arXiv subjects

Hongyuan Cao

Publications and source records attributed to Hongyuan Cao.

13 recordsLinked to original sources

arXiv2026

Selective Inference in Growth Curve Models

Growth curve models are widely used in psychological research, and variable selection can help identify baseline characteristics associated with longitudinal heterogeneity. However, conventional inference after data-driven variable selection can be invalid because the same outcome data are used for both selection and inference. We develop a data-fission framework for post-selection inference in growth-curve models that separates the information used for selection and inference while retaining all participants in both stages through the addition and subtraction of Gaussian noise. The framework accommodates flexible variable-selection procedures and targets covariance-weighted linear projection parameters in the selected working model. It provides exact inference when the covariance structure is known, and we establish asymptotic validity under suitable regularity conditions when the covariance structure is estimated. Simulations show that the proposed method provides valid inference and improves efficiency over subject-level data splitting, whereas na\"ıve post-selection inference can be biased. An application to the Longitudinal Study of American Youth illustrates the proposed framework.

stat.ME↗

arXiv2026

Testing composite null hypotheses with high-dimensional dependent data: a computationally scalable FDR-controlling procedure

Testing composite null hypotheses is fundamental to many scientific applications, including mediation and replicability analyses, and becomes particularly challenging in high-throughput settings involving tens of thousands of features. Existing high-dimensional composite null hypotheses testing often ignores the dependence structure among features, leading to overly conservative or liberal results. To address this limitation, we develop a four-state hidden Markov model (HMM) for bivariate $p$-value sequences arising from two-study replicability analysis. This model captures local dependence among features and accommodates study-specific heterogeneity. Based on the HMM, we propose a multiple testing procedure that asymptotically controls the false discovery rate (FDR). Extending this framework to more than two studies is computationally intensive, with complexity growing exponentially in the number of studies $n$. To address this scalability issue, we introduce a novel e-value framework that reduces computational complexity to quadratic in $n$, while preserving asymptotic FDR control. Extensive simulations demonstrate that our method achieves higher power than existing approaches at the same FDR levels. When applied to genome-wide association studies (GWAS), the proposed approach identifies replicable SNP-level signals that are not detected at the same significance threshold by competing methods.

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arXiv2026

Heritability: A Counterfactual Perspective

Heritability is a central concept in the long-standing debate about nature versus nurture in biological and social sciences. However, existing notions of heritability are based on strong assumptions and do not use explicit causal models. We propose a new, counterfactual definition of heritability by adopting the potential outcomes model in causal inference. Our counterfactual heritability measures the importance of genetic inheritance by the average magnitude of difference between an individual with their hypothetical ``non-identical twin'' that is exposed to the exact same environment. We provide bounds on the counterfactual heritability that can, in principle, be computed from observational data. We then compare counterfactual heritability and its associated bounds with common notions of heritability in population-based studies, twin and sibling studies, and plant breeding experiments. Our results and comparisons highlight the importance of clarifying the causal structural assumptions and counterfactual comparisons in reasoning about heritability.

stat.AP↗

arXiv2026

A robust and powerful method for assessing replicability of high dimensional data

Identifying signals that replicate across multiple studies is essential for establishing robust scientific evidence, yet existing methods for high-dimensional replicability analysis either rely on restrictive modeling assumptions, are limited to two-study settings, or lack statistical power. We propose a general empirical Bayes framework for multi-study replicability analysis that jointly models summary-level $p$-values while explicitly accounting for between-study heterogeneity. Within each study, non-null $p$-value densities are estimated nonparametrically under monotonicity constraints, enabling flexible and tuning-free inference. For two studies, we develop a local false discovery rate (Lfdr) statistic for the composite null of non-replicability and establish identifiability, consistency, and a cubic-rate convergence of the nonparametric MLE, along with minimax optimality. Extending replicability analysis to $n$ studies typically requires estimating $2^n$ latent configurations, which is computationally infeasible. To address this challenge, we introduce a scalable pairwise rejection strategy that decomposes the exponentially large composite null into disjoint components, yielding linear complexity in the number of studies. We prove asymptotic FDR control under mild regularity conditions and show that Lfdr-based thresholding is power-optimal. Extensive simulations demonstrate that our method provides substantial power gains while maintaining valid FDR control, outperforming state-of-the-art alternatives across a wide range of scenarios. Applying our framework to East Asian- and European-ancestry genome-wide association studies of type 2 diabetes reveals replicable genetic associations that competing approaches fail to detect, illustrating the method's practical utility in large-scale biomedical research.

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arXiv2025

Regression analysis of multiplicative hazards model with time-dependent coefficient for sparse longitudinal covariates

We study the multiplicative hazards model with intermittently observed longitudinal covariates and time-varying coefficients. For such models, the existing ad hoc approach, such as the last value carried forward, is biased. We propose a kernel weighting approach to get an unbiased estimation of the non-parametric coefficient function and establish asymptotic normality for any fixed time point. Furthermore, we construct the simultaneous confidence band to examine the overall magnitude of the variation. Simulation studies support our theoretical predictions and show favorable performance of the proposed method. A data set from Alzheimer's Disease Neuroimaging Initiative study is used to illustrate our methodology.

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arXiv2024

Change point analysis with irregular signals

This paper considers the problem of testing and estimation of change point where signals after the change point can be highly irregular, which departs from the existing literature that assumes signals after the change point to be piece-wise constant or vary smoothly. A two-step approach is proposed to effectively estimate the location of the change point. The first step consists of a preliminary estimation of the change point that allows us to obtain unknown parameters for the second step. In the second step we use a new procedure to determine the position of the change point. We show that, under suitable conditions, the desirable $\mathcal{O}_P(1)$ rate of convergence of the estimated change point can be obtained. We apply our method to analyze the Baidu search index of COVID-19 related symptoms and find 8~December 2019 to be the starting date of the COVID-19 pandemic.

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arXiv2023

Kernel meets sieve: transformed hazards models with sparse longitudinal covariates

We study the transformed hazards model with time-dependent covariates observed intermittently for the censored outcome. Existing work assumes the availability of the whole trajectory of the time-dependent covariates, which is unrealistic. We propose to combine kernel-weighted log-likelihood and sieve maximum log-likelihood estimation to conduct statistical inference. The method is robust and easy to implement. We establish the asymptotic properties of the proposed estimator and contribute to a rigorous theoretical framework for general kernel-weighted sieve M-estimators. Numerical studies corroborate our theoretical results and show that the proposed method performs favorably over existing methods. Applying to a COVID-19 study in Wuhan illustrates the practical utility of our method.

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arXiv2023

Regression analysis of mixed sparse synchronous and asynchronous longitudinal covariates with varying-coefficient models

We consider varying-coefficient models for mixed synchronous and asynchronous longitudinal covariates, where asynchronicity refers to the misalignment of longitudinal measurement times within an individual. We propose three different methods of parameter estimation and inference. The first method is a one-step approach that estimates non-parametric regression functions for synchronous and asynchronous longitudinal covariates simultaneously. The second method is a two-step approach in which synchronous longitudinal covariates are regressed with the longitudinal response by centering the synchronous longitudinal covariates first and, in the second step, the residuals from the first step are regressed with asynchronous longitudinal covariates. The third method is the same as the second method except that in the first step, we omit the asynchronous longitudinal covariate and include a non-parametric intercept in the regression analysis of synchronous longitudinal covariates and the longitudinal response. We further construct simultaneous confidence bands for the non-parametric regression functions to quantify the overall magnitude of variation. Extensive simulation studies provide numerical support for the theoretical findings. The practical utility of the methods is illustrated on a dataset from the ADNI study.

stat.ME↗

arXiv2023

Regression analysis of longitudinal data with mixed synchronous and asynchronous longitudinal covariates

In linear models, omitting a covariate that is orthogonal to covariates in the model does not result in biased coefficient estimation. This in general does not hold for longitudinal data, where additional assumptions are needed to get unbiased coefficient estimation in addition to the orthogonality between omitted longitudinal covariates and longitudinal covariates in the model. We propose methods to mitigate the omitted variable bias under weaker assumptions. A two-step estimation procedure is proposed for inference about the asynchronous longitudinal covariates, when such covariates are observed. For mixed synchronous and asynchronous longitudinal covariates, we get parametric rate of convergence for the coefficient estimation of the synchronous longitudinal covariates by the two-step method. Extensive simulation studies provide numerical support for the theoretical findings. We illustrate the performance of our method on dataset from the Alzheimers Disease Neuroimaging Initiative study.

math.ST↗

arXiv2022

Scalable lipid droplet microarray fabrication, validation, and screening

High throughput screening of small molecules and natural products is costly, requiring significant amounts of time, reagents, and operating space. Although microarrays have proven effective in the miniaturization of screening for certain biochemical assays, such as nucleic acid hybridization or antibody binding, they are not widely used for drug discovery in cell culture due to the need for cells to internalize lipophilic drug candidates. Lipid droplet microarrays are a promising solution to this problem as they are capable of delivering lipophilic drugs to cells at dosages comparable to solution delivery. However, the scalablility of the array fabrication, assay validation, and screening steps has limited the utility of this approach. Here we demonstrate a scalable process for lipid droplet array fabrication, assay validation in cell culture, and drug screening. A nanointaglio printing process has been adapted for use with a printing press. The arrays are stabilized for immersion into aqueous solution using a vapor coating process. In addition to delivery of lipophilic compounds, we found that we are also able to encapsulate and deliver a water-soluble compound in this way. The arrays can be functionalized by extracellular matrix proteins such as collagen prior to cell culture as the mechanism for uptake is based on direct contact with the lipid delivery vehicles rather than diffusion of the drug out of the microarray spots. We demonstrate this method for delivery to 3 different cell types and the screening of 90 natural product extracts on a microarray covering an area of less than 0.1 cm2. The arrays are suitable for miniaturized screening, for instance in BSL-3 conditions where space is limited and for applications where cell numbers are limited, such as in functional precision medicine.

q-bio.BM↗

arXiv2021

Testing and estimation of clustered signals

We propose a change-point detection method for large scale multiple testing problems with data having clustered signals. Unlike the classic change-point setup, the signals can vary in size within a cluster. The clustering structure on the signals enables us to effectively delineate the boundaries between signal and non-signal segments. New test statistics are proposed for observations from one and/or multiple realizations. Their asymptotic distributions are derived. We also study the associated variance estimation problem. We allow the variances to be heteroscedastic in the multiple realization case, which substantially expands the applicability of the proposed method. Simulation studies demonstrate that the proposed approach has a favorable performance. Our procedure is applied to {an array based Comparative Genomic Hybridization (aCGH)} dataset.

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arXiv2021

Optimal False Discovery Rate Control for Large Scale Multiple Testing with Auxiliary Information

Large-scale multiple testing is a fundamental problem in high dimensional statistical inference. It is increasingly common that various types of auxiliary information, reflecting the structural relationship among the hypotheses, are available. Exploiting such auxiliary information can boost statistical power. To this end, we propose a framework based on a two-group mixture model with varying probabilities of being null for different hypotheses a priori, where a shape-constrained relationship is imposed between the auxiliary information and the prior probabilities of being null. An optimal rejection rule is designed to maximize the expected number of true positives when average false discovery rate is controlled. Focusing on the ordered structure, we develop a robust EM algorithm to estimate the prior probabilities of being null and the distribution of $p$-values under the alternative hypothesis simultaneously. We show that the proposed method has better power than state-of-the-art competitors while controlling the false discovery rate, both empirically and theoretically. Extensive simulations demonstrate the advantage of the proposed method. Datasets from genome-wide association studies are used to illustrate the new methodology.

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arXiv2011

Simultaneous critical values for $t$-tests in very high dimensions

This article considers the problem of multiple hypothesis testing using $t$-tests. The observed data are assumed to be independently generated conditional on an underlying and unknown two-state hidden model. We propose an asymptotically valid data-driven procedure to find critical values for rejection regions controlling the $k$-familywise error rate ($k$-FWER), false discovery rate (FDR) and the tail probability of false discovery proportion (FDTP) by using one-sample and two-sample $t$-statistics. We only require a finite fourth moment plus some very general conditions on the mean and variance of the population by virtue of the moderate deviations properties of $t$-statistics. A new consistent estimator for the proportion of alternative hypotheses is developed. Simulation studies support our theoretical results and demonstrate that the power of a multiple testing procedure can be substantially improved by using critical values directly, as opposed to the conventional $p$-value approach. Our method is applied in an analysis of the microarray data from a leukemia cancer study that involves testing a large number of hypotheses simultaneously.

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