A flexible approach for causal inference with multiple treatments and clustered survival outcomes

Abstract

When drawing causal inferences about the effects of multiple treatments on clustered survival outcomes using observational data, we need to address implications of the multilevel data structure, multiple treatments, censoring, and unmeasured confounding for causal analyses. Few off-the-shelf causal inference tools are available to simultaneously tackle these issues. We develop a flexible random-intercept accelerated failure time model, in which we use Bayesian additive regression trees to capture arbitrarily complex relationships between censored survival times and pre-treatment covariates and use the random intercepts to capture cluster-specific main effects. We develop an efficient Markov chain Monte Carlo algorithm to draw posterior inferences about the population survival effects of multiple treatments and examine the variability in cluster-level effects. We further propose an interpretable sensitivity analysis approach to evaluate the sensitivity of drawn causal inferences about treatment effect to the potential magnitude of departure from the causal assumption of no unmeasured confounding. Expansive simulations empirically validate and demonstrate good practical operating characteristics of our proposed methods. Applying the proposed methods to a dataset on older high-risk localized prostate cancer patients drawn from the National Cancer Database, we evaluate the comparative effects of three treatment approaches on patient survival, and assess the ramifications of potential unmeasured confounding.

A Flexible Approach for Assessing Heterogeneity of Causal Treatment Effects on Patient Survival Using Large Datasets with Clustered Observations

“…We first used simulated data to evaluate the proposed method. An expansive and representative simulation was conducted following the state-of-the-art guidance [ 6 , 10 , 15 ] on generating data adhering to the structure of multiple treatments with heterogeneous treatment effects on clustered survival outcomes. We based our simulation procedures on real data from the National Cancer Database (NCDB) [ 16 ].…”

“…We developed a random-intercept accelerated failure time model leveraging a probabilistic machine learning technique, Bayesian additive regression trees (BART) [ 3 , 4 , 5 ], for causal inferences about multiple treatments and clustered survival outcomes. This method, termed riAFT-BART [ 6 ], flexibly and accurately captures the relationships among the patient survival times, treatment and covariates via a sum of the tree models; it also accounts for the cluster-specific main effects using the random intercepts. Regularizing priors are placed on the parameters of riAFT-BART to ensure that the model is flexible in capturing nonlinearity and interactions but not overfitted [ 7 , 8 ].…”

“…An efficient and stable Markov chain Monte Carlo algorithm is developed for posterior inferences about the parameters. The formal statistical methodology was described in our earlier work [ 6 ] and in the Supplementary Material .…”

“…Values in each node correspond to the posterior mean and 95% credible intervals of the average treatment effect, in terms of the ratio of expected survival time, for the subgroup of individuals represented in that node; Figure S5: Final Random Forests model fit to the posterior mean of the individual survival treatment effect comparing external beam radiotherapy combined with androgen deprivation (EBRT + AD) to external beam radiotherapy plus brachytherapy with or without androgen deprivation (EBRT + brachy ± AD). Values in each node correspond to the posterior mean and 95% credible intervals of the average treatment effect, in terms of the ratio of expected survival time, for the subgroup of individuals represented in that node; Figure S6: The institutional (location) effects in terms of the expected survival months represented by the posterior mean and credible intervals of random intercept b, k, k = 1, 2, …, 9; References [ 6 , 11 , 17 , 18 , 19 , 20 ] are cited in the supplementary materials.…”

Using Tree-Based Machine Learning for Health Studies: Literature Review and Case Series

“…Variable selection is useful for discovering important risk factors that were previously less known for diseases of interest, identifying key confounding variables for a causal comparative effectiveness analysis, and reducing dimension of large genomic data sets. Turning to problem (ii), a popular way to estimate the causal treatment effect is via outcome modeling, which requires the prediction of the counterfactual outcomes from a model linking the observed outcomes and covariates [ 2 , 9 , 10 ,]. An additional utility of using tree-based methods for this problem is the exploration and estimation of treatment effect heterogeneity using the conditional models built for estimating the average causal effects [ 11 , 12 ].…”