We propose a model-free framework for sensitivity analysis of individual treatment effects (ITEs), building upon ideas from conformal inference. For any unit, our procedure reports the Γ-value, a number which quantifies the minimum strength of confounding needed to explain away the evidence for ITE. Our approach rests on the reliable predictive inference of counterfactuals and ITEs in situations where the training data are confounded. Under the marginal sensitivity model of [Z. Tan, J. Am. Stat. Assoc. 101, 1619-1637 (2006)], we characterize the shift between the distribution of the observations and that of the counterfactuals. We first develop a general method for predictive inference of test samples from a shifted distribution; we then leverage this to construct covariate-dependent prediction sets for counterfactuals. No matter the value of the shift, these prediction sets (resp. approximately) achieve marginal coverage if the propensity score is known exactly (resp. estimated). We describe a distinct procedure also attaining coverage, however, conditional on the training data. In the latter case, we prove a sharpness result showing that for certain classes of prediction problems, the prediction intervals cannot possibly be tightened. We verify the validity and performance of the methods via simulation studies and apply them to analyze real datasets.
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The limits of distribution-free conditional predictive inference
Abstract We consider the problem of distribution-free predictive inference, with the goal of producing predictive coverage guarantees that hold conditionally rather than marginally. Existing methods such as conformal prediction offer marginal coverage guarantees, where predictive coverage holds on average over all possible test points, but this is not sufficient for many practical applications where we would like to know that our predictions are valid for a given individual, not merely on average over a population. On the other hand, exact conditional inference guarantees are known to be impossible without imposing assumptions on the underlying distribution. In this work, we aim to explore the space in between these two and examine what types of relaxations of the conditional coverage property would alleviate some of the practical concerns with marginal coverage guarantees while still being possible to achieve in a distribution-free setting.
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- Award ID(s):
- 1654076
- NSF-PAR ID:
- 10253824
- Date Published:
- Journal Name:
- Information and Inference: A Journal of the IMA
- Volume:
- 10
- Issue:
- 2
- ISSN:
- 2049-8764
- Page Range / eLocation ID:
- 455 to 482
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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We develop fast distribution-free conformal prediction algorithms for obtaining multivalid coverage on exchangeable data in the batch setting. Multivalid coverage guarantees are stronger than marginal coverage guarantees in two ways: (1) They hold even conditional on group membership---that is, the target coverage level holds conditionally on membership in each of an arbitrary (potentially intersecting) group in a finite collection of regions in the feature space. (2) They hold even conditional on the value of the threshold used to produce the prediction set on a given example. In fact multivalid coverage guarantees hold even when conditioning on group membership and threshold value simultaneously. We give two algorithms: both take as input an arbitrary non-conformity score and an arbitrary collection of possibly intersecting groups , and then can equip arbitrary black-box predictors with prediction sets. Our first algorithm is a direct extension of quantile regression, needs to solve only a single convex minimization problem, and produces an estimator which has group-conditional guarantees for each group in . Our second algorithm is iterative, and gives the full guarantees of multivalid conformal prediction: prediction sets that are valid conditionally both on group membership and non-conformity threshold. We evaluate the performance of both of our algorithms in an extensive set of experiments.more » « less
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Estimating an individual treatment effect (ITE) is essential to personalized decision making. However, existing methods for estimating the ITE often rely on unconfoundedness, an assumption that is fundamentally untestable with observed data. To assess the robustness of individual-level causal conclusion with unconfoundedness, this article proposes a method for sensitivity analysis of the ITE, a way to estimate a range of the ITE under unobserved confounding. The method we develop quantifies unmeasured confounding through a marginal sensitivity model, and adapts the framework of conformal inference to estimate an ITE interval at a given confounding strength. In particular, we formulate this sensitivity analysis as a conformal inference problem under distribution shift, and we extend existing methods of covariate-shifted conformal inference to this more general setting. The resulting predictive interval has guaranteed nominal coverage of the ITE and provides this coverage with distribution-free and nonasymptotic guarantees.We evaluate the method on synthetic data and illustrate its application in an observational study. Supplementary materials for this article are available online.more » « less
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Estimating an individual treatment effect (ITE) is essential to personalized decision making. However, existing methods for estimating the ITE often rely on unconfoundedness, an assumption that is fundamentally untestable with observed data. To assess the robustness of individual-level causal conclusion with unconfoundedness, this article proposes a method for sensitivity analysis of the ITE, a way to estimate a range of the ITE under unobserved confounding. The method we develop quantifies unmeasured confounding through a marginal sensitivity model, and adapts the framework of conformal inference to estimate an ITE interval at a given confounding strength. In particular, we formulate this sensitivity analysis as a conformal inference problem under distribution shift, and we extend existing methods of covariate-shifted conformal inference to this more general setting. The resulting predictive interval has guaranteed nominal coverage of the ITE and provides this coverage with distribution-free and nonasymptotic guarantees.We evaluate the method on synthetic data and illustrate its application in an observational study. Supplementary materials for this article are available online.more » « less
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Summary The goal of expression quantitative trait loci (eQTL) studies is to identify the genetic variants that influence the expression levels of the genes in an organism. High throughput technology has made such studies possible: in a given tissue sample, it enables us to quantify the expression levels of approximately 20 000 genes and to record the alleles present at millions of genetic polymorphisms. While obtaining this data is relatively cheap once a specimen is at hand, obtaining human tissue remains a costly endeavor: eQTL studies continue to be based on relatively small sample sizes, with this limitation particularly serious for tissues as brain, liver, etc.—often the organs of most immediate medical relevance. Given the high-dimensional nature of these datasets and the large number of hypotheses tested, the scientific community has adopted early on multiplicity adjustment procedures. These testing procedures primarily control the false discoveries rate for the identification of genetic variants with influence on the expression levels. In contrast, a problem that has not received much attention to date is that of providing estimates of the effect sizes associated with these variants, in a way that accounts for the considerable amount of selection. Yet, given the difficulty of procuring additional samples, this challenge is of practical importance. We illustrate in this work how the recently developed conditional inference approach can be deployed to obtain confidence intervals for the eQTL effect sizes with reliable coverage. The procedure we propose is based on a randomized hierarchical strategy with a 2-fold contribution: (1) it reflects the selection steps typically adopted in state of the art investigations and (2) it introduces the use of randomness instead of data-splitting to maximize the use of available data. Analysis of the GTEx Liver dataset (v6) suggests that naively obtained confidence intervals would likely not cover the true values of effect sizes and that the number of local genetic polymorphisms influencing the expression level of genes might be underestimated.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1093/imaiai/iaaa017
