables that act as mediators between treatment and outcome. In some settings, the problem can be addressed simply by including treatment–covariate interaction terms in the statistical regression model used to analyze the RCT dataset. However, if the RCT entry criteria exclude a new patient seen in the clinic, it may be necessary to combine the RCT data with external data from other RCTs, single-arm trials, or preclinical experiments evaluating biological treatment effects. For example, external data may show that treatment effects differ between histological subgroups not recorded in an RCT. A causal diagram may be used to decide whether external observational or experimental data should be obtained and combined with RCT data to compute statistical estimates for making individualized treatment decisions. We use adjuvant treatment of renal cell carcinoma as our motivating example to illustrate how to construct causal diagrams and apply them to guide clinical decisions.

A Causal Framework for Cross-Cultural Generalizability

Behavioral researchers increasingly recognize the need for more diverse samples that capture the breadth of human experience. Current attempts to establish generalizability across populations focus on threats to validity, constraints on generalization, and the accumulation of large, cross-cultural data sets. But for continued progress, we also require a framework that lets us determine which inferences can be drawn and how to make informative cross-cultural comparisons. We describe a generative causal-modeling framework and outline simple graphical criteria to derive analytic strategies and implied generalizations. Using both simulated and real data, we demonstrate how to project and compare estimates across populations and further show how to formally represent measurement equivalence or inequivalence across societies. We conclude with a discussion of how a formal framework for generalizability can assist researchers in designing more informative cross-cultural studies and thus provides a more solid foundation for cumulative and generalizable behavioral research.