Spatial-temporal Bayesian accelerated failure time models for survival endpoints with applications to prostate cancer registry data.

Prostate cancer is the most common cancer after non-melanoma skin cancer and the second leading cause of cancer deaths in US men. Its incidence and mortality rates vary substantially across geographical regions and over time, with large disparities by race, geographic regions (i.e., Appalachia), among others. The widely used Cox proportional hazards model is usually not applicable in such scenarios owing to the violation of the proportional hazards assumption. In this paper, we fit Bayesian accelerated failure time models for the analysis of prostate cancer survival and take dependent spatial structures and temporal information into account by incorporating random effects with multivariate conditional autoregressive priors. In particular, we relax the proportional hazards assumption, consider flexible frailty structures in space and time, and also explore strategies for handling the temporal variable. The parameter estimation and inference are based on a Monte Carlo Markov chain technique under a Bayesian framework. The deviance information criterion is used to check goodness of fit and to select the best candidate model. Extensive simulations are performed to examine and compare the performances of models in different contexts. Finally, we illustrate our approach by using the 2004-2014 Pennsylvania Prostate Cancer Registry data to explore spatial-temporal heterogeneity in overall survival and identify significant risk factors.

Comparison of stochastic and deterministic models for gambiense sleeping sickness at different spatial scales: A health area analysis in the DRC.

The intensification of intervention activities against the fatal vector-borne disease gambiense human African trypanosomiasis (gHAT, sleeping sickness) in the last two decades has led to a large decline in the number of annually reported cases. However, while we move closer to achieving the ambitious target of elimination of transmission (EoT) to humans, pockets of infection remain, and it becomes increasingly important to quantitatively assess if different regions are on track for elimination, and where intervention efforts should be focused. We present a previously developed stochastic mathematical model for gHAT in the Democratic Republic of Congo (DRC) and show that this same formulation is able to capture the dynamics of gHAT observed at the health area level (approximately 10,000 people). This analysis was the first time any stochastic gHAT model has been fitted directly to case data and allows us to better quantify the uncertainty in our results. The analysis focuses on utilising a particle filter Markov chain Monte Carlo (MCMC) methodology to fit the model to the data from 16 health areas of Mosango health zone in Kwilu province as a case study. The spatial heterogeneity in cases is reflected in modelling results, where we predict that under the current intervention strategies, the health area of Kinzamba II, which has approximately one third of the health zone's cases, will have the latest expected year for EoT. We find that fitting the analogous deterministic version of the gHAT model using MCMC has substantially faster computation times than fitting the stochastic model using pMCMC, but produces virtually indistinguishable posterior parameterisation. This suggests that expanding health area fitting, to cover more of the DRC, should be done with deterministic fits for efficiency, but with stochastic projections used to capture both the parameter and stochastic variation in case reporting and elimination year estimations.

Inference of genomic landscapes using ordered Hidden Markov Models with emission densities (oHMMed).

BACKGROUND: Genomes are inherently inhomogeneous, with features such as base composition, recombination, gene density, and gene expression varying along chromosomes. Evolutionary, biological, and biomedical analyses aim to quantify this variation, account for it during inference procedures, and ultimately determine the causal processes behind it. Since sequential observations along chromosomes are not independent, it is unsurprising that autocorrelation patterns have been observed e.g., in human base composition. In this article, we develop a class of Hidden Markov Models (HMMs) called oHMMed (ordered HMM with emission densities, the corresponding R package of the same name is available on CRAN): They identify the number of comparably homogeneous regions within autocorrelated observed sequences. These are modelled as discrete hidden states; the observed data points are realisations of continuous probability distributions with state-specific means that enable ordering of these distributions. The observed sequence is labelled according to the hidden states, permitting only neighbouring states that are also neighbours within the ordering of their associated distributions. The parameters that characterise these state-specific distributions are inferred. RESULTS: We apply our oHMMed algorithms to the proportion of G and C bases (modelled as a mixture of normal distributions) and the number of genes (modelled as a mixture of poisson-gamma distributions) in windows along the human, mouse, and fruit fly genomes. This results in a partitioning of the genomes into regions by statistically distinguishable averages of these features, and in a characterisation of their continuous patterns of variation. In regard to the genomic G and C proportion, this latter result distinguishes oHMMed from segmentation algorithms based in isochore or compositional domain theory. We further use oHMMed to conduct a detailed analysis of variation of chromatin accessibility (ATAC-seq) and epigenetic markers H3K27ac and H3K27me3 (modelled as a mixture of poisson-gamma distributions) along the human chromosome 1 and their correlations. CONCLUSIONS: Our algorithms provide a biologically assumption free approach to characterising genomic landscapes shaped by continuous, autocorrelated patterns of variation. Despite this, the resulting genome segmentation enables extraction of compositionally distinct regions for further downstream analyses.

stDiff: a diffusion model for imputing spatial transcriptomics through single-cell transcriptomics.

Spatial transcriptomics (ST) has become a powerful tool for exploring the spatial organization of gene expression in tissues. Imaging-based methods, though offering superior spatial resolutions at the single-cell level, are limited in either the number of imaged genes or the sensitivity of gene detection. Existing approaches for enhancing ST rely on the similarity between ST cells and reference single-cell RNA sequencing (scRNA-seq) cells. In contrast, we introduce stDiff, which leverages relationships between gene expression abundance in scRNA-seq data to enhance ST. stDiff employs a conditional diffusion model, capturing gene expression abundance relationships in scRNA-seq data through two Markov processes: one introducing noise to transcriptomics data and the other denoising to recover them. The missing portion of ST is predicted by incorporating the original ST data into the denoising process. In our comprehensive performance evaluation across 16 datasets, utilizing multiple clustering and similarity metrics, stDiff stands out for its exceptional ability to preserve topological structures among cells, positioning itself as a robust solution for cell population identification. Moreover, stDiff's enhancement outcomes closely mirror the actual ST data within the batch space. Across diverse spatial expression patterns, our model accurately reconstructs them, delineating distinct spatial boundaries. This highlights stDiff's capability to unify the observed and predicted segments of ST data for subsequent analysis. We anticipate that stDiff, with its innovative approach, will contribute to advancing ST imputation methodologies.

A Bayesian model-based reduced major axis regression.

Reduced major axis (RMA) regression, widely used in the fields of zoology, botany, ecology, biology, spectroscopy, and among others, outweighs the ordinary least square regression by relaxing the assumption that the covariates are without measurement errors. A Bayesian implementation of the RMA regression is presented in this paper, and the equivalence of the estimates of the parameters under the Bayesian and the frequentist frameworks is proved. This model-based Bayesian RMA method is advantageous since the posterior estimates, the standard deviations, as well as the credible intervals of the estimates can be obtained through Markov chain Monte Carlo methods directly. In addition, it is straightforward to extend to the multivariate RMA case. The performance of the Bayesian RMA approach is evaluated in the simulation study, and, finally, the proposed method is applied to analyze a dataset in the plantation.

The entropy rate of Linear Additive Markov Processes.

This work derives a theoretical value for the entropy of a Linear Additive Markov Process (LAMP), an expressive but simple model able to generate sequences with a given autocorrelation structure. Our research establishes that the theoretical entropy rate of a LAMP model is equivalent to the theoretical entropy rate of the underlying first-order Markov Chain. The LAMP model captures complex relationships and long-range dependencies in data with similar expressibility to a higher-order Markov process. While a higher-order Markov process has a polynomial parameter space, a LAMP model is characterised only by a probability distribution and the transition matrix of an underlying first-order Markov Chain. This surprising result can be explained by the information balance between the additional structure imposed by the next state distribution of the LAMP model, and the additional randomness of each new transition. Understanding the entropy of the LAMP model provides a tool to model complex dependencies in data while retaining useful theoretical results. To emphasise the practical applications, we use the LAMP model to estimate the entropy rate of the LastFM, BrightKite, Wikispeedia and Reuters-21578 datasets. We compare estimates calculated using frequency probability estimates, a first-order Markov model and the LAMP model, also considering two approaches to ensure the transition matrix is irreducible. In most cases the LAMP entropy rates are lower than those of the alternatives, suggesting that LAMP model is better at accommodating structural dependencies in the processes, achieving a more accurate estimate of the true entropy.

How to account for behavioral states in step-selection analysis: a model comparison.

Step-selection models are widely used to study animals' fine-scale habitat selection based on movement data. Resource preferences and movement patterns, however, often depend on the animal's unobserved behavioral states, such as resting or foraging. As this is ignored in standard (integrated) step-selection analyses (SSA, iSSA), different approaches have emerged to account for such states in the analysis. The performance of these approaches and the consequences of ignoring the states in step-selection analysis, however, have rarely been quantified. We evaluate the recent idea of combining iSSAs with hidden Markov models (HMMs), which allows for a joint estimation of the unobserved behavioral states and the associated state-dependent habitat selection. Besides theoretical considerations, we use an extensive simulation study and a case study on fine-scale interactions of simultaneously tracked bank voles (Myodes glareolus) to compare this HMM-iSSA empirically to both the standard and a widely used classification-based iSSA (i.e., a two-step approach based on a separate prior state classification). Moreover, to facilitate its use, we implemented the basic HMM-iSSA approach in the R package HMMiSSA available on GitHub.

Analyzing entropy features in time-series data for pattern recognition in neurological conditions.

In the field of medical diagnosis and patient monitoring, effective pattern recognition in neurological time-series data is essential. Traditional methods predominantly based on statistical or probabilistic learning and inference often struggle with multivariate, multi-source, state-varying, and noisy data while also posing privacy risks due to excessive information collection and modeling. Furthermore, these methods often overlook critical statistical information, such as the distribution of data points and inherent uncertainties. To address these challenges, we introduce an information theory-based pipeline that leverages specialized features to identify patterns in neurological time-series data while minimizing privacy risks. We incorporate various entropy methods based on the characteristics of different scenarios and entropy. For stochastic state transition applications, we incorporate Shannon's entropy, entropy rates, entropy production, and the von Neumann entropy of Markov chains. When state modeling is impractical, we select and employ approximate entropy, increment entropy, dispersion entropy, phase entropy, and slope entropy. The pipeline's effectiveness and scalability are demonstrated through pattern analysis in a dementia care dataset and also an epileptic and a myocardial infarction dataset. The results indicate that our information theory-based pipeline can achieve average performance improvements across various models on the recall rate, F1 score, and accuracy by up to 13.08 percentage points, while enhancing inference efficiency by reducing the number of model parameters by an average of 3.10 times. Thus, our approach opens a promising avenue for improved, efficient, and critical statistical information-considered pattern recognition in medical time-series data.

Goal-oriented inference of environment from redundant observations.

The agent learns to organize decision behavior to achieve a behavioral goal, such as reward maximization, and reinforcement learning is often used for this optimization. Learning an optimal behavioral strategy is difficult under the uncertainty that events necessary for learning are only partially observable, called as Partially Observable Markov Decision Process (POMDP). However, the real-world environment also gives many events irrelevant to reward delivery and an optimal behavioral strategy. The conventional methods in POMDP, which attempt to infer transition rules among the entire observations, including irrelevant states, are ineffective in such an environment. Supposing Redundantly Observable Markov Decision Process (ROMDP), here we propose a method for goal-oriented reinforcement learning to efficiently learn state transition rules among reward-related "core states" from redundant observations. Starting with a small number of initial core states, our model gradually adds new core states to the transition diagram until it achieves an optimal behavioral strategy consistent with the Bellman equation. We demonstrate that the resultant inference model outperforms the conventional method for POMDP. We emphasize that our model only containing the core states has high explainability. Furthermore, the proposed method suits online learning as it suppresses memory consumption and improves learning speed.

The effect of demographic stochasticity on Zika virus transmission dynamics: Probability of disease extinction, sensitivity analysis, and mean first passage time.

Viral infections spread by mosquitoes are a growing threat to human health and welfare. Zika virus (ZIKV) is one of them and has become a global worry, particularly for women who are pregnant. To study ZIKV dynamics in the presence of demographic stochasticity, we consider an established ZIKV transmission model that takes into consideration the disease transmission from human to mosquito, mosquito to human, and human to human. In this study, we look at the local stability of the disease-free and endemic equilibriums. By conducting the sensitivity analysis both locally and globally, we assess the effect of the model parameters on the model outcomes. In this work, we use the continuous-time Markov chain (CTMC) process to develop and analyze a stochastic model. The main distinction between deterministic and stochastic models is that, in the absence of any preventive measures such as avoiding travel to infected areas, being careful from mosquito bites, taking precautions to reduce the risk of sexual transmission, and seeking medical care for any acute illness with a rash or fever, the stochastic model shows the possibility of disease extinction in a finite amount of time, unlike the deterministic model shows disease persistence. We found that the numerically estimated disease extinction probability agrees well with the analytical probability obtained from the Galton-Watson branching process approximation. We have discovered that the disease extinction probability is high if the disease emerges from infected mosquitoes rather than infected humans. In the context of the stochastic model, we derive the implicit equation of the mean first passage time, which computes the average amount of time needed for a system to undergo its first state transition.

Tutorial on how to build non-Markovian dynamic models from molecular dynamics simulations for studying protein conformational changes.

Protein conformational changes play crucial roles in their biological functions. In recent years, the Markov State Model (MSM) constructed from extensive Molecular Dynamics (MD) simulations has emerged as a powerful tool for modeling complex protein conformational changes. In MSMs, dynamics are modeled as a sequence of Markovian transitions among metastable conformational states at discrete time intervals (called lag time). A major challenge for MSMs is that the lag time must be long enough to allow transitions among states to become memoryless (or Markovian). However, this lag time is constrained by the length of individual MD simulations available to track these transitions. To address this challenge, we have recently developed Generalized Master Equation (GME)-based approaches, encoding non-Markovian dynamics using a time-dependent memory kernel. In this Tutorial, we introduce the theory behind two recently developed GME-based non-Markovian dynamic models: the quasi-Markov State Model (qMSM) and the Integrative Generalized Master Equation (IGME). We subsequently outline the procedures for constructing these models and provide a step-by-step tutorial on applying qMSM and IGME to study two peptide systems: alanine dipeptide and villin headpiece. This Tutorial is available at https://github.com/xuhuihuang/GME_tutorials. The protocols detailed in this Tutorial aim to be accessible for non-experts interested in studying the biomolecular dynamics using these non-Markovian dynamic models.

Modelling the impact of human behavior using a two-layer Watts-Strogatz network for transmission and control of Mpox.

PURPOSE: This study aims to evaluate the effectiveness of mitigation strategies and analyze the impact of human behavior on the transmission of Mpox. The results can provide guidance to public health authorities on comprehensive prevention and control for the new Mpox virus strain in the Democratic Republic of Congo as of December 2023. METHODS: We develop a two-layer Watts-Strogatz network model. The basic reproduction number is calculated using the next-generation matrix approach. Markov chain Monte Carlo (MCMC) optimization algorithm is used to fit Mpox cases in Canada into the network model. Numerical simulations are used to assess the impact of mitigation strategies and human behavior on the final epidemic size. RESULTS: Our results show that the contact transmission rate of low-risk groups and susceptible humans increases when the contact transmission rate of high-risk groups and susceptible humans is controlled as the Mpox epidemic spreads. The contact transmission rate of high-risk groups after May 18, 2022, is approximately 20% lower than that before May 18, 2022. Our findings indicate a positive correlation between the basic reproduction number and the level of heterogeneity in human contacts, with the basic reproduction number estimated at 2.3475 (95% CI: 0.0749-6.9084). Reducing the average number of sexual contacts to two per week effectively reduces the reproduction number to below one. CONCLUSION: We need to pay attention to the re-emergence of the epidemics caused by low-risk groups when an outbreak dominated by high-risk groups is under control. Numerical simulations show that reducing the average number of sexual contacts to two per week is effective in slowing down the rapid spread of the epidemic. Our findings offer guidance for the public health authorities of the Democratic Republic of Congo in developing effective mitigation strategies.

Evaluating the lifetime performance index of omega distribution based on progressive type-II censored samples.

Besides achieving high quality products, statistical techniques are applied in many fields associated with health such as medicine, biology and etc. Adhering to the quality performance of an item to the desired level is a very important issue in various fields. Process capability indices play a vital role in evaluating the performance of an item. In this paper, the larger-the-better process capability index for the three-parameter Omega model based on progressive type-II censoring sample is calculated. On the basis of progressive type-II censoring the statistical inference about process capability index is carried out through the maximum likelihood. Also, the confidence interval is proposed and the hypothesis test for estimating the lifetime performance of products. Gibbs within Metropolis-Hasting samplers procedure is used for performing Markov Chain Monte Carlo (MCMC) technique to achieve Bayes estimation for unknown parameters. Simulation study is calculated to show that Omega distribution's performance is more effective. At the end of this paper, there are two real-life applications, one of them is about high-performance liquid chromatography (HPLC) data of blood samples from organ transplant recipients. The other application is about real-life data of ball bearing data. These applications are used to illustrate the importance of Omega distribution in lifetime data analysis.

Source tracing and contagion measurement of carbon emission trading price fluctuation in China from the perspective of major emergencies.

Based on monthly economic data spanning from January 2015 to December 2022, we have established an analytical framework to examine the "Russia-Ukraine conflict-financial market pressure and energy market-China carbon emission trading prices." To achieve this objective, we developed indices for financial system pressure, the energy market, and investor sentiment, applying a mediation effects model to validate their transmission mechanisms. Subsequently, the TVP-SV-VAR model was employed to scrutinize the nonlinear impact of the Russia-Ukraine conflict on the valuation of China's carbon emission trading rights. This model integrates time-varying parameters (TVP) and stochastic volatility (SV), utilizing Markov Chain Monte Carlo (MCMC) technology for parameter estimation. Finally, various wavelet analysis techniques, including continuous wavelet transform, cross-wavelet transform, and wavelet coherence spectrum, were applied to decompose time series data into distinct time-frequency scales, facilitating an analysis of the lead-lag relationships within each time series. The research outcomes provide crucial insights for safeguarding the interests of trading organizations, refining the structure of the carbon market, and mitigating systemic risks on a global scale.

Regional differences and dynamic evolution of high-quality development in service industry: A case study of the Chengdu-Chongqing economic circle.

The high-quality development of service industry has become an important engine for promoting sustainable economic development. This paper first constructed the evaluation index system of high-quality development of service industry, based on panel data from 2005 to 2020. Second, Kernel density, Markov chain and Dagum Gini coefficient were used to represent the regional differences and dynamic evolution of service industry, and the Koo method was used to explore the characteristics of spatial agglomeration. Finally, social network analysis was used to identify core indicators. The study found that: (1) From 2005 to 2020, the overall level of service industry first decreases and then increases, with Chengdu and Chongqing leading other cities. (2) The development of service industry in the CCEC has large spatial differences, mainly due to inter-regional differences. (3) The level of spatial agglomeration is less variable, with high agglomeration mainly in Chengdu. (4) Indicators such as the level of human capital are the core factors of its high-quality development. This study is of great theoretical and practical significance for the optimization and upgrading of service industry in the CCEC and the synergetic development of the region.

Markov modeling for cost-effectiveness using federated health data network.

OBJECTIVE: To introduce 2 R-packages that facilitate conducting health economics research on OMOP-based data networks, aiming to standardize and improve the reproducibility, transparency, and transferability of health economic models. MATERIALS AND METHODS: We developed the software tools and demonstrated their utility by replicating a UK-based heart failure data analysis across 5 different international databases from Estonia, Spain, Serbia, and the United States. RESULTS: We examined treatment trajectories of 47 163 patients. The overall incremental cost-effectiveness ratio (ICER) for telemonitoring relative to standard of care was 57 472 €/QALY. Country-specific ICERs were 60 312 €/QALY in Estonia, 58 096 €/QALY in Spain, 40 372 €/QALY in Serbia, and 90 893 €/QALY in the US, which surpassed the established willingness-to-pay thresholds. DISCUSSION: Currently, the cost-effectiveness analysis lacks standard tools, is performed in ad-hoc manner, and relies heavily on published information that might not be specific for local circumstances. Published results often exhibit a narrow focus, central to a single site, and provide only partial decision criteria, limiting their generalizability and comprehensive utility. CONCLUSION: We created 2 R-packages to pioneer cost-effectiveness analysis in OMOP CDM data networks. The first manages state definitions and database interaction, while the second focuses on Markov model learning and profile synthesis. We demonstrated their utility in a multisite heart failure study, comparing telemonitoring and standard care, finding telemonitoring not cost-effective.

Application of multistate modeling to clinical data analysis.

Multistate models have been used for decades to analyze the economics of expensive and long-lasting treatments. More recently they also served to address questions in clinical drug development. It seems timely to introduce the broader pharmacometrics community to the technical aspects and the problem-solving capabilities of these models. A minimal model is introduced that can answer questions of interest to drug developers, regulatory agencies, and patients (with their carers and payers). A clinical study is simulated where 1000 patients are randomly allocated (1:1) to placebo and active treatment. After a recruitment phase, deaths are counted, and an administrative data cutoff occurs 858 days after the first patient is randomized. The minimal model has one initial state, two transient states, and two absorbing states. Fully parameterized semi-Markov processes govern the unidirectional transitions between states. Simulations explore the influence of parameter uncertainty and sample size on the validity of statistical inferences. The questions of interest to stakeholders are addressed predominantly with graphic displays. All programming codes are made available. Both drug developers and regulators are invited to re-evaluate the methods currently in use to assess the benefits and risks of new treatments.

The value-based price of transformative gene therapy for sickle cell disease: a modeling analysis.

Sickle cell disease (SCD) is an inherited, progressively debilitating blood disorder. Emerging gene therapies (GTx) may lead to a complete remission, the benefits of such can only be realized if GTx is affordable and accessible in the low-and middle-income countries (LMIC) with the greatest SCD burden. To estimate the health impacts and country-specific value-based prices (VBP) of a future gene therapy for SCD using a cost-utility model framework. We developed a lifetime Markov model to compare the costs and health outcomes of GTx versus standard of care for SCD. We modeled populations in seven LMICs and six high-income countries (HICs) estimating lifetime costs and disability-adjusted life-years (DALYs) in comparison to estimates of a country's cost-effectiveness threshold. Each country's unique VBP for GTx was calculated via threshold analysis. Relative to SOC treatment alone, we found that hypothetical GTx reduced the number of people symptomatic with SCD over time leading to fewer DALYs. Across countries, VBPs ranged from $3.6 million (US) to $700 (Uganda). Our results indicate a wide range of GTx prices are required if it is to be made widely available and may inform burden and affordability for 'target product profiles' of GTx in SCD.

A shiny app for modeling the lifetime in primary breast cancer patients through phase-type distributions.

Phase-type distributions (PHDs), which are defined as the distribution of the lifetime up to the absorption in an absorbent Markov chain, are an appropriate candidate to model the lifetime of any system, since any non-negative probability distribution can be approximated by a PHD with sufficient precision. Despite PHD potential, friendly statistical programs do not have a module implemented in their interfaces to handle PHD. Thus, researchers must consider others statistical software such as R, Matlab or Python that work with the compilation of code chunks and functions. This fact might be an important handicap for those researchers who do not have sufficient knowledge in programming environments. In this paper, a new interactive web application developed with shiny is introduced in order to adjust PHD to an experimental dataset. This open access app does not require any kind of knowledge about programming or major mathematical concepts. Users can easily compare the graphic fit of several PHDs while estimating their parameters and assess the goodness of fit with just several clicks. All these functionalities are exhibited by means of a numerical simulation and modeling the time to live since the diagnostic in primary breast cancer patients.

kalis: a modern implementation of the Li & Stephens model for local ancestry inference in R.

BACKGROUND: Approximating the recent phylogeny of N phased haplotypes at a set of variants along the genome is a core problem in modern population genomics and central to performing genome-wide screens for association, selection, introgression, and other signals. The Li & Stephens (LS) model provides a simple yet powerful hidden Markov model for inferring the recent ancestry at a given variant, represented as an N × N distance matrix based on posterior decodings. RESULTS: We provide a high-performance engine to make these posterior decodings readily accessible with minimal pre-processing via an easy to use package kalis, in the statistical programming language R. kalis enables investigators to rapidly resolve the ancestry at loci of interest and developers to build a range of variant-specific ancestral inference pipelines on top. kalis exploits both multi-core parallelism and modern CPU vector instruction sets to enable scaling to hundreds of thousands of genomes. CONCLUSIONS: The resulting distance matrices accessible via kalis enable local ancestry, selection, and association studies in modern large scale genomic datasets.