arXiv subjects

Edward H. Kennedy

Publications and source records attributed to Edward H. Kennedy.

At least 55 records · Page 3Linked to original sources

arXiv2023

An Efficient Doubly-Robust Test for the Kernel Treatment Effect

The average treatment effect, which is the difference in expectation of the counterfactuals, is probably the most popular target effect in causal inference with binary treatments. However, treatments may have effects beyond the mean, for instance decreasing or increasing the variance. We propose a new kernel-based test for distributional effects of the treatment. It is, to the best of our knowledge, the first kernel-based, doubly-robust test with provably valid type-I error. Furthermore, our proposed algorithm is computationally efficient, avoiding the use of permutations.

stat.ME↗

arXiv2023

Covariate-assisted bounds on causal effects with instrumental variables

When an exposure of interest is confounded by unmeasured factors, an instrumental variable (IV) can be used to identify and estimate certain causal contrasts. Identification of the marginal average treatment effect (ATE) from IVs relies on strong untestable structural assumptions. When one is unwilling to assert such structure, IVs can nonetheless be used to construct bounds on the ATE. Famously, Balke and Pearl (1997) proved tight bounds on the ATE for a binary outcome, in a randomized trial with noncompliance and no covariate information. We demonstrate how these bounds remain useful in observational settings with baseline confounders of the IV, as well as randomized trials with measured baseline covariates. The resulting bounds on the ATE are non-smooth functionals, and thus standard nonparametric efficiency theory is not immediately applicable. To remedy this, we propose (1) under a novel margin condition, influence function-based estimators of the bounds that can attain parametric convergence rates when the nuisance functions are modeled flexibly, and (2) estimators of smooth approximations of these bounds. We propose extensions to continuous outcomes, explore finite sample properties in simulations, and illustrate the proposed estimators in an observational study targeting the effect of higher education on wages.

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arXiv2023

Effects of Adolescent Victimization on Offending: Flexible Methods for Missing Data & Unmeasured Confounding

The causal link between victimization and violence later in life is largely accepted but has been understudied for victimized adolescents. In this work we use the Add Health dataset, the largest nationally representative longitudinal survey of adolescents, to estimate the relationship between victimization and future offending in this population. To accomplish this, we derive a new doubly robust estimator for the average treatment effect on the treated (ATT) when the treatment and outcome are not always observed. We then find that the offending rate among victimized individuals would have been 3.86 percentage points lower if none of them had been victimized (95% CI: [0.28, 7.45]). This contributes positive evidence of a causal effect of victimization on future offending among adolescents. We further present statistical evidence of heterogeneous effects by age, under which the ATT decreases according to the age at which victimization is experienced. We then devise a novel risk-ratio-based sensitivity analysis and conclude that our results are robust to modest unmeasured confounding. Finally, we show that the found effect is mainly driven by non-violent offending.

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arXiv2023

Towards optimal doubly robust estimation of heterogeneous causal effects

Heterogeneous effect estimation plays a crucial role in causal inference, with applications across medicine and social science. Many methods for estimating conditional average treatment effects (CATEs) have been proposed in recent years, but there are important theoretical gaps in understanding if and when such methods are optimal. This is especially true when the CATE has nontrivial structure (e.g., smoothness or sparsity). Our work contributes in several main ways. First, we study a two-stage doubly robust CATE estimator and give a generic model-free error bound, which, despite its generality, yields sharper results than those in the current literature. We apply the bound to derive error rates in nonparametric models with smoothness or sparsity, and give sufficient conditions for oracle efficiency. Underlying our error bound is a general oracle inequality for regression with estimated or imputed outcomes, which is of independent interest; this is the second main contribution. The third contribution is aimed at understanding the fundamental statistical limits of CATE estimation. To that end, we propose and study a local polynomial adaptation of double-residual regression. We show that this estimator can be oracle efficient under even weaker conditions, if used with a specialized form of sample splitting and careful choices of tuning parameters. These are the weakest conditions currently found in the literature, and we conjecture that they are minimal in a minimax sense. We go on to give error bounds in the non-trivial regime where oracle rates cannot be achieved. Some finite-sample properties are explored with simulations.

math.ST↗

arXiv2023

Minimax optimal subgroup identification

Quantifying treatment effect heterogeneity is a crucial task in many areas of causal inference, e.g. optimal treatment allocation and estimation of subgroup effects. We study the problem of estimating the level sets of the conditional average treatment effect (CATE), identified under the no-unmeasured-confounders assumption. Given a user-specified threshold, the goal is to estimate the set of all units for whom the treatment effect exceeds that threshold. For example, if the cutoff is zero, the estimand is the set of all units who would benefit from receiving treatment. Assigning treatment just to this set represents the optimal treatment rule that maximises the mean population outcome. Similarly, cutoffs greater than zero represent optimal rules under resource constraints. The level set estimator that we study follows the plug-in principle and consists of simply thresholding a good estimator of the CATE. While many CATE estimators have been recently proposed and analysed, how their properties relate to those of the corresponding level set estimators remains unclear. Our first goal is thus to fill this gap by deriving the asymptotic properties of level set estimators depending on which estimator of the CATE is used. Next, we identify a minimax optimal estimator in a model where the CATE, the propensity score and the outcome model are Holder-smooth of varying orders. We consider data generating processes that satisfy a margin condition governing the probability of observing units for whom the CATE is close to the threshold. We investigate the performance of the estimators in simulations and illustrate our methods on a dataset used to study the effects on mortality of laparoscopic vs open surgery in the treatment of various conditions of the colon.

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arXiv2023

Nonparametric Estimation of Conditional Incremental Effects

Conditional effect estimation has great scientific and policy importance because interventions may impact subjects differently depending on their characteristics. Most research has focused on estimating the conditional average treatment effect (CATE). However, identification of the CATE requires all subjects have a non-zero probability of receiving treatment, or positivity, which may be unrealistic in practice. Instead, we propose conditional effects based on incremental propensity score interventions, which are stochastic interventions where the odds of treatment are multiplied by some factor. These effects do not require positivity for identification and can be better suited for modeling scenarios in which people cannot be forced into treatment. We develop a projection estimator and a flexible nonparametric estimator that can each estimate all the conditional effects we propose and derive model-agnostic error guarantees showing both estimators satisfy a form of double robustness. Further, we propose a summary of treatment effect heterogeneity and a test for any effect heterogeneity based on the variance of a conditional derivative effect and derive a nonparametric estimator that also satisfies a form of double robustness. Finally, we demonstrate our estimators by analyzing the effect of intensive care unit admission on mortality using a dataset from the (SPOT)light study.

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arXiv2023

Heterogeneous interventional indirect effects with multiple mediators: non-parametric and semi-parametric approaches

We propose semi- and non-parametric methods to estimate conditional interventional effects in the setting of two discrete mediators whose causal ordering is unknown. Average interventional indirect effects have been shown to decompose an average treatment effect into a direct effect and interventional indirect effects that quantify effects of hypothetical interventions on mediator distributions. Yet these effects may be heterogeneous across the covariate distribution. We consider the problem of estimating these effects at particular points. We propose an influence-function based estimator of the projection of the conditional effects onto a working model, and show under some conditions that we can achieve root-n consistent and asymptotically normal estimates. Second, we propose a fully non-parametric approach to estimation and show the conditions where this approach can achieve oracle rates of convergence. Finally, we propose a sensitivity analysis for the conditional effects in the presence of mediator-outcome confounding. We propose estimating bounds on the conditional effects using these same methods, and show that these results easily extend to allow for influence-function based estimates of the bounds on the average effects. We conclude examining heterogeneous effects with respect to the effect of COVID-19 vaccinations on depression during February 2021.

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arXiv2023

Semiparametric doubly robust targeted double machine learning: a review

In this review we cover the basics of efficient nonparametric parameter estimation (also called functional estimation), with a focus on parameters that arise in causal inference problems. We review both efficiency bounds (i.e., what is the best possible performance for estimating a given parameter?) and the analysis of particular estimators (i.e., what is this estimator's error, and does it attain the efficiency bound?) under weak assumptions. We emphasize minimax-style efficiency bounds, worked examples, and practical shortcuts for easing derivations. We gloss over most technical details, in the interest of highlighting important concepts and providing intuition for main ideas.

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arXiv2023

Doubly Robust Counterfactual Classification

We study counterfactual classification as a new tool for decision-making under hypothetical (contrary to fact) scenarios. We propose a doubly-robust nonparametric estimator for a general counterfactual classifier, where we can incorporate flexible constraints by casting the classification problem as a nonlinear mathematical program involving counterfactuals. We go on to analyze the rates of convergence of the estimator and provide a closed-form expression for its asymptotic distribution. Our analysis shows that the proposed estimator is robust against nuisance model misspecification, and can attain fast $\sqrt{n}$ rates with tractable inference even when using nonparametric machine learning approaches. We study the empirical performance of our methods by simulation and apply them for recidivism risk prediction.

cs.LG↗

arXiv2022

The role of the geometric mean in case-control studies

Historically used in settings where the outcome is rare or data collection is expensive, outcome-dependent sampling is relevant to many modern settings where data is readily available for a biased sample of the target population, such as public administrative data. Under outcome-dependent sampling, common effect measures such as the average risk difference and the average risk ratio are not identified, but the conditional odds ratio is. Aggregation of the conditional odds ratio is challenging since summary measures are generally not identified. Furthermore, the marginal odds ratio can be larger (or smaller) than all conditional odds ratios. This so-called non-collapsibility of the odds ratio is avoidable if we use an alternative aggregation to the standard arithmetic mean. We provide a new definition of collapsibility that makes this choice of aggregation method explicit, and we demonstrate that the odds ratio is collapsible under geometric aggregation. We describe how to partially identify, estimate, and do inference on the geometric odds ratio under outcome-dependent sampling. Our proposed estimator is based on the efficient influence function and therefore has doubly robust-style properties.

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arXiv2022

Median Optimal Treatment Regimes

Optimal treatment regimes are personalized policies for making a treatment decision based on subject characteristics, with the policy chosen to maximize some value. It is common to aim to maximize the mean outcome in the population, via a regime assigning treatment only to those whose mean outcome is higher under treatment versus control. However, the mean can be an unstable measure of centrality, resulting in imprecise statistical procedures, as well as unrobust decisions that can be overly influenced by a small fraction of subjects. In this work, we propose a new median optimal treatment regime that instead treats individuals whose conditional median is higher under treatment. This ensures that optimal decisions for individuals from the same group are not overly influenced either by (i) a small fraction of the group (unlike the mean criterion), or (ii) unrelated subjects from different groups (unlike marginal median/quantile criteria). We introduce a new measure of value, the Average Conditional Median Effect (ACME), which summarizes across-group median treatment outcomes of a policy, and which the median optimal treatment regime maximizes. After developing key motivating examples that distinguish median optimal treatment regimes from mean and marginal median optimal treatment regimes, we give a nonparametric efficiency bound for estimating the ACME of a policy, and propose a new doubly robust-style estimator that achieves the efficiency bound under weak conditions. To construct the median optimal treatment regime, we introduce a new doubly robust-style estimator for the conditional median treatment effect. Finite-sample properties are explored via numerical simulations and the proposed algorithm is illustrated using data from a randomized clinical trial in patients with HIV.

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arXiv2021

Doubly Robust Adaptive LASSO for Effect Modifier Discovery

Effect modification occurs when the effect of the treatment on an outcome differs according to the level of a third variable (the effect modifier, EM). A natural way to assess effect modification is by subgroup analysis or include the interaction terms between the treatment and the covariates in an outcome regression. The latter, however, does not target a parameter of a marginal structural model (MSM) unless a correctly specified outcome model is specified. Our aim is to develop a data-adaptive method to select effect modifying variables in an MSM with a single time point exposure. A two-stage procedure is proposed. First, we estimate the conditional outcome expectation and propensity score and plug these into a doubly robust loss function. Second, we use the adaptive LASSO to select the EMs and estimate MSM coefficients. Post-selection inference is then used to obtain coverage on the selected EMs. Simulations studies are performed in order to verify the performance of the proposed methods.

stat.ME↗

arXiv2021

Incremental Intervention Effects in Studies with Dropout and Many Timepoints

Modern longitudinal studies collect feature data at many timepoints, often of the same order of sample size. Such studies are typically affected by {dropout} and positivity violations. We tackle these problems by generalizing effects of recent incremental interventions (which shift propensity scores rather than set treatment values deterministically) to accommodate multiple outcomes and subject dropout. We give an identifying expression for incremental intervention effects when dropout is conditionally ignorable (without requiring treatment positivity), and derive the nonparametric efficiency bound for estimating such effects. Then we present efficient nonparametric estimators, showing that they converge at fast parametric rates and yield uniform inferential guarantees, even when nuisance functions are estimated flexibly at slower rates. We also study the variance ratio of incremental intervention effects relative to more conventional deterministic effects in a novel infinite time horizon setting, where the number of timepoints can grow with sample size, and show that incremental intervention effects yield near-exponential gains in statistical precision in this setup. Finally we conclude with simulations and apply our methods in a study of the effect of low-dose aspirin on pregnancy outcomes.

stat.ME↗

arXiv2021

drpop: Efficient and Doubly Robust Population Size Estimation in R

This paper introduces the R package drpop to flexibly estimate total population size from incomplete lists. Total population estimation, also called capture-recapture, is an important problem in many biological and social sciences. A typical dataset consists of incomplete lists of individuals from the population of interest along with some covariate information. The goal is to estimate the number of unobserved individuals and equivalently, the total population size. drpop flexibly models heterogeneity using the covariate information, under the assumption that two lists are conditionally independent given covariates. This can be a much weaker assumption than full marginal independence often required by classical methods. Moreover, it can incorporate complex and high dimensional covariates, and does not require parametric models like other popular methods. In particular, our estimator is doubly robust and has fast convergence rates even under flexible non-parametric set-ups. drpop provides the user with the flexibility to choose the model for estimation of intermediate parameters and returns the estimated population size, confidence interval and some other related quantities. In this paper, we illustrate the applications of drpop in different scenarios and we also present some performance summaries.

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arXiv2021

Incremental causal effects: an introduction and review

In this chapter, we review the class of causal effects based on incremental propensity scores interventions proposed by Kennedy [2019]. The aim of incremental propensity score interventions is to estimate the effect of increasing or decreasing subjects' odds of receiving treatment; this differs from the average treatment effect, where the aim is to estimate the effect of everyone deterministically receiving versus not receiving treatment. We first present incremental causal effects for the case when there is a single binary treatment, such that it can be compared to average treatment effects and thus shed light on key concepts. In particular, a benefit of incremental effects is that positivity - a common assumption in causal inference - is not needed to identify causal effects. Then we discuss the more general case where treatment is measured at multiple time points, where positivity is more likely to be violated and thus incremental effects can be especially useful. Throughout, we motivate incremental effects with real-world applications, present nonparametric estimators for these effects, and discuss their efficiency properties, while also briefly reviewing the role of influence functions in functional estimation. Finally, we show how to interpret and analyze results using these estimators in practice, and discuss extensions and future directions.

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arXiv2021

Fairness in Risk Assessment Instruments: Post-Processing to Achieve Counterfactual Equalized Odds

In domains such as criminal justice, medicine, and social welfare, decision makers increasingly have access to algorithmic Risk Assessment Instruments (RAIs). RAIs estimate the risk of an adverse outcome such as recidivism or child neglect, potentially informing high-stakes decisions such as whether to release a defendant on bail or initiate a child welfare investigation. It is important to ensure that RAIs are fair, so that the benefits and harms of such decisions are equitably distributed. The most widely used algorithmic fairness criteria are formulated with respect to observable outcomes, such as whether a person actually recidivates, but these criteria are misleading when applied to RAIs. Since RAIs are intended to inform interventions that can reduce risk, the prediction itself affects the downstream outcome. Recent work has argued that fairness criteria for RAIs should instead utilize potential outcomes, i.e. the outcomes that would occur in the absence of an appropriate intervention. However, no methods currently exist to satisfy such fairness criteria. In this paper, we target one such criterion, counterfactual equalized odds. We develop a post-processed predictor that is estimated via doubly robust estimators, extending and adapting previous post-processing approaches to the counterfactual setting. We also provide doubly robust estimators of the risk and fairness properties of arbitrary fixed post-processed predictors. Our predictor converges to an optimal fair predictor at fast rates. We illustrate properties of our method and show that it performs well on both simulated and real data.

stat.ME↗

arXiv2021

Doubly robust capture-recapture methods for estimating population size

Estimation of population size using incomplete lists (also called the capture-recapture problem) has a long history across many biological and social sciences. For example, human rights and other groups often construct partial and overlapping lists of victims of armed conflicts, with the hope of using this information to estimate the total number of victims. Earlier statistical methods for this setup either use potentially restrictive parametric assumptions, or else rely on typically suboptimal plug-in-type nonparametric estimators; however, both approaches can lead to substantial bias, the former via model misspecification and the latter via smoothing. Under an identifying assumption that two lists are conditionally independent given measured covariate information, we make several contributions. First, we derive the nonparametric efficiency bound for estimating the capture probability, which indicates the best possible performance of any estimator, and sheds light on the statistical limits of capture-recapture methods. Then we present a new estimator, and study its finite-sample properties, showing that it has a double robustness property new to capture-recapture, and that it is near-optimal in a non-asymptotic sense, under relatively mild nonparametric conditions. Next, we give a method for constructing confidence intervals for total population size from generic capture probability estimators, and prove non-asymptotic near-validity. Finally, we study our methods in simulations, and apply them to estimate the number of killings and disappearances attributable to different groups in Peru during its internal armed conflict between 1980 and 2000.

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arXiv2021

Counterfactual Predictions under Runtime Confounding

Algorithms are commonly used to predict outcomes under a particular decision or intervention, such as predicting whether an offender will succeed on parole if placed under minimal supervision. Generally, to learn such counterfactual prediction models from observational data on historical decisions and corresponding outcomes, one must measure all factors that jointly affect the outcomes and the decision taken. Motivated by decision support applications, we study the counterfactual prediction task in the setting where all relevant factors are captured in the historical data, but it is either undesirable or impermissible to use some such factors in the prediction model. We refer to this setting as runtime confounding. We propose a doubly-robust procedure for learning counterfactual prediction models in this setting. Our theoretical analysis and experimental results suggest that our method often outperforms competing approaches. We also present a validation procedure for evaluating the performance of counterfactual prediction methods.

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