Fast estimation of posterior probabilities in change-point analysis through a constrained hidden Markov model

The Shortest Duration Constrained Hidden Markov Model: Data denoise and forecast optimization on the country-product matrix for the Fitness-Complexity Algorithm

The Economic Fitness Index describes industrial completeness and comprehensively reflects product diversification with competitiveness and product complexity in production globalization. The Fitness-Complexity Algorithm offers a scientific approach to predicting GDP and obtains fruitful results. As a recursion algorithm, the non-linear iteration processes give novel insights into product complexity and country fitness without noise data. However, the Country-Product Matrix and Revealed Comparative Advantage data have abnormal noises which contradict the relative stability of product diversity and the transformation of global production. The data noise entering the iteration algorithm, combined with positively related Fitness and Complexity, will be amplified in each recursion step. We introduce the Shortest Duration Constrained Hidden Markov Model (SDC-HMM) to denoise the Country-Product Matrix for the first time. After the country-product matrix test, the country case test, the noise estimation test and the panel regression test of national economic fitness indicators to predict GDP growth, we show that the SDC-HMM could reduce abnormal noise by about 25% and identify change points. This article provides intra-sample predictions that theoretically confirm that the SDC-HMM can improve the effectiveness of economic fitness indicators in interpreting economic growth.

Binary genetic algorithm for optimal joinpoint detection: Application to cancer trend analysis

The joinpoint regression model (JRM) is used to describe trend changes in many applications and relies on the detection of joinpoints (changepoints). However, the existing joinpoint detection methods, namely, the grid search (GS)-based methods, are computationally demanding, and hence, the maximum number of computable joinpoints is limited. Herein, we developed a genetic algorithm-based joinpoint (GAJP) model in which an explicitly decoupled computing procedure for optimization and regression is used to embed a binary genetic algorithm into the JRM for optimal joinpoint detection. The combinations of joinpoints were represented as binary chromosomes, and genetic operations were performed to determine the optimum solution by minimizing the fitness function, the Bayesian information criterion (BIC) and BIC₃ . The accuracy and computational performance of the GAJP model were evaluated via intensive simulation studies and compared with those of the GS-based methods using BIC, BIC₃ , and permutation test. The proposed method showed an outstanding computational efficiency in detecting multiple joinpoints. Finally, the suitability of the GAJP model for the analysis of cancer incidence trends was demonstrated by applying this model to data on the incidence of colorectal cancer in the United States from 1975 to 2016 from the National Cancer Institute's Surveillance, Epidemiology, and End Results program. Thus, the GAJP model was concluded to be practically feasible to detect multiple joinpoints up to the number of grids without requirement to preassign the number of joinpoints and be easily extendable to cancer trend analysis utilizing large datasets.

Detecting latent exposure in genome-wide association studies using a breakpoint model for logistic regression

Detecting gene-environment (G × E) interactions in the context of genome-wide association studies (GWAS) is a challenging problem since standard methods generally present a lack of power. An additional difficulty arises from the fact that the causal exposure is seldom observed and only a proxy of this exposure is observed. This leads to an additional drop in terms of power and it explains the failure of standard methods in detecting interactions, even very strong ones. In this article, we consider the latent exposure as a source of heterogeneity and we propose a new powerful method, named "Breakpoint Model for Logistic Regression" (BMLR), based on a breakpoint model, in order to detect G × E interactions when causal exposure is unobserved. First, the BMLR method is compared to the ordered-subset analysis for case-control method, which has been developed for the same purpose, through simulations. This highlights the ability of BMLR to detect the heterogeneity, and therefore, to detect interaction with latent exposure. Finally, the BMLR method is compared to standard methods, such as Plink, to perform a GWAS on a published realistic benchmark.

A change-point model for detecting heterogeneity in ordered survival responses

In this article, we suggest a new statistical approach considering survival heterogeneity as a breakpoint model in an ordered sequence of time-to-event variables. The survival responses need to be ordered according to a numerical covariate. Our estimation method will aim at detecting heterogeneity that could arise through the ordering covariate. We formally introduce our model as a constrained Hidden Markov Model, where the hidden states are the unknown segmentation (breakpoint locations) and the observed states are the survival responses. We derive an efficient Expectation-Maximization framework for maximizing the likelihood of this model for a wide range of baseline hazard forms (parametrics or nonparametric). The posterior distribution of the breakpoints is also derived, and the selection of the number of segments using penalized likelihood criterion is discussed. The performance of our survival breakpoint model is finally illustrated on a diabetes dataset where the observed survival times are ordered according to the calendar time of disease onset.