Single-molecule fluorescence microscopy probes nanoscale, subcellular biology in real time. Existing methods for analyzing single-particle tracking data provide dynamical information, but can suffer from supervisory biases and high uncertainties. Here, we develop a method for the case of multiple interconverting species undergoing free diffusion and introduce a new approach to analyzing single-molecule trajectories: the Single-Molecule Analysis by Unsupervised Gibbs sampling (SMAUG) algorithm, which uses nonparametric Bayesian statistics to uncover the whole range of information contained within a single-particle trajectory dataset. Even in complex systems where multiple biological states lead to a number of observed mobility states, SMAUG provides the number of mobility states, the average diffusion coefficient of single molecules in that state, the fraction of single molecules in that state, the localization noise, and the probability of transitioning between two different states. In this paper, we provide the theoretical background for the SMAUG analysis and then we validate the method using realistic simulations of single-particle trajectory datasets as well as experiments on a controlled in vitro system. Finally, we demonstrate SMAUG on real experimental systems in both prokaryotes and eukaryotes to measure the motions of the regulatory protein TcpP in Vibrio cholerae and the dynamics of the B-cell receptor antigen response pathway in lymphocytes. Overall, SMAUG provides a mathematically rigorous approach to measuring the real-time dynamics of molecular interactions in living cells.

Genetic prediction of complex traits has great promise for disease prevention, monitoring, and treatment. The development of accurate risk prediction models is hindered by the wide diversity of genetic architecture across different traits, limited access to individual level data for training and parameter tuning, and the demand for computational resources. To overcome the limitations of the most existing methods that make explicit assumptions on the underlying genetic architecture and need a separate validation data set for parameter tuning, we develop a summary statistics-based nonparametric method that does not rely on validation datasets to tune parameters. In our implementation, we refine the commonly used likelihood assumption to deal with the discrepancy between summary statistics and external reference panel. We also leverage the block structure of the reference linkage disequilibrium matrix for implementation of a parallel algorithm. Through simulations and applications to twelve traits, we show that our method is adaptive to different genetic architectures, statistically robust, and computationally efficient. Our method is available at https://github.com/eldronzhou/SDPR.

Network representations of biological systems are widespread and reconstructing unknown networks from data is a focal problem for computational biologists. For example, the series of biochemical reactions in a metabolic pathway can be represented as a network, with nodes corresponding to metabolites and edges linking reactants to products. In a different context, regulatory relationships among genes are commonly represented as directed networks with edges pointing from influential genes to their targets. Reconstructing such networks from data is a challenging problem receiving much attention in the literature. There is a particular need for approaches tailored to time-series data and not reliant on direct intervention experiments, as the former are often more readily available. In this paper, we introduce an approach to reconstructing directed networks based on dynamic systems models. Our approach generalizes commonly used ODE models based on linear or nonlinear dynamics by extending the functional class for the functions involved from parametric to nonparametric models. Concomitantly we limit the complexity by imposing an additive structure on the estimated slope functions. Thus the submodel associated with each node is a sum of univariate functions. These univariate component functions form the basis for a novel coupling metric that we define in order to quantify the strength of proposed relationships and hence rank potential edges. We show the utility of the method by reconstructing networks using simulated data from computational models for the glycolytic pathway of Lactocaccus Lactis and a gene network regulating the pluripotency of mouse embryonic stem cells. For purposes of comparison, we also assess reconstruction performance using gene networks from the DREAM challenges. We compare our method to those that similarly rely on dynamic systems models and use the results to attempt to disentangle the distinct roles of linearity, sparsity, and derivative estimation.

Our work is motivated by an interest in constructing a protein-protein interaction network that captures key features associated with Parkinson's disease. While there is an abundance of subnetwork construction methods available, it is often far from obvious which subnetwork is the most suitable starting point for further investigation.

Spatial scan statistics are widely used for spatial cluster detection, and several parametric models exist. For continuous data, a normal-based scan statistic can be used. However, the performance of the model has not been fully evaluated for non-normal data.

I provide a selective review of the literature on the multiple testing problem in fMRI. By drawing connections with the older modalities, PET in particular, and how software implementations have tracked (or lagged behind) theoretical developments, my narrative aims to give the methodological researcher a historical perspective on this important aspect of fMRI data analysis.

An important inferential task in functional linear models is to test the dependence between the response and the functional predictor. The traditional testing theory was constructed based on the functional principle component analysis which requires estimating the covariance operator of the functional predictor. Due to the intrinsic high-dimensionality of functional data, the sample is often not large enough to allow accurate estimation of the covariance operator and hence causes the follow-up test underpowered. To avoid the expensive estimation of the covariance operator, we propose a nonparametric method called Functional Linear models with U-statistics TEsting (FLUTE) to test the dependence assumption. We show that the FLUTE test is more powerful than the current benchmark method (Kokoszka P,2008; Patilea V,2016) in the small or moderate sample case. We further prove the asymptotic normality of our test statistic under both the null hypothesis and a local alternative hypothesis. The merit of our method is demonstrated by both simulation studies and real examples.

With recent development in sequencing technology, a large number of genome-wide DNA methylation studies have generated massive amounts of bisulfite sequencing data. The analysis of DNA methylation patterns helps researchers understand epigenetic regulatory mechanisms. Highly variable methylation patterns reflect stochastic fluctuations in DNA methylation, whereas well-structured methylation patterns imply deterministic methylation events. Among these methylation patterns, bipolar patterns are important as they may originate from allele-specific methylation (ASM) or cell-specific methylation (CSM).

Detecting the targets of drugs and other molecules in intact cellular contexts is a major objective in drug discovery and in biology more broadly. Thermal proteome profiling (TPP) pursues this aim at proteome-wide scale by inferring target engagement from its effects on temperature-dependent protein denaturation. However, a key challenge of TPP is the statistical analysis of the measured melting curves with controlled false discovery rates at high proteome coverage and detection power. We present nonparametric analysis of response curves (NPARC), a statistical method for TPP based on functional data analysis and nonlinear regression. We evaluate NPARC on five independent TPP data sets and observe that it is able to detect subtle changes in any region of the melting curves, reliably detects the known targets, and outperforms a melting point-centric, single-parameter fitting approach in terms of specificity and sensitivity. NPARC can be combined with established analysis of variance (ANOVA) statistics and enables flexible, factorial experimental designs and replication levels. An open source software implementation of NPARC is provided.

The genetic basis of many common human diseases is expected to be highly heterogeneous, with multiple causative loci and multiple alleles at some of the causative loci. Analyzing the association of disease with one genetic marker at a time can have weak power, because of relatively small genetic effects and the need to correct for multiple testing. Testing the simultaneous effects of multiple markers by multivariate statistics might improve power, but they too will not be very powerful when there are many markers, because of the many degrees of freedom. To overcome some of the limitations of current statistical methods for case-control studies of candidate genes, we develop a new class of nonparametric statistics that can simultaneously test the association of multiple markers with disease, with only a single degree of freedom. Our approach, which is based on U-statistics, first measures a score over all markers for pairs of subjects and then compares the averages of these scores between cases and controls. Genetic scoring for a pair of subjects is measured by a "kernel" function, which we allow to be fairly general. However, we provide guidelines on how to choose a kernel for different types of genetic effects. Our global statistic has the advantage of having only one degree of freedom and achieves its greatest power advantage when the contrasts of average genotype scores between cases and controls are in the same direction across multiple markers. Simulations illustrate that our proposed methods have the anticipated type I-error rate and that they can be more powerful than standard methods. Application of our methods to a study of candidate genes for prostate cancer illustrates their potential merits, and offers guidelines for interpretation.

Estimation and inferences for the hemodynamic response functions (HRF) using multi-subject fMRI data are considered. Within the context of the General Linear Model, two new nonparametric estimators for the HRF are proposed. The first is a kernel-smoothed estimator, which is used to construct hypothesis tests on the entire HRF curve, in contrast to only summaries of the curve as in most existing tests. To cope with the inherent large data variance, we introduce a second approach which imposes Tikhonov regularization on the kernel-smoothed estimator. An additional bias-correction step, which uses multi-subject averaged information, is introduced to further improve efficiency and reduce the bias in estimation for individual HRFs. By utilizing the common properties of brain activity shared across subjects, this is the main improvement over the standard methods where each subject's data is usually analyzed independently. A fast algorithm is also developed to select the optimal regularization and smoothing parameters. The proposed methods are compared with several existing regularization methods through simulations. The methods are illustrated by an application to the fMRI data collected under a psychology design employing the Monetary Incentive Delay (MID) task.

MicroRNA is a set of small RNA molecules mediating gene expression at post-transcriptional/translational levels. Most of well-established high throughput discovery platforms, such as microarray, real time quantitative PCR, and sequencing, have been adapted to study microRNA in various human diseases. The total number of microRNAs in humans is approximately 1,800, which challenges some analytical methodologies requiring a large number of entries. Unlike messenger RNA, the majority of microRNA (>60%) maintains relatively low abundance in the cells. When analyzed using microarray, the signals of these low-expressed microRNAs are influenced by other non-specific signals including the background noise. It is crucial to distinguish the true microRNA signals from measurement errors in microRNA array data analysis. In this study, we propose a novel measurement error model-based normalization method and differentially-expressed microRNA detection method for microRNA profiling data acquired from locked nucleic acids (LNA) microRNA array. Compared with some existing methods, the proposed method significantly improves the detection among low-expressed microRNAs when assessed by quantitative real-time PCR assay.

In an attempt to identify similarities between methods for estimating a mean function with different types of response or observation processes, we explore a general theoretical framework for nonparametric estimation of the mean function of a response process subject to incomplete observations. Special cases of the response process include quantitative responses and discrete state processes such as survival processes, counting processes and alternating binary processes. The incomplete data are assumed to arise from a general response-independent observation process, which includes right-censoring, interval censoring, periodic observation, and mixtures of these as special cases. We explore two criteria for defining nonparametric estimators, one based on the sample mean of available data and the other inspired by the construction of Kaplan-Meier (or product-limit) estimator [J. Am. Statist. Assoc. 53 (1958) 457] for right-censored survival data. We show that under regularity conditions the estimated mean functions resulting from both criteria are consistent and converge weakly to Gaussian processes, and provide consistent estimators of their covariance functions. We then evaluate these general criteria for specific responses and observation processes, and show how they lead to familiar estimators for some response and observation processes and new estimators for others. We illustrate the latter with data from an recently completed AIDS clinical trial.

Recently, in genetic epidemiology, Mendelian randomization (MR) has become a popular approach to estimate causal exposure effects by using single nucleotide polymorphisms from genome-wide association studies (GWAS) as instruments. The most popular type of MR study, a two-sample summary-data MR study, relies on having summary statistics from two independent GWAS and using parametric methods for estimation. However, little is understood about using a nonparametric bound-based analysis, a popular approach in traditional instrumental variables frameworks, to study causal effects in two-sample MR. In this article, we explore using a nonparametric, bound-based analysis in two-sample MR studies, focusing primarily on implications for practice. We also propose a framework to assess how likely one can obtain more informative bounds if we used a different MR design, notably a one-sample MR design. We conclude by demonstrating our findings through two real data analyses concerning the causal effect of smoking on lung cancer and the causal effect of high cholesterol on heart attacks. Overall, our results suggest that while a bound-based analysis may be appealing due to its nonparametric nature, it is far more conservative in two-sample settings than in one-sample settings to get informative bounds on the causal exposure effect.

Drop plate technique has a priority and preference compared with the spread plate procedure, because of less time, quantity of media, effort requirement, little incubator space, and less labor intensive. The objective of this research was to compare the accuracy and fidelity of drop plate method vs. spread plate method by parametric and nonparametric statistical tests. For bacterial enumeration by drop and spread plate methods, successive dilutions of second subculture of Lactobacillus casei and Salmonella Typhimurium were transferred to selective agar. The correlation of agreement between both methods was evaluated by using statistical proofs. Results showed that mean value (parametric unpaired t-test) comparison at 95 percent confidence level did not reject null hypothesis, which it meant that the equality of the mean data could not be ruled out. Nonparametric method was used because of approximately Gaussian pattern of data distribution. For this purpose, Mann-Whitney test (equivalent nonparametric t-test) was used. It meant that the equality of medians obtained from two methods were similar. Spearman's rho correlation coefficient (r) via both methods due to data distribution patterns for enumeration of S. Typhimurium and L. casei were 0.62 and 0.87, respectively; which represented moderately strong and strong relationship between two methods, respectively. Besides, there was a significant and strong positive correlation (p < 0.001) between spread and drop plate procedures. Because of aforementioned reasons, the spread plate method can be replaced by drop plate method.

Given a dataset of careers and incomes, how large a difference of incomes between any pair of careers would be? Given a dataset of travel time records, how long do we need to spend more when choosing a public transportation mode A instead of B to travel? In this paper, we propose a framework that is able to infer orders of categories as well as magnitudes of difference of real numbers between each pair of categories using an estimation statistics framework. Our framework not only reports whether an order of categories exists, but it also reports magnitudes of difference of each consecutive pair of categories in the order. In a large dataset, our framework is scalable well compared with existing frameworks. The proposed framework has been applied to two real-world case studies: 1) ordering careers by incomes from 350,000 households living in Khon Kaen province, Thailand, and 2) ordering sectors by closing prices from 1,060 companies in NASDAQ stock market between years 2000 and 2016. The results of careers ordering demonstrate income inequality among different careers. The stock market results illustrate dynamics of sector domination that can change over time. Our approach is able to be applied in any research area that has category-real pairs. Our proposed Dominant-Distribution Network provides a novel approach to gain new insight of analyzing category orders. A software of this framework is available for researchers or practitioners in an R CRAN package: EDOIF.

We discuss the identification of features that are associated with an outcome in RNA-Sequencing (RNA-Seq) and other sequencing-based comparative genomic experiments. RNA-Seq data takes the form of counts, so models based on the normal distribution are generally unsuitable. The problem is especially challenging because different sequencing experiments may generate quite different total numbers of reads, or 'sequencing depths'. Existing methods for this problem are based on Poisson or negative binomial models: they are useful but can be heavily influenced by 'outliers' in the data. We introduce a simple, non-parametric method with resampling to account for the different sequencing depths. The new method is more robust than parametric methods. It can be applied to data with quantitative, survival, two-class or multiple-class outcomes. We compare our proposed method to Poisson and negative binomial-based methods in simulated and real data sets, and find that our method discovers more consistent patterns than competing methods.

Among the various statistical methods for identifying gene⁻gene interactions in qualitative genome-wide association studies (GWAS), gene-based methods have recently grown in popularity because they confer advantages in both statistical power and biological interpretability. However, most of these methods make strong assumptions about the form of the relationship between traits and single-nucleotide polymorphisms, which result in limited statistical power. In this paper, we propose a gene-based method based on the distance correlation coefficient called gene-based gene-gene interaction via distance correlation coefficient (GBDcor). The distance correlation (dCor) is a measurement of the dependency between two random vectors with arbitrary, and not necessarily equal, dimensions. We used the difference in dCor in case and control datasets as an indicator of gene⁻gene interaction, which was based on the assumption that the joint distribution of two genes in case subjects and in control subjects should not be significantly different if the two genes do not interact. We designed a permutation-based statistical test to evaluate the difference between dCor in cases and controls for a pair of genes, and we provided the p-value for the statistic to represent the significance of the interaction between the two genes. In experiments with both simulated and real-world data, our method outperformed previous approaches in detecting interactions accurately.

The Cox proportional hazards regression model has become the traditional choice for modeling survival data in medical studies. To introduce flexibility into the Cox model, several smoothing methods may be applied, and approaches based on splines are the most frequently considered in this context. To better understand the effects that each continuous covariate has on the outcome, results can be expressed in terms of splines-based hazard ratio (HR) curves, taking a specific covariate value as reference. Despite the potential advantages of using spline smoothing methods in survival analysis, there is currently no analytical method in the R software to choose the optimal degrees of freedom in multivariable Cox models (with two or more nonlinear covariate effects). This paper describes an R package, called smoothHR, that allows the computation of pointwise estimates of the HRs--and their corresponding confidence limits--of continuous predictors introduced nonlinearly. In addition the package provides functions for choosing automatically the degrees of freedom in multivariable Cox models. The package is available from the R homepage. We illustrate the use of the key functions of the smoothHR package using data from a study on breast cancer and data on acute coronary syndrome, from Galicia, Spain.

Statistical association between a single nucleotide polymorphism (SNP) genotype and a quantitative trait in genome-wide association studies is usually assessed using a linear regression model, or, in the case of non-normally distributed trait values, using the Kruskal-Wallis test. While linear regression models assume an additive mode of inheritance via equi-distant genotype scores, Kruskal-Wallis test merely tests global differences in trait values associated with the three genotype groups. Both approaches thus exhibit suboptimal power when the underlying inheritance mode is dominant or recessive. Furthermore, these tests do not perform well in the common situations when only a few trait values are available in a rare genotype category (disbalance), or when the values associated with the three genotype categories exhibit unequal variance (variance heterogeneity). We propose a maximum test based on Marcus-type multiple contrast test for relative effect sizes. This test allows model-specific testing of either dominant, additive or recessive mode of inheritance, and it is robust against variance heterogeneity. We show how to obtain mode-specific simultaneous confidence intervals for the relative effect sizes to aid in interpreting the biological relevance of the results. Further, we discuss the use of a related all-pairwise comparisons contrast test with range preserving confidence intervals as an alternative to Kruskal-Wallis heterogeneity test. We applied the proposed maximum test to the Bogalusa Heart Study dataset, and gained a remarkable increase in the power to detect association, particularly for rare genotypes. Our simulation study also demonstrated that the proposed non-parametric tests control family-wise error rate in the presence of non-normality and variance heterogeneity contrary to the standard parametric approaches. We provide a publicly available R library nparcomp that can be used to estimate simultaneous confidence intervals or compatible multiplicity-adjusted p-values associated with the proposed maximum test.