arXiv subjects

Prabrisha Rakshit

Publications and source records attributed to Prabrisha Rakshit.

5 recordsLinked to original sources

arXiv2025

Adaptive Proximal Causal Inference with Some Invalid Proxies

Proximal causal inference (PCI) is a recently proposed framework to identify and estimate the causal effect of an exposure on an outcome in the presence of hidden confounders, using observed proxies. Specifically, PCI relies on two types of proxies: a treatment-inducing confounding proxy, related to the outcome only through its association with unmeasured confounders (given treatment and covariates), and an outcome-inducing confounding proxy, related to the treatment only through such association (given covariates). These proxies must satisfy stringent exclusion restrictions - namely, the treatment proxy must not affect the outcome, and the outcome proxy must not be affected by the treatment. To improve identification and potentially efficiency, multiple proxies are often used, raising concerns about bias from exclusion violations. To address this, we introduce necessary and sufficient conditions for identifying causal effects in the presence of many proxies, some potentially invalid. Under a canonical proximal linear structural equations model, we propose a LASSO-based median estimator that jointly selects valid proxies and estimates the causal effect, with theoretical guarantees. Recognizing LASSO's limitations in consistently selecting valid treatment proxies, we develop an adaptive LASSO-based estimator with differential penalization. We show that it is root-n consistent and yields valid confidence intervals when a valid outcome proxy is available. We also extend the approach to settings with many potentially invalid outcome proxies. Theoretical results are supported by simulations and an application assessing the effect of right heart catheterization on 30-day survival in ICU patient.

stat.ME↗

arXiv2024

Statistical Inference in High-dimensional Poisson Regression with Applications to Mediation Analysis

Large-scale datasets with count outcome variables are widely present in various applications, and the Poisson regression model is among the most popular models for handling count outcomes. This paper considers the high-dimensional sparse Poisson regression model and proposes bias-corrected estimators for both linear and quadratic transformations of high-dimensional regression vectors. We establish the asymptotic normality of the estimators, construct asymptotically valid confidence intervals, and conduct related hypothesis testing. We apply the devised methodology to high-dimensional mediation analysis with count outcome, with particular application of testing for the existence of interaction between the treatment variable and high-dimensional mediators. We demonstrate the proposed methods through extensive simulation studies and application to real-world epigenetic data.

stat.ME↗

arXiv2024

Local Effects of Continuous Instruments without Positivity

Instrumental variables are a popular study design for the estimation of treatment effects in the presence of unobserved confounders. In the canonical instrumental variables design, the instrument is a binary variable. In many settings, however, the instrument is continuous. Standard estimation methods can be applied with continuous instruments, but they require strong assumptions. While recent work has introduced more flexible estimation approaches, these methods require a positivity assumption that is implausible in many applications. We derive a novel family of causal estimands using stochastic dynamic interventions that allows a range of intervention distributions that are continuous with respect to the observed distribution of the instrument. These estimands focus on a specific local effect but do not require a positivity assumption. Next, we develop doubly robust estimators for these estimands that allow for estimation of the nuisance functions via nonparametric estimators. We use empirical process theory and sample splitting to derive asymptotic properties of the proposed estimators under weak conditions. In addition, we derive methods for profiling the principal strata as well as a method of sensitivity analysis. We evaluate our methods via simulation and demonstrate their feasibility using an application on the effectiveness of surgery for specific emergency conditions.

stat.ME↗

arXiv2023

SIHR: Statistical Inference in High-Dimensional Linear and Logistic Regression Models

We introduce the R package \CRANpkg{SIHR} for statistical inference in high-dimensional generalized linear models with continuous and binary outcomes. The package provides functionalities for constructing confidence intervals and performing hypothesis tests for low-dimensional objectives in both one-sample and two-sample regression settings. We illustrate the usage of \CRANpkg{SIHR} through numerical examples and present real data applications to demonstrate the package's performance and practicality.

stat.CO↗

arXiv2021

Inference for the Case Probability in High-dimensional Logistic Regression

Labeling patients in electronic health records with respect to their statuses of having a disease or condition, i.e. case or control statuses, has increasingly relied on prediction models using high-dimensional variables derived from structured and unstructured electronic health record data. A major hurdle currently is a lack of valid statistical inference methods for the case probability. In this paper, considering high-dimensional sparse logistic regression models for prediction, we propose a novel bias-corrected estimator for the case probability through the development of linearization and variance enhancement techniques. We establish asymptotic normality of the proposed estimator for any loading vector in high dimensions. We construct a confidence interval for the case probability and propose a hypothesis testing procedure for patient case-control labelling. We demonstrate the proposed method via extensive simulation studies and application to real-world electronic health record data.

stat.ME↗