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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., Comment: 18 pages, 6 figures

Replicability is the cornerstone of scientific research. We study the replicability of data from high-throughput experiments, where tens of thousands of features are examined simultaneously. Existing replicability analysis methods either ignore the dependence among features or impose strong modelling assumptions, producing overly conservative or overly liberal results. Based on $p$-values from two studies, we use a four-state hidden Markov model to capture the structure of local dependence. Our method effectively borrows information from different features and studies while accounting for dependence among features and heterogeneity across studies. We show that the proposed method has better power than competing methods while controlling the false discovery rate, both empirically and theoretically. Analyzing datasets from genome-wide association studies reveals new biological insights that otherwise cannot be obtained by using existing methods.

We study the multiplicative hazards model with intermittently observed longitudinal covariates and time-varying coefficients. For such models, the existing {\it 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 cerebral infarction is used to illustrate our methodology.

Identifying replicable signals across different studies provides stronger scientific evidence and more powerful inference. Existing literature on high dimensional applicability analysis either imposes strong modeling assumptions or has low power. We develop a powerful and robust empirical Bayes approach for high dimensional replicability analysis. Our method effectively borrows information from different features and studies while accounting for heterogeneity. We show that the proposed method has better power than competing methods while controlling the false discovery rate, both empirically and theoretically. Analyzing datasets from the genome-wide association studies reveals new biological insights that otherwise cannot be obtained by using existing methods.

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.

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.

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., Comment: 57 pages, 5 figures

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., Comment: 13 pages, 9 figures

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.

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.

Contamination of water resources with pathogenic microorganisms excreted in human feces is a worldwide public health concern. Surveillance of fecal contamination is commonly performed by routine monitoring for a single type or a few types of microorganism(s). To design a feasible routine for periodic monitoring and to control risks of exposure to pathogens, reliable statistical algorithms for inferring correlations between concentrations of microorganisms in water need to be established. Moreover, because pathogens are often present in low concentrations, some contaminations are likely to be under a detection limit. This yields a pairwise left-censored dataset and complicates computation of correlation coefficients. Errors of correlation estimation can be smaller if undetected values are imputed better. To obtain better imputations, we utilize side information and develop a new technique, the \emph{asymmetric Tobit model} which is an extension of the Tobit model so that domain knowledge can be exploited effectively when fitting the model to a censored dataset. The empirical results demonstrate that imputation with domain knowledge is effective for this task.

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., Comment: Published in at http://dx.doi.org/10.3150/10-BEJ272 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)