Non-parametric treatment time-lag effect estimation

In general, the change point problem considers inference of a change in distribution for a set of time-ordered observations. This has applications in a large variety of fields, and can also apply to survival data. In survival analysis, most existing methods compare two treatment groups for the entirety of the study period. Some treatments may take a length of time to show effects in subjects. This has been called the time-lag effect in the literature, and in cases where time-lag effect is considerable, such methods may not be appropriate to detect significant differences between two groups. In this paper, we propose a novel non-parametric approach for estimating the point of treatment time-lag effect by using an empirical divergence measure. Theoretical properties of the estimator are studied. The results from the simulated data and the applications to real data examples support our proposed method.

Dynamic Functional Connectivity Change-Point Detection With Random Matrix Theory Inference

To study the dynamic nature of brain activity, functional magnetic resonance imaging (fMRI) data is useful including some temporal dependencies between the corresponding neural activity estimates. Recent studies have shown that the functional connectivity (FC) varies according to time and location which should be incorporated into the model. Modeling this dynamic FC (DFC) requires time-varying measures of spatial region of interest (ROI) sets. To know about the DFC, change-point detection in FC is of particular interest. In this paper, we propose a method of detecting a change-point based on the maximum of eigenvalues via random matrix theory (RMT). From covariance matrices for FC of all ROI's, the temporal change-point of FC is decided by an RMT approach. Simulation results show that our proposed method can detect meaningful FC change-points. We also illustrate the effectiveness of our FC detection approach by applying our method to epilepsy data where change-points detected are explained by the changes in memory capacity. Our study shows the possibility of RMT based approach in DFC change-point problem and in studying the complex dynamic pattern of functional brain interactions.

Vitamin D and Anti-Müllerian Hormone Levels in Infertility Treatment: The Change-Point Problem

Background: Anti-Müllerian hormone (AMH) is considered to be one of the most significant indicators of women’s fertility. Many studies have shown that vitamin D may modify human reproductive functions; however, the results are conflicting. The composition of follicular fluid (FF) creates the biochemical environment of the oocyte and affects its quality, which later determines the embryo quality. In this study, we aimed to revise with advanced statistical techniques the relationship between AMH and vitamin D in FF. Methods: The study was designed as a prospective single-center study in infertile patients with AMH ≥ 0.7 ng/mL who underwent controlled ovarian hyperstimulation for in vitro fertilization. AMH and vitamin D levels in FF were measured. Next, the standard and advanced statistical (including segmented regression) techniques were applied. Results: We observed a negative linear correlation between levels of AMH in serum and FF and total vitamin D concentrations up to approximately 30 ng/mL; with a statistically significant relationship in FF. Beyond that concentration, the trend was positive but statistically insignificant. Conclusions: As an existing “change-point problem” was noticed, we suggest segmentation in the relationship between vitamin D and AMH during infertility treatment.

A change-point problem and inference for segment signals

We address the problem of detection and estimation of one or two change-points in the mean of a series of random variables. We use the formalism of set estimation in regression: to each point of a design is attached a binary label that indicates whether that point belongs to an unknown segment and this label is contaminated with noise. The endpoints of the unknown segment are the change-points. We study the minimal size of the segment which allows statistical detection in different scenarios, including when the endpoints are separated from the boundary of the domain of the design, or when they are separated from one another. We compare this minimal size with the minimax rates of convergence for estimation of the segment under the same scenarios. The aim of this extensive study of a simple yet fundamental version of the change-point problem is two-fold: understanding the impact of the location and the separation of the change points on detection and estimation and bringing insights about the estimation and detection of convex bodies in higher dimensions.

iSeg: an efficient algorithm for segmentation of genomic and epigenomic data

BackgroundIdentification of functional elements of a genome often requires dividing a sequence of measurements along a genome into segments where adjacent segments have different properties, such as different mean values. This problem is often called the segmentation problem in the field of genomics, and the change-point problem in other scientific disciplines. Despite dozens of algorithms developed to address this problem in genomics research, methods with improved accuracy and speed are still needed to effectively tackle both existing and emerging genomic and epigenomic segmentation problems.ResultsWe designed an efficient algorithm, called iSeg, for segmentation of genomic and epigenomic profiles. iSeg first utilizes dynamic programming to identify candidate segments and test for significance. It then uses a novel data structure based on two coupled balanced binary trees to detect overlapping significant segments and update them simultaneously during searching and refinement stages. Refinement and merging of significant segments are performed at the end to generate the final set of segments. By using an objective function based on the p-values of the segments, the algorithm can serve as a general computational framework to be combined with different assumptions on the distributions of the data. As a general segmentation method, it can segment different types of genomic and epigenomic data, such as DNA copy number variation, nucleosome occupancy, nuclease sensitivity, and differential nuclease sensitivity data. Using simple t-tests to compute p-values across multiple datasets of different types, we evaluate iSeg using both simulated and experimental datasets and show that it performs satisfactorily when compared with some other popular methods, which often employ more sophisticated statistical models. Implemented in C++, iSeg is also very computationally efficient, well suited for large numbers of input profiles and data with very long sequences.ConclusionsWe have developed an effective and efficient general-purpose segmentation tool for sequential data and illustrated its use in segmentation of genomic and epigenomic profiles.