Survival outcomes are common in comparative effectiveness studies and require unique handling because they are usually incompletely observed due to right-censoring. A ``once for all'' approach for causal inference with survival outcomes constructs pseudo-observations and allows standard methods such as propensity score weighting to proceed as if the outcomes are completely observed. For a general class of model-free causal estimands with survival outcomes on user-specified target populations, we develop corresponding propensity score weighting estimators based on the pseudo-observations and establish their asymptotic properties. In particular, utilizing the functional delta-method and the von Mises expansion, we derive a new closed-form variance of the weighting estimator that takes into account the uncertainty due to both pseudo-observation calculation and propensity score estimation. This allows valid and computationally efficient inference without resampling. We also prove the optimal efficiency property of the overlap weights within the class of balancing weights for survival outcomes. The proposed methods are applicable to both binary and multiple treatments. Extensive simulations are conducted to explore the operating characteristics of the proposed method versus other commonly used alternatives. We apply the proposed method to compare the causal effects of three popular treatment approaches for prostate cancer patients.
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We propose a general formulation for continuous treatment recommendation problems in settings with clinical survival data, which we call the Deep Survival Dose Response Function (DeepSDRF). That is, we consider the problem of learning the conditional average dose response (CADR) function solely from historical data in which unobserved factors (confounders) affect both observed treatment and time-to-event outcomes. The estimated treatment effect from DeepSDRF enables us to develop recommender algorithms with explanatory insights. We compared two recommender approaches based on random search and reinforcement learning and found similar performance in terms of patient outcome. We tested the DeepSDRF and the corresponding recommender on extensive simulation studies and two empirical databases: 1) the Clinical Practice Research Datalink (CPRD) and 2) the eICU Research Institute (eRI) database. To the best of our knowledge, this is the first time that confounders are taken into consideration for addressing the continuous treatment effect with observational data in a medical context.
Bayesian nonparametric methods are a popular choice for analysing survival data due to their ability to flexibly model the distribution of survival times. These methods typically employ a nonparametric prior on the survival function that is conjugate with respect to right-censored data. Eliciting these priors, particularly in the presence of covariates, can be challenging and inference typically relies on computationally intensive Markov chain Monte Carlo schemes. In this paper, we build on recent work that recasts Bayesian inference as assigning a predictive distribution on the unseen values of a population conditional on the observed samples, thus avoiding the need to specify a complex prior. We describe a copula-based predictive update which admits a scalable sequential importance sampling algorithm to perform inference that properly accounts for right-censoring. We provide theoretical justification through an extension of Doob's consistency theorem and illustrate the method on a number of simulated and real data sets, including an example with covariates. Our approach enables analysts to perform Bayesian nonparametric inference through only the specification of a predictive distribution.
Despite the availability of large amounts of genomics data, medical treatment recommendations have not successfully used them. In this paper, we consider the utility of high dimensional genomic-clinical data and nonparametric methods for making cancer treatment recommendations. This builds upon the framework of the individualized treatment rule [Qian and Murphy 2011] but we aim to overcome their method's limitations, specifically in the instances when the method encounters a large number of covariates and an issue of model misspecification. We tackle this problem using a dimension reduction method, namely Sliced Inverse Regression (SIR, [Li 1991]), with a rich class of models for the treatment response. Notably, SIR defines a feature space for high-dimensional data, offering an advantage similar to those found in the popular neural network models. With the features obtained from SIR, a simple visualization is used to compare different treatment options and present the recommended treatment. Additionally, we derive the consistency and the convergence rate of the proposed recommendation approach through a value function. The effectiveness of the proposed approach is demonstrated through simulation studies and the promising results from a real-data example of the treatment of multiple myeloma.
The sequential treatment decisions made by physicians to treat chronic diseases are formalized in the statistical literature as dynamic treatment regimes. To date, methods for dynamic treatment regimes have been developed under the assumption that observation times, i.e., treatment and outcome monitoring times, are determined by study investigators. That assumption is often not satisfied in electronic health records data in which the outcome, the observation times, and the treatment mechanism are associated with patients' characteristics. The treatment and observation processes can lead to spurious associations between the treatment of interest and the outcome to be optimized under the dynamic treatment regime if not adequately considered in the analysis. We address these associations by incorporating two inverse weights that are functions of a patient's covariates into dynamic weighted ordinary least squares to develop optimal single stage dynamic treatment regimes, known as individualized treatment rules. We show empirically that our methodology yields consistent, multiply robust estimators. In a cohort of new users of antidepressant drugs from the United Kingdom's Clinical Practice Research Datalink, the proposed method is used to develop an optimal treatment rule that chooses between two antidepressants to optimize a utility function related to the change in body mass index.
Delineating the associations between images and a vector of covariates is of central interest in medical imaging studies. To tackle this problem of image response regression, we propose a novel nonparametric approach in the framework of spatially varying coefficient models, where the spatially varying functions are estimated through deep neural networks. Compared to existing solutions, the proposed method explicitly accounts for spatial smoothness and subject heterogeneity, has straightforward interpretations, and is highly flexible and accurate in capturing complex association patterns. A key idea in our approach is to treat the image voxels as the effective samples, which not only alleviates the limited sample size issue that haunts the majority of medical imaging studies, but also leads to more robust and reproducible results. Focusing on a broad family of piecewise smooth functions, we establish the estimation and selection consistency, and derive the asymptotic error bounds. We demonstrate the efficacy of the method through intensive simulations, and further illustrate its advantages with analyses of two functional magnetic resonance imaging datasets.
There has been significant attention given to developing data-driven methods for tailoring patient care based on individual patient characteristics. Dynamic treatment regimes formalize this through a sequence of decision rules that map patient information to a suggested treatment. The data for estimating and evaluating treatment regimes are ideally gathered through the use of Sequential Multiple Assignment Randomized Trials (SMARTs) though longitudinal observational studies are commonly used due to the potentially prohibitive costs of conducting a SMART. These studies are typically sized for simple comparisons of fixed treatment sequences or, in the case of observational studies, a priori sample size calculations are often not performed. We develop sample size procedures for the estimation of dynamic treatment regimes from observational studies. Our approach uses pilot data to ensure a study will have sufficient power for comparing the value of the optimal regime, i.e. the expected outcome if all patients in the population were treated by following the optimal regime, with a known comparison mean. Our approach also ensures the value of the estimated optimal treatment regime is within an a priori set range of the value of the true optimal regime with a high probability. We examine the performance of the proposed procedure with a simulation study and use it to size a study for reducing depressive symptoms using data from electronic health records.
Data-driven methods for personalizing treatment assignment have garnered much attention from clinicians and researchers. Dynamic treatment regimes formalize this through a sequence of decision rules that map individual patient characteristics to a recommended treatment. Observational studies are commonly used for estimating dynamic treatment regimes due to the potentially prohibitive costs of conducting sequential multiple assignment randomized trials. However, estimating a dynamic treatment regime from observational data can lead to bias in the estimated regime due to unmeasured confounding. Sensitivity analyses are useful for assessing how robust the conclusions of the study are to a potential unmeasured confounder. A Monte Carlo sensitivity analysis is a probabilistic approach that involves positing and sampling from distributions for the parameters governing the bias. We propose a method for performing a Monte Carlo sensitivity analysis of the bias due to unmeasured confounding in the estimation of dynamic treatment regimes. We demonstrate the performance of the proposed procedure with a simulation study and apply it to an observational study examining tailoring the use of antidepressants for reducing symptoms of depression using data from Kaiser Permanente Washington (KPWA).
Observational studies can play a useful role in assessing the comparative effectiveness of competing treatments. In a clinical trial the randomization of participants to treatment and control groups generally results in well-balanced groups with respect to possible confounders, which makes the analysis straightforward. However, when analysing observational data, the potential for unmeasured confounding makes comparing treatment effects much more challenging. Causal inference methods such as the Instrumental Variable and Prior Even Rate Ratio approaches make it possible to circumvent the need to adjust for confounding factors that have not been measured in the data or measured with error. Direct confounder adjustment via multivariable regression and Propensity score matching also have considerable utility. Each method relies on a different set of assumptions and leverages different data. In this paper, we describe the assumptions of each method and assess the impact of violating these assumptions in a simulation study. We propose the prior outcome augmented Instrumental Variable method that leverages data from before and after treatment initiation, and is robust to the violation of key assumptions. Finally, we propose the use of a heterogeneity statistic to decide two or more estimates are statistically similar, taking into account their correlation. We illustrate our causal framework to assess the risk of genital infection in patients prescribed Sodium-glucose Co-transporter-2 inhibitors versus Dipeptidyl Peptidase-4 inhibitors as second-line treatment for type 2 diabets using observational data from the Clinical Practice Research Datalink.
Ensemble methods based on subsampling, such as random forests, are popular in applications due to their high predictive accuracy. Existing literature views a random forest prediction as an infinite-order incomplete U-statistic to quantify its uncertainty. However, these methods focus on a small subsampling size of each tree, which is theoretically valid but practically limited. This paper develops an unbiased variance estimator based on incomplete U-statistics, which allows the tree size to be comparable with the overall sample size, making statistical inference possible in a broader range of real applications. Simulation results demonstrate that our estimators enjoy lower bias and more accurate confidence interval coverage without additional computational costs. We also propose a local smoothing procedure to reduce the variation of our estimator, which shows improved numerical performance when the number of trees is relatively small. Further, we investigate the ratio consistency of our proposed variance estimator under specific scenarios. In particular, we develop a new "double U-statistic" formulation to analyze the Hoeffding decomposition of the estimator's variance.
In observational studies, causal inference relies on several key identifying assumptions. One identifiability condition is the positivity assumption, which requires the probability of treatment be bounded away from 0 and 1. That is, for every covariate combination, it should be possible to observe both treated and control subjects, i.e., the covariate distributions should overlap between treatment arms. If the positivity assumption is violated, population-level causal inference necessarily involves some extrapolation. Ideally, a greater amount of uncertainty about the causal effect estimate should be reflected in such situations. With that goal in mind, we construct a Gaussian process model for estimating treatment effects in the presence of practical violations of positivity. Advantages of our method include minimal distributional assumptions, a cohesive model for estimating treatment effects, and more uncertainty associated with areas in the covariate space where there is less overlap. We assess the performance of our approach with respect to bias and efficiency using simulation studies. The method is then applied to a study of critically ill female patients to examine the effect of undergoing right heart catheterization.
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