Estimation Of Average Causal Effect Research Articles

Causal effect estimation with censored outcome and covariate selection

We estimate the causal effect in the presence of censored outcome and high-dimensional covariates. To improve the efficiency of the estimation of average causal effect, we propose the censored outcome adaptive Lasso (COAL) to select covariates.

Estimation of the Average Causal Effect in Longitudinal Data With Time-Varying Exposures: The Challenge of Nonpositivity and the Impact of Model Flexibility.

There are important challenges to the estimation and identification of average causal effects in longitudinal data with time-varying exposures. Here, we discuss the difficulty in meeting the positivity condition. Our motivating example is the per-protocol analysis of the Effects of Aspirin in Gestation and Reproduction (EAGeR) Trial. We estimated the average causal effect comparing the incidence of pregnancy by 26 weeks that would have occurred if all women had been assigned to aspirin and complied versus the incidence if all women had been assigned to placebo and complied. Using flexible targeted minimum loss-based estimation, we estimated a risk difference of 1.27% (95% CI: -9.83, 12.38). Using a less flexible inverse probability weighting approach, the risk difference was 5.77% (95% CI: -1.13, 13.05). However, the cumulative probability of compliance conditional on covariates approached 0 as follow-up accrued, indicating a practical violation of the positivity assumption, which limited our ability to make causal interpretations. The effects of nonpositivity were more apparent when using a more flexible estimator, as indicated by the greater imprecision. When faced with nonpositivity, one can use a flexible approach and be transparent about the uncertainty, use a parametric approach and smooth over gaps in the data, or target a different estimand that will be less vulnerable to positivity violations.

AIPW: An R Package for Augmented Inverse Probability-Weighted Estimation of Average Causal Effects.

An increasing number of recent studies have suggested that doubly robust estimators with cross-fitting should be used when estimating causal effects with machine learning methods. However, not all existing programs that implement doubly robust estimators support machine learning methods and cross-fitting, or provide estimates on multiplicative scales. To address these needs, we developed AIPW, a software package implementing augmented inverse probability weighting (AIPW) estimation of average causal effects in R (R Foundation for Statistical Computing, Vienna, Austria). Key features of the AIPW package include cross-fitting and flexible covariate adjustment for observational studies and randomized controlled trials (RCTs). In this paper, we use a simulated RCT to illustrate implementation of the AIPW estimator. We also perform a simulation study to evaluate the performance of the AIPW package compared with other doubly robust implementations, including CausalGAM, npcausal, tmle, and tmle3. Our simulation showed that the AIPW package yields performance comparable to that of other programs. Furthermore, we also found that cross-fitting substantively decreases the bias and improves the confidence interval coverage for doubly robust estimators fitted with machine learning algorithms. Our findings suggest that the AIPW package can be a useful tool for estimating average causal effects with machine learning methods in RCTs and observational studies.

Structural Equation Model Averaging: Methodology and Application

The instrumental variable (IV) methods are attractive since they can lead to a consistent answer to the main question in causal modeling, that is, the estimation of average causal effect of an exposure on the outcome in the presence of unmeasured confounding. However, it is now acknowledged in the literature that using weak IVs might not suit the inference goal satisfactorily. We consider the problem of estimating causal effects in an observational study in this article, allowing some IVs to be weak. In many modern learning jobs, we may face a large number of instruments and their quality could range from poor to strong. To incorporate them in a 2-stage least squares estimation procedure, we consider a model averaging technique. The proposed methods only involve a few layers of least squares estimation with closed-form solutions and thus is easy to implement in practice. Theoretical properties are carefully established, including the consistency and asymptotic normality of the estimated causal parameter. Numerical studies are carried out to assess the performance in low- and high-dimensional settings and comparisons are made between our proposed method and a wide range of existing alternative methods. A real data example on home price is analyzed to illustrate our methodology.

Machine learning outcome regression improves doubly robust estimation of average causal effects.

Doubly robust estimation produces an unbiased estimator for the average treatment effect unless both propensity score (PS) and outcome models are incorrectly specified. Studies have shown that the doubly robust estimator is subject to more bias than the standard weighting estimator when both PS and outcome models are incorrectly specified. We evaluated whether various machine learning methods can be used for estimating conditional means of the potential outcomes to enhance the robustness of the doubly robust estimator to various degrees of model misspecification in terms of reducing bias and standard error. We considered four types of methods to predict the outcomes: least squares, tree-based methods, generalized additive models and shrinkage methods. We also considered an ensemble method called the Super Learner (SL), which is a linear combination of multiple learners. We conducted simulations considering different scenarios by the complexity of PS and outcome-generating models and some ranges of treatment prevalence. The shrinkage methods performed well with robust doubly robust estimates in term of bias and mean squared error across the scenarios when the models became rich by including all 2-way interactions of the covariates. The SL performed similarly to the best method in each scenario. Our findings indicate that machine learning methods such as the SL or the shrinkage methods using interaction models should be used for more accurate doubly robust estimators.

Identification and estimation of average causal effects when treatment status is ignorable within unobserved strata

This paper extends matching and propensity-score reweighting methods to settings in which unobserved variables influence both treatment assignment and counterfactual outcomes. Identification proceeds under the assumption that counterfactual outcomes are independent of treatment status conditional on observed covariates and membership in one of a finite set of latent classes. Individuals are first assigned to latent classes according to posterior probabilities of class membership derived from a finite-mixture model that relates a set of auxiliary variables to latent class membership. Average causal effects are then identified by comparing outcomes among treated and untreated individuals assigned to the same class, correcting for misclassifications arising in the first step. The identification procedure suggests computationally attractive latent-class matching and propensity-score reweighting estimators that obviate the need to directly estimate the distributions of counterfactual outcomes. In Monte Carlo studies, the resulting estimates are centered around the correct average causal effects with minimal loss of precision compared to competing estimators that misstate those effects. I apply the methods to estimate the effect of gang membership on violent delinquency.

Defining standard of practice: pros and cons of the usual care arm.

The aim of this review is to describe the use of usual care arms in randomized trials. Randomization of patients to an experimental or a control arm remains paramount for the estimation of average causal effects. Selection of the control arm is as important as the definition of the intervention, and it might include a placebo control, specific standards of care, protocolized usual care, or unrestricted clinical practice. Usual care control arms may enhance generalizability, clinician acceptability of the protocol, patient recruitment, and ensure community equipoise, while at the same time introducing significant variability in the care delivered in the control group. This effect may reduce the difference in treatments delivered between the two groups and lead to a negative result or the requirement for a larger sample size. Moreover, usual care control groups can be subject to changes in clinician behavior induced by the trial itself, or by secular trends in time. Usual care control arms may enhance generalizability while introducing significant limitations. Potential solutions include the use of pretrial surveys to evaluate the extent to which a protocolized control arm reflects the current standard of care and the implementation of adaptive trials.

Using propensity scores for causal inference in ecology: Options, considerations, and a case study

Abstract Applied ecologists are often interested in understanding the effects of management on ecological systems. If management (treatment) is applied nonrandomly, as in observational studies, then analysis must account for the potential confounding caused by variables that could have influenced both treatment assignment and the outcome of interest. Methods that do not adjust for all confounding variables can only estimate associations between treatment and outcome, not treatment effects. Data collected in observational studies are usually analysed with linear or generalized linear models, which can estimate treatment effects by adjusting for confounding variables. However, if there is little overlap in the distributions of confounding variables among the treatment groups then conventional regression extrapolates to areas of the covariate space where at least one of the treatment groups was unlikely to be observed. An alternative procedure for assessing treatment effects is to use the propensity score, which is the probability of treatment assignment given potential confounding variables. The propensity score can be used to reduce systematic differences in confounding variables among the treatment groups, ensuring that data more closely resemble that expected under a randomized experiment. The propensity score also identifies situations where treatment inferences must rely on strong assumptions. We used Monte Carlo simulation to examine the properties of commonly used propensity score methods for estimating treatment effects in the presence of nonrandom allocation of treatments. We then illustrated their application in a case study estimating the effects of invasive herbivore management on tree condition. Our results indicate that propensity score methods can be robust to model misspecification, allowing the estimation of average causal effects and resulting in more reliable inferences. We discuss key considerations for using propensity score methods for analysing ecological data.

Data-driven confounder selection via Markov and Bayesian networks.

To unbiasedly estimate a causal effect on an outcome unconfoundedness is often assumed. If there is sufficient knowledge on the underlying causal structure then existing confounder selection criteria can be used to select subsets of the observed pretreatment covariates, X, sufficient for unconfoundedness, if such subsets exist. Here, estimation of these target subsets is considered when the underlying causal structure is unknown. The proposed method is to model the causal structure by a probabilistic graphical model, for example, a Markov or Bayesian network, estimate this graph from observed data and select the target subsets given the estimated graph. The approach is evaluated by simulation both in a high-dimensional setting where unconfoundedness holds given X and in a setting where unconfoundedness only holds given subsets of X. Several common target subsets are investigated and the selected subsets are compared with respect to accuracy in estimating the average causal effect. The proposed method is implemented with existing software that can easily handle high-dimensional data, in terms of large samples and large number of covariates. The results from the simulation study show that, if unconfoundedness holds given X, this approach is very successful in selecting the target subsets, outperforming alternative approaches based on random forests and LASSO, and that the subset estimating the target subset containing all causes of outcome yields smallest MSE in the average causal effect estimation.

Estimation of average causal effect using the restricted mean residual lifetime as effect measure.

Although mean residual lifetime is often of interest in biomedical studies, restricted mean residual lifetime must be considered in order to accommodate censoring. Differences in the restricted mean residual lifetime can be used as an appropriate quantity for comparing different treatment groups with respect to their survival times. In observational studies where the factor of interest is not randomized, covariate adjustment is needed to take into account imbalances in confounding factors. In this article, we develop an estimator for the average causal treatment difference using the restricted mean residual lifetime as target parameter. We account for confounding factors using the Aalen additive hazards model. Large sample property of the proposed estimator is established and simulation studies are conducted in order to assess small sample performance of the resulting estimator. The method is also applied to an observational data set of patients after an acute myocardial infarction event.

Targeted smoothing parameter selection for estimating average causal effects

The non-parametric estimation of average causal effects in observational studies often relies on controlling for confounding covariates through smoothing regression methods such as kernel, splines or local polynomial regression. Such regression methods are tuned via smoothing parameters which regulates the amount of degrees of freedom used in the fit. In this paper we propose data-driven methods for selecting smoothing parameters when the targeted parameter is an average causal effect. For this purpose, we propose to estimate the exact expression of the mean squared error of the estimators. Asymptotic approximations indicate that the smoothing parameters minimizing this mean squared error converges to zero faster than the optimal smoothing parameter for the estimation of the regression functions. In a simulation study we show that the proposed data-driven methods for selecting the smoothing parameters yield lower empirical mean squared error than other methods available such as, e.g., cross-validation.

The role of the propensity score in estimating dose-response functions

SUMMARY Estimation of average treatment effects in observational studies often requires adjustment for differences in pre-treatment variables. If the number of pre-treatment variables is large, standard covariance adjustment methods are often inadequate. Rosenbaum & Rubin (1983) propose an alternative method for adjusting for pre-treatment variables for the binary treatment case based on the so-called propensity score. Here an extension of the propensity score methodology is proposed that allows for estimation of average casual effects with multi-valued treatments. Estimation of average treatment effects in observational studies often requires adjustment for differences in pre-treatment variables. If the number of pre-treatment variables is large and their distribution varies substantially with treatment status, standard adjustment methods such as covari- ance adjustment are often inadequate. Rosenbaum & Rubin (1983, 1984) propose an alternative method for adjusting for pre-treatment variables based on the propensity score, the conditional probability of receiving the treatment given pre-treatment variables. They demonstrate that adjusting solely for the propensity score removes all bias associated with differences in the pre- treatment variables. The Rosenbaum-Rubin proposals deal exclusively with binary-valued treat- ments. In many cases of interest, however, treatments take on more than two values. Here an extension of the propensity score methodology is proposed that allows for estimation of average causal effects with multi-valued treatments. The key insight is that for estimation of average causal effects it is not necessary to divide the population into subpopulations where causal comparisons are valid, as the propensity score does; it is sufficient to divide the population into subpopulations where average potential outcomes can be estimated.

Two-Stage Least Squares Estimation of Average Causal Effects in Models with Variable Treatment Intensity

Two-Stage Least Squares Estimation of Average Causal Effects in Models with Variable Treatment Intensity

Two-Stage Least Squares Estimation of Average Causal Effects in Models with Variable Treatment Intensity

Abstract Two-stage least squares (TSLS) is widely used in econometrics to estimate parameters in systems of linear simultaneous equations and to solve problems of omitted-variables bias in single-equation estimation. We show here that TSLS can also be used to estimate the average causal effect of variable treatments such as drug dosage, hours of exam preparation, cigarette smoking, and years of schooling. The average causal effect in which we are interested is a conditional expectation of the difference between the outcomes of the treated and what these outcomes would have been in the absence of treatment. Given mild regularity assumptions, the probability limit of TSLS is a weighted average of per-unit average causal effects along the length of an appropriately defined causal response function. The weighting function is illustrated in an empirical example based on the relationship between schooling and earnings.