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In social and behavioral sciences, the mediation test based on the indirect effect is an important topic. There are many methods to assess intervening variable effects. In this paper, we focus on the difference method and the product method in mediation models. Firstly, we analyze the regression functions in the simple mediation model, and provide an expectation-consistent condition. We further show that the difference estimator and the product estimator are numerically equivalent based on the least-squares regression regardless of the error distribution. Secondly, we generalize the equivalence result to the three-path model and the multiple mediators model, and prove a general equivalence result in a class of restricted linear mediation models. Thirdly, we investigate the empirical distributions of the indirect effect estimators in the simple mediation model by simulations, and show that the indirect effect estimators are normally distributed as long as one multiplicand of the product estimator is large. Finally, we introduce some popular R packages for mediation analysis and also provide some useful suggestions on how to correctly conduct mediation analysis., Author(s): WenWu Wang [sup.1] [sup.2] , Ping Yu [sup.3] , Yuejin Zhou [sup.4] , Tiejun Tong [sup.5] , Zhonghua Liu [sup.2] Author Affiliations: (1) grid.412638.a, 0000 0001 0227 8151, School [...]

A reference interval provides a basis for physicians to determine whether a measurement is typical of a healthy individual. It can be interpreted as a prediction interval for a new individual from the overall population. However, a reference interval based on a single study may not be representative of the broader population. Meta-analysis can provide a general reference interval based on the overall population by combining results from multiple studies. Methods for estimating the reference interval from a random effects meta-analysis have been recently proposed to incorporate the within and between-study variation, but a random effects model may give imprecise estimates of the between-study variation with only few studies. In addition, the normal distribution of underlying study-specific means, and equal within-study variance assumption in these methods may be inappropriate in some settings. In this article, we aim to estimate the reference interval based on the fixed effects model assuming study effects are unrelated, which is useful for a meta-analysis with only a few studies (e.g., [less than or equal to]5). We propose a mixture distribution method only assuming parametric distributions (e.g., normal) for individuals within each study and integrating them to form the overall population distribution. This method is compared to an empirical method only assuming a parametric overall population distribution. Simulation studies have shown that both methods can estimate a reference interval with coverage close to the targeted value (i.e., 95%). Meta-analyses of women daytime urination frequency and frontal subjective postural vertical measurements are reanalyzed to demonstrate the application of our methods.

When reporting the results of clinical studies, some researchers may choose the five-number summary (including the sample median, the first and third quartiles, and the minimum and maximum values) rather than the sample mean and standard deviation (SD), particularly for skewed data. For these studies, when included in a meta-analysis, it is often desired to convert the five-number summary back to the sample mean and SD. For this purpose, several methods have been proposed in the recent literature and they are increasingly used nowadays. In this article, we propose to further advance the literature by developing a smoothly weighted estimator for the sample SD that fully utilizes the sample size information. For ease of implementation, we also derive an approximation formula for the optimal weight, as well as a shortcut formula for the sample SD. Numerical results show that our new estimator provides a more accurate estimate for normal data and also performs favorably for non-normal data. Together with the optimal sample mean estimator in Luo et al., our new methods have dramatically improved the existing methods for data transformation, and they are capable to serve as "rules of thumb" in meta-analysis for studies reported with the five-number summary. Finally for practical use, an Excel spreadsheet and an online calculator are also provided for implementing our optimal estimators.

Summary: The binomial proportion is a classic parameter with many applications and has also been extensively studied in the literature. By contrast, the reciprocal of the binomial proportion, or the inverse proportion, is often overlooked, even though it also plays an important role in various fields. To estimate the inverse proportion, the maximum likelihood method fails to yield a valid estimate when there is no successful event in the Bernoulli trials. To overcome this zero‐event problem, several methods have been introduced in the previous literature. Yet to the best of our knowledge, there is little work on a theoretical comparison of the existing estimators. In this paper, we first review some commonly used estimators for the inverse proportion, study their asymptotic properties, and then develop a new estimator that aims to eliminate the estimation bias. We further conduct Monte Carlo simulations to compare the finite sample performance of the existing and new estimators, and also apply them to handle the zero‐event problem in a meta‐analysis of COVID‐19 data for assessing the relative risks of physical distancing on the infection of coronavirus. [ABSTRACT FROM AUTHOR]

Causal mediation analysis is a popular approach for investigating whether the effect of an exposure on an outcome is through a mediator to better understand the underlying causal mechanism. In recent literature, mediation analysis with multiple mediators has been proposed for continuous and dichotomous outcomes. In contrast, methods for mediation analysis for an ordinal outcome are still underdeveloped. In this paper, we first review mediation analysis methods with a continuous mediator for an ordinal outcome and then develop mediation analysis with a binary mediator for an ordinal outcome. We further consider multiple mediators for an ordinal outcome in the counterfactual framework and provide identification assumptions for identifying the mediation effects. Under the identification assumptions, we propose a regression-based method to estimate the mediation effects through multiple mediators while allowing the presence of exposure-mediator interactions. The closed-form expressions of mediation effects are also obtained for three scenarios: multiple continuous mediators, multiple binary mediators, and multiple mixed mediators. We conduct simulation studies to assess the finite sample performance of our new methods and present the biases, standard errors, and confidence intervals to demonstrate that our proposed estimators perform well in a wide range of practical settings. Finally, we apply our proposed methods to assess the mediation effects of candidate DNA methylation CpG sites in the causal pathway from socioeconomic index to body mass index. [ABSTRACT FROM AUTHOR]

The Sharpe ratio function is a commonly used risk/return measure in financial econometrics. To estimate this function, most existing methods take a two-step procedure that first estimates the mean and volatility functions separately and then applies the plug-in method. In this paper, we propose a direct method via local maximum likelihood to simultaneously estimate the Sharpe ratio function and the negative log-volatility function as well as their derivatives. We establish the joint limiting distribution of the proposed estimators, and moreover extend the proposed method to estimate the multivariate Sharpe ratio function. We also evaluate the numerical performance of the proposed estimators through simulation studies, and compare them with existing methods. Finally, we apply the proposed method to the three-month US Treasury bill data and that captures a well-known covariate-dependent effect on the Sharpe ratio. [ABSTRACT FROM AUTHOR]

For gene expression data analysis, an important task is to identify genes that are differentially expressed between two or more groups. Nevertheless, as biological experiments are often measured with a relatively small number of samples, how to accurately estimate the variances of gene expression becomes a challenging issue. To tackle this problem, we introduce a regularized t$$ t $$ distribution and derive its statistical properties including the probability density function and the moment generating function. The noncentral regularized t$$ t $$ distribution is also introduced for computing the statistical power of hypothesis testing. For practical applications, we apply the regularized t$$ t $$ distribution to establish the null distribution of the regularized t$$ t $$ statistic, and then formulate it as a regularized t$$ t $$‐test for detecting the differentially expressed genes. Simulation studies and real data analysis show that our regularized t$$ t $$‐test performs much better than the Bayesian t$$ t $$‐test in the "limma" package, in particular when the sample sizes are small. [ABSTRACT FROM AUTHOR]

This paper studies the estimation and inference of a partially linear varying coefficient spatial autoregressive panel data model with fixed effects. By means of the basis function approximations and the instrumental variable methods, we propose a two-stage least squares estimation procedure to estimate the unknown parametric and nonparametric components, and meanwhile study the asymptotic properties of the proposed estimators. Together with an empirical log-likelihood ratio function for the regression parameters, which follows an asymptotic chi-square distribution under some regularity conditions, we can further construct accurate confidence regions for the unknown parameters. Simulation studies show that the finite sample performance of the proposed methods are satisfactory in a wide range of settings. Lastly, when applied to the public capital data, our proposed model can also better reflect the changing characteristics of the US economy compared to the parametric panel data models. [ABSTRACT FROM AUTHOR]

For clinical studies with continuous outcomes, when the data are potentially skewed, researchers may choose to report the whole or part of the five-number summary (the sample median, the first and third quartiles, and the minimum and maximum values) rather than the sample mean and standard deviation. In the recent literature, it is often suggested to transform the five-number summary back to the sample mean and standard deviation, which can be subsequently used in a meta-analysis. However, if a study contains skewed data, this transformation and hence the conclusions from the meta-analysis are unreliable. Therefore, we introduce a novel method for detecting the skewness of data using only the five-number summary and the sample size, and meanwhile, propose a new flow chart to handle the skewed studies in a different manner. We further show by simulations that our skewness tests are able to control the type I error rates and provide good statistical power, followed by a simulated meta-analysis and a real data example that illustrate the usefulness of our new method in meta-analysis and evidence-based medicine. [ABSTRACT FROM AUTHOR]

Abstract Chromatin immunoprecipitation followed by massively parallel next-generation sequencing (ChIP-seq) is a valuable experimental strategy for assaying protein-DNA interaction over the whole genome. Many computational tools have been designed to find the peaks of the signals corresponding to protein binding sites. In this paper, three computational methods, ChIP-seq processing pipeline (spp), PeakSeq and CisGenome, used in ChIP-seq data analysis are reviewed. There is also a comparison of how they agree and disagree on finding peaks using the publically available Signal Transducers and Activators of Transcription protein 1 (STAT1) and RNA polymerase II (PolII) datasets with corresponding negative controls.

Abstract High-throughput RNA sequencing is rapidly emerging as a favourite method for gene expression studies. We review three software packages -- edgeR, DEGseq and baySeq -- from Bioconductor http://bioconductor.org for analysing RNA-sequencing data. We focus on three aspects: normalisation, statistical models and the testing employed on these methods. We also discuss the advantages and limitations of these software packages.

Abstract Breast cancer tumours among African Americans are usually more aggressive than those found in Caucasian populations. African-American patients with breast cancer also have higher mortality rates than Caucasian women. A better understanding of the disease aetiology of these breast cancers can help to improve and develop new methods for cancer prevention, diagnosis and treatment. The main goal of this project was to identify genes that help differentiate between oestrogen receptor-positive and -negative samples among a small group of African-American patients with breast cancer. Breast cancer microarrays from one of the largest genomic consortiums were analysed using 13 African-American and 201 Caucasian samples with oestrogen receptor status. We used a shrinkage-based classification method to identify genes that were informative in discriminating between oestrogen receptor-positive and -negative samples. Subset analysis and permutation were performed to obtain a set of genes unique to the African-American population. We identified a set of 156 probe sets, which gave a misclassification rate of 0.16 in distinguishing between oestrogen receptor-positive and -negative patients. The biological relevance of our findings was explored through literature-mining techniques and pathway mapping. An independent dataset was used to validate our findings and we found that the top ten genes mapped onto this dataset gave a misclassification rate of 0.15. The described method allows us best to utilise the information available from small sample size microarray data in the context of ethnic minorities.