arXiv subjects

Nima S. Hejazi

Publications and source records attributed to Nima S. Hejazi.

21 records · Page 2Linked to original sources

arXiv2020

Non-parametric efficient causal mediation with intermediate confounders

Interventional effects for mediation analysis were proposed as a solution to the lack of identifiability of natural (in)direct effects in the presence of a mediator-outcome confounder affected by exposure. We present a theoretical and computational study of the properties of the interventional (in)direct effect estimands based on the efficient influence fucntion (EIF) in the non-parametric statistical model. We use the EIF to develop two asymptotically optimal, non-parametric estimators that leverage data-adaptive regression for estimation of the nuisance parameters: a one-step estimator and a targeted minimum loss estimator. A free and open source \texttt{R} package implementing our proposed estimators is made available on GitHub. We further present results establishing the conditions under which these estimators are consistent, multiply robust, $n^{1/2}$-consistent and efficient. We illustrate the finite-sample performance of the estimators and corroborate our theoretical results in a simulation study. We also demonstrate the use of the estimators in our motivating application to elucidate the mechanisms behind the unintended harmful effects that a housing intervention had on adolescent girls' risk behavior.

stat.ME↗

arXiv2020

Efficient nonparametric inference on the effects of stochastic interventions under two-phase sampling, with applications to vaccine efficacy trials

The advent and subsequent widespread availability of preventive vaccines has altered the course of public health over the past century. Despite this success, effective vaccines to prevent many high-burden diseases, including HIV, have been slow to develop. Vaccine development can be aided by the identification of immune response markers that serve as effective surrogates for clinically significant infection or disease endpoints. However, measuring immune response marker activity is often costly, which has motivated the usage of two-phase sampling for immune response evaluation in clinical trials of preventive vaccines. In such trials, the measurement of immunological markers is performed on a subset of trial participants, where enrollment in this second phase is potentially contingent on the observed study outcome and other participant-level information. We propose nonparametric methodology for efficiently estimating a counterfactual parameter that quantifies the impact of a given immune response marker on the subsequent probability of infection. Along the way, we fill in theoretical gaps pertaining to the asymptotic behavior of nonparametric efficient estimators in the context of two-phase sampling, including a multiple robustness property enjoyed by our estimators. Techniques for constructing confidence intervals and hypothesis tests are presented, and an open source software implementation of the methodology, the txshift R package, is introduced. We illustrate the proposed techniques using data from a recent preventive HIV vaccine efficacy trial.

stat.ME↗

arXiv2017

Data-adaptive statistics for multiple hypothesis testing in high-dimensional settings

Current statistical inference problems in areas like astronomy, genomics, and marketing routinely involve the simultaneous testing of thousands -- even millions -- of null hypotheses. For high-dimensional multivariate distributions, these hypotheses may concern a wide range of parameters, with complex and unknown dependence structures among variables. In analyzing such hypothesis testing procedures, gains in efficiency and power can be achieved by performing variable reduction on the set of hypotheses prior to testing. We present in this paper an approach using data-adaptive multiple testing that serves exactly this purpose. This approach applies data mining techniques to screen the full set of covariates on equally sized partitions of the whole sample via cross-validation. This generalized screening procedure is used to create average ranks for covariates, which are then used to generate a reduced (sub)set of hypotheses, from which we compute test statistics that are subsequently subjected to standard multiple testing corrections. The principal advantage of this methodology lies in its providing valid statistical inference without the \textit{a priori} specifying which hypotheses will be tested. Here, we present the theoretical details of this approach, confirm its validity via a simulation study, and exemplify its use by applying it to the analysis of data on microRNA differential expression.

stat.ME↗