Using Ensemble-Based Methods for Directly Estimating Causal Effects: An Investigation of Tree-Based G-Computation

In sequential causal inference, two types of causal effects are of practical interest, namely, the causal effect of the treatment regime (called the sequential causal effect) and the blip effect of treatmenton on the potential outcome after the last treatment. The well-known G-formula expresses these causal effects in terms of the standard paramaters. In this article, we obtain a new G-formula that expresses these causal effects in terms of the point observable effects of treatments similar to treatment in the framework of single-point causal inference. Based on the new G-formula, we estimate these causal effects by maximum likelihood via point observable effects with methods extended from single-point causal inference. We are able to increase precision of the estimation without introducing biases by an unsaturated model imposing constraints on the point observable effects. We are also able to reduce the number of point observable effects in the estimation by treatment assignment conditions.

A central problem in public health studies is how to make inferences about the causal effects of treatments or agents. In this article we review an approach to making such inferences via potential outcomes. In this approach, the causal effect is defined as a comparison of results from two or more alternative treatments, with only one of the results actually observed. We discuss the application of this approach to a number of data collection designs and associated problems commonly encountered in clinical research and epidemiology. Topics considered include the fundamental role of the assignment mechanism, in particular the importance of randomization as an unconfounded method of assignment; randomization-based and model-based methods of statistical inference for causal effects; methods for handling noncompliance and missing data; and methods for limiting bias in the analysis of observational data, including propensity score matching and sensitivity analysis.

To test whether an observational study employing propensity score matching could accurately estimate the causal treatment effects of rectus femoris transfer (RFT) as part of single-event multilevel surgery (SEMLS) in ambulatory children with cerebral palsy. We used a large clinical database to derive a propensity score for treatment assignment (SEMLS±RFT) and used this score to generate a matched patient cohort. We compared the causal treatment effects estimated from this matched cohort with a previously published randomized controlled trial (RCT). The treated arms of the observational study and RCT were well matched. There were 129 limbs (81 males) with a mean age of 10years 7months (4y 7mo) in the treated arm of the observational study, and 129 limbs (68 males) with a mean age of 10years 2months (3y 9mo) in the control arm of the observational study. Differences between the observational study and RCT cohorts were clinically meaningless for knee flexion kinematics (1-4°), timing of knee angle extrema (<3% gait cycle), and speed (<5mm/s). Postoperative changes in the observational study matched those from the RCT. All but one of the observational study confidence intervals were completely contained within the corresponding RCT confidence interval; there were no meaningful differences in magnitude or sign of key outcomes related to stiff knee gait. Propensity score matching is an accurate method for estimating the causal treatment effects of RFT as part of an SEMLS. It seems reasonable to extend this approach to other common components of SEMLS treatment in this population. Propensity score matching is an accurate method for estimating the causal treatment effects of rectus femoris transfer (RFT) in ambulatory children with cerebral palsy (CP). The causal treatment effects for RFT surgery in ambulatory children diagnosed with CP were validated.

Causal inference is a permanent challenge topic in statistics, data science, and many other scientific fields.In this paper, we give an overview of statistical methods for causal inference. There are two main frameworks of causal inference: the potential outcome model and the causal network model. The potential outcome framework is used to evaluate causal effects of a known treatment or exposure variable on a given response or outcome variable. We review several commonly-used approaches in this framework for causal effect evaluation.The causal network framework is used to depict causal relationships among variables and the data generation mechanism in complex systems.We review two main approaches for structural learning: the constraint-based method and the score-based method.In the recent years, the evaluation of causal effects and the structural learning of causal networks are combined together.At the first stage, the hybrid approach learns a Markov equivalent class of causal networks from observed data;then at the second stage, it evaluates the causal effect for each causal network in the class; it also obtains a set of causal effects.The current frameworks of causal inference still have various demerits and disadvantages.We discuss these challenges and possible solutions in modern big data studies.

Frangakis and Rubin (2002, Biometrics 58, 21-29) proposed a new definition of a surrogate endpoint (a "principal" surrogate) based on causal effects. We introduce an estimand for evaluating a principal surrogate, the causal effect predictiveness (CEP) surface, which quantifies how well causal treatment effects on the biomarker predict causal treatment effects on the clinical endpoint. Although the CEP surface is not identifiable due to missing potential outcomes, it can be identified by incorporating a baseline covariate(s) that predicts the biomarker. Given case-cohort sampling of such a baseline predictor and the biomarker in a large blinded randomized clinical trial, we develop an estimated likelihood method for estimating the CEP surface. This estimation assesses the "surrogate value" of the biomarker for reliably predicting clinical treatment effects for the same or similar setting as the trial. A CEP surface plot provides a way to compare the surrogate value of multiple biomarkers. The approach is illustrated by the problem of assessing an immune response to a vaccine as a surrogate endpoint for infection.

The high placebo responses observed in many placebo-controlled randomized clinical trials, particularly in psychiatric research, have hindered the demonstration of treatment efficacy. To address this issue, Fava proposed the Sequential Parallel Comparison Design (SPCD) in 2003, which aims to mitigate the placebo response by estimating a pooled treatment effect (denoted by ). This is achieved by combining the treatment effect observed in the first stage among intention-to-treat (ITT) subjects with the second-stage treatment effect among placebo non-responders through a weighted average approach. However, the challenges in interpreting this pooled treatment effect causally complicate the review of SPCD-designed studies. This paper explored the pooled SPCD treatment effect and contrasted it with two causal estimators: The causal average treatment effect among non-responders (denoted by ) and the causal average treatment effect had all ITT subjects exhibited low responses during the study (denoted by ). These estimators reflect two opposing views of the placebo response, either as an immutable personal trait or as a manipulable feature. Through carefully designed simulation studies, we demonstrated the direction and magnitude of bias when interpreting as either or . In these simulation studies, tends to underestimate the treatment benefit when compared to two causal estimators in most scenarios. Furthermore, , developed to overcome the interpretational limitations of , exhibits statistically superior performance over and in terms of bias and MSE when using the G-formula approach. As such, we recommend its adoption where applicable. The first completed trial using the SPCD design, ADAPT-A, is reanalyzed to further confirm these findings.

BackgroundPropensity score matching is a statistical method that is often used to make inferences on the treatment effects in observational studies. In recent years, there has been widespread use of the technique in the cardiothoracic surgery literature to evaluate to potential benefits of new surgical therapies or procedures. However, the small sample size and the strong dependence of the treatment assignment on the baseline covariates that often characterize these studies make such an evaluation challenging from a statistical point of view. In such settings, the use of propensity score matching in combination with oversampling and replacement may provide a solution to these issues by increasing the initial sample size of the study and thus improving the statistical power that is needed to detect the effect of interest. In this study, we review the use of propensity score matching in combination with oversampling and replacement in small sample size settings.MethodsWe performed a series of Monte Carlo simulations to evaluate how the sample size, the proportion of treated, and the assignment mechanism affect the performances of the proposed approaches. We assessed the performances with overall balance, relative bias, root mean squared error and nominal coverage. Moreover, we illustrate the methods using a real case study from the cardiac surgery literature.ResultsMatching without replacement produced estimates with lower bias and better nominal coverage than matching with replacement when 1:1 matching was considered. In contrast to that, matching with replacement showed better balance, relative bias, and root mean squared error than matching without replacement for increasing levels of oversampling. The best nominal coverage was obtained by using the estimator that accounts for uncertainty in the matching procedure on sets of units obtained after matching with replacement.ConclusionsThe use of replacement provides the most reliable treatment effect estimates and that no more than 1 or 2 units from the control group should be matched to each treated observation. Moreover, the variance estimator that accounts for the uncertainty in the matching procedure should be used to estimate the treatment effect.

Assessing the causal effects of interventions on ordinal outcomes is an important objective of many educational and behavioral studies. Under the potential outcomes framework, we can define causal effects as comparisons between the potential outcomes under treatment and control. However, unfortunately, the average causal effect, often the parameter of interest, is difficult to interpret for ordinal outcomes. To address this challenge, we propose to use two causal parameters, which are defined as the probabilities that the treatment is beneficial and strictly beneficial for the experimental units. However, although well-defined for any outcomes and of particular interest for ordinal outcomes, the two aforementioned parameters depend on the association between the potential outcomes and are therefore not identifiable from the observed data without additional assumptions. Echoing recent advances in the econometrics and biostatistics literature, we present the sharp bounds of the aforementioned causal parameters for ordinal outcomes, under fixed marginal distributions of the potential outcomes. Because the causal estimands and their corresponding sharp bounds are based on the potential outcomes themselves, the proposed framework can be flexibly incorporated into any chosen models of the potential outcomes and is directly applicable to randomized experiments, unconfounded observational studies, and randomized experiments with noncompliance. We illustrate our methodology via numerical examples and three real-life applications related to educational and behavioral research.

Estimating individual-level average treatment effects: Challenges, modeling approaches, and practical applications

BackgroundObservational post-marketing assessment studies often involve evaluating the effect of a rare treatment on a time-to-event outcome, through the estimation of a marginal hazard ratio. Propensity score (PS) methods are the most used methods to estimate marginal effect of an exposure in observational studies. However there is paucity of data concerning their performance in a context of low prevalence of exposure.MethodsWe conducted an extensive series of Monte Carlo simulations to examine the performance of the two preferred PS methods, known as PS-matching and PS-weighting to estimate marginal hazard ratios, through various scenarios.ResultsWe found that both PS-weighting and PS-matching could be biased when estimating the marginal effect of rare exposure. The less biased results were obtained with estimators of average treatment effect in the treated population (ATT), in comparison with estimators of average treatment effect in the overall population (ATE). Among ATT estimators, PS-weighting using ATT weights outperformed PS-matching. These results are illustrated using a real observational study.ConclusionsWhen clinical objectives are focused on the treated population, applied researchers are encouraged to estimate ATT with PS-weighting for studying the relative effect of a rare treatment on time-to-event outcomes.Electronic supplementary materialThe online version of this article (doi:10.1186/s12874-016-0135-1) contains supplementary material, which is available to authorized users.

In observational studies, covariates are often confounding factors for treatment assignment. Such covariates need to be adjusted to estimate the causal treatment effect. For observational studies with survival outcomes, it is usually more challenging to adjust for the confounding covariates for causal effect estimation because of censoring. The challenge becomes even thornier when there exists a nonignorable cure fraction in the population. In this paper, we propose a causal effect estimation approach in observational studies for survival data with a cure fraction. We extend the absolute treatment effects on survival outcomes-including the restricted average causal effect and SPCE-to survival outcomes with cure fractions, and construct the corresponding causal effect estimators based on propensity score stratification. We prove the asymptotic properties of the proposed estimators and conduct simulation studies to evaluate their performances. As an illustration, the method is applied to a stomach cancerstudy.

A randomized trial is the gold standard for assessing the benefit of a treatment versus a control. When noncompliance is present, treatment effect depends on the tendency to comply—an attribute that is not directly measurable. Though the principal causal effect has been the most important for handling noncompliance, it is not immediately applicable to clinical decision-making as it targets the average effect in the latent strata of potential compliance. In this work, we propose the concept of compliance score, a linear combination of baseline characteristics, that uncovers the inherent attribute of compliance. We then assess the heterogeneous causal effect, namely, the causal effect of treatment as a function of baseline characteristics through the compliance score. A pseudo-response, along with a nonparametric estimation procedure, is proposed to ensure consistent and optimally efficient estimation. Compare to principal causal effect, the proposed effect is actionable and allows prediction of treatment effect at individual level. This work is motivated by and applied to a clinical trial to evaluate the benefit of antiretroviral regimens in HIV-infected patients.

Randomized controlled trials are the gold standard for measuring the causal effects of treatments on clinical outcomes. However, randomized trials are not always feasible, and causal treatment effects must, therefore,...

In a study comparing the effects of two treatments, the propensity score is the probability of assignment to one treatment conditional on a subject's measured baseline covariates. Propensity-score matching is increasingly being used to estimate the effects of exposures using observational data. In the most common implementation of propensity-score matching, pairs of treated and untreated subjects are formed whose propensity scores differ by at most a pre-specified amount (the caliper width). There has been a little research into the optimal caliper width. We conducted an extensive series of Monte Carlo simulations to determine the optimal caliper width for estimating differences in means (for continuous outcomes) and risk differences (for binary outcomes). When estimating differences in means or risk differences, we recommend that researchers match on the logit of the propensity score using calipers of width equal to 0.2 of the standard deviation of the logit of the propensity score. When at least some of the covariates were continuous, then either this value, or one close to it, minimized the mean square error of the resultant estimated treatment effect. It also eliminated at least 98% of the bias in the crude estimator, and it resulted in confidence intervals with approximately the correct coverage rates. Furthermore, the empirical type I error rate was approximately correct. When all of the covariates were binary, then the choice of caliper width had a much smaller impact on the performance of estimation of risk differences and differences in means. Copyright © 2010 John Wiley & Sons, Ltd.

In randomised controlled trials, the effect of treatment on those who comply with allocation to active treatment can be estimated by comparing their outcome to those in the comparison group who would have complied with active treatment had they been allocated to it. We compare three estimators of the causal effect of treatment on compliers when this is a parameter in a proportional hazards model and quantify the bias due to omitting baseline prognostic factors. Causal estimates are found directly by maximising a novel partial likelihood; based on a structural proportional hazards model; and based on a 'corrected dataset' derived after fitting a rank-preserving structural failure time model. Where necessary, we extend these methods to incorporate baseline covariates. Comparisons use simulated data and a real data example. Analysing the simulated data, we found that all three methods are accurate when an important covariate was included in the proportional hazards model (maximum bias 5.4%). However, failure to adjust for this prognostic factor meant that causal treatment effects were underestimated (maximum bias 11.4%), because estimators were based on a misspecified marginal proportional hazards model. Analysing the real data example, we found that adjusting causal estimators is important to correct for residual imbalances in prognostic factors present between trial arms after randomisation. Our results show that methods of estimating causal treatment effects for time-to-event outcomes should be extended to incorporate covariates, thus providing an informative compliment to the corresponding intention-to-treat analysis.