Discrete Homogeneous and Non-Homogeneous Markov Chains Enhance Predictive Modelling for Dairy Cow Diseases.

Modelling and predicting dairy cow diseases empowers farmers with valuable information for herd health management, thereby decreasing costs and increasing profits. For this purpose, predictive models were developed based on machine learning algorithms. However, machine-learning based approaches require the development of a specific model for each disease, and their consistency is limited by low farm data availability. To overcome this lack of complete and accurate data, we developed a predictive model based on discrete Homogeneous and Non-homogeneous Markov chains. After aggregating data into categories, we developed a method for defining the adequate number of Markov chain states. Subsequently, we selected the best prediction model through Chebyshev distance minimization. For 14 of 19 diseases, less than 15% maximum differences were measured between the last month of actual and predicted disease data. This model can be easily implemented in low-tech dairy farms to project costs with antibiotics and other treatments. Furthermore, the model's adaptability allows it to be extended to other disease types or conditions with minimal adjustments. Therefore, including this predictive model for dairy cow diseases in decision support systems may enhance herd health management and streamline the design of evidence-based farming strategies.

Recombination fraction in pre-recombinant inbred lines (PRERIL) - revisiting a century old problem in genetics.

BACKGROUND: Traditional recombinant inbred lines (RILs) are generated from repeated self-fertilization or brother-sister mating from the F1 hybrid of two inbred parents. Compared with the F2 population, RILs cumulate more crossovers between loci and thus increase the number of recombinants, resulting in an increased resolution of genetic mapping. Since they are inbred to the isogenic stage, another consequence of the heterozygosity reduction is the increased genetic variance and thus the increased power of QTL detection. Self-fertilization is the primary form of developing RILs in plants. Brother-sister mating is another way to develop RILs but in small laboratory animals. To ensure that the RILs have at least 98% of homozygosity, we need about seven generations of self-fertilization or 20 generations of brother-sister mating. Prior to homozygosity, these lines are called pre-recombinant inbred lines (PRERIL). Phenotypic values of traits in PRERILs are often collected but not used in QTL mapping. To perform QTL mapping in PRERILs, we need the recombination fraction between two markers at generation t for t < 7 (selfing) or t < 20 (brother-sister mating) so that the genotypes of QTL flanked by the markers can be inferred. RESULTS: In this study, we developed formulas to calculate the recombination fractions of PRERILs at generation t in self-fertilization, brother-sister mating, and random mating. In contrast to existing works in this topic, we used computer code to construct the transition matrix to form the Markov chain of genotype array between consecutive generations, the so-called recurrent equations. CONCLUSIONS: We provide R functions to calculate the recombination fraction using the newly developed recurrent equations of ordered genotype array. With the recurrent equations and the R code, users can perform QTL mapping in PRERILs. Substantial time and effort can be saved compared with QTL mapping in RILs.

Disease progression in chronic heart failure is linear: Insights from multistate modelling.

AIMS: Understanding the pattern of disease progression in chronic heart failure (HF) may inform patient care and healthcare system design. We used a four-state Markov model to describe the disease trajectory of patients with HF. METHODS AND RESULTS: Consecutive patients (n = 4918) were enrolled (median age 75 [67-81] years, 61.3% men, 44% with HF and reduced ejection fraction). We generated a model by observing events during the first 2 years of follow-up. The model yielded surprisingly accurate predictions of how a population with HF will behave during subsequent years. As examples, the predicted transition probability from hospitalization to death was 0.11; the observed probabilities were 0.13, 0.14, and 0.16 at 3, 4, and 5 years, respectively. Similarly, the predicted transition intensity for rehospitalization was 0.35; the observed probabilities were 0.38, 0.34, and 0.35 at 3, 4, and 5 years, respectively. A multivariable model including covariates thought to influence outcome did not improve accuracy. Predicted average life expectancy was approximately 10 years for the unadjusted model and 13 years for the multivariable model, consistent with the observed mortality of 41% at 5 years. CONCLUSIONS: A multistate Markov chain model for patients with chronic HF suggests that the proportion of patients transitioning each year from a given state to another remains constant. This finding suggests that the course of HF at a population level is more linear than is commonly supposed and predictable based on current patient status.

On the Interplay between Deadline-Constrained Traffic and the Number of Allowed Retransmissions in Random Access Networks.

In this paper, a network comprising wireless devices equipped with buffers transmitting deadline-constrained data packets over a slotted-ALOHA random-access channel is studied. Although communication protocols facilitating retransmissions increase reliability, a packet awaiting transmission from the queue experiences delays. Thus, packets with time constraints might be dropped before being successfully transmitted, while at the same time causing the queue size of the buffer to increase. To understand the trade-off between reliability and delays that might lead to packet drops due to deadline-constrained bursty traffic with retransmissions, the scenario of a wireless network utilizing a slotted-ALOHA random-access channel is investigated. The main focus is to reveal the trade-off between the number of retransmissions and the packet deadline as a function of the arrival rate. Towards this end, analysis of the system is performed by means of discrete-time Markov chains. Two scenarios are studied: (i) the collision channel model (in which a receiver can decode only when a single packet is transmitted), and (ii) the case for which receivers have multi-packet reception capabilities. A performance evaluation for a user with different transmit probabilities and number of retransmissions is conducted. We are able to determine numerically the optimal probability of transmissions and the number of retransmissions, given the packet arrival rate and the packet deadline. Furthermore, we highlight the impact of transmit probability and the number of retransmissions on the average drop rate and throughput.

Longitudinal Analysis of the Overall Survival Rates and Transitional Probabilities of Endometrial Cancer Patients: A Comprehensive Retrospective Study in Thailand.

BACKGROUND: This investigation delineated the survival rates and transitional probability trends of patients with endometrial cancer. This information is pivotal for optimizing patient management and counseling strategies. METHODS: We conducted a retrospective cohort analysis of patients diagnosed with stage I or II endometrial cancer between November 2006 and October 2012 and those diagnosed with stage III or IV endometrial cancer between January 2012 and May 2017 at Siriraj Hospital, Bangkok, Thailand. Our examination included baseline demographics, clinical characteristics, and adjuvant therapy data. Survival rates and transitional probabilities were assessed using the Kaplan-Meier method for survival curve construction and Markov models, respectively. RESULTS: After exclusions, 229 individuals with early-stage endometrial cancer and 119 with advanced-stage histologically verified endometrial cancer were included in the final cohort. Throughout a median follow-up duration of 12.8 years, the 5-year overall survival rates were 89.05% for the early-stage cohort and 50.42% for the advanced-stage cohort. The transitional probability analysis revealed an elevated likelihood of achieving a curative state in early-stage patients, contrasting with a greater propensity for disease progression or distant metastasis in advanced-stage patients. CONCLUSIONS: The findings from this study offer critical insights into the overall survival rates and transitional probabilities of endometrial cancer patients. These insights underscore the importance of strategies focused on preventing recurrence and enhancing treatment. Moreover, the results serve as a cornerstone for clinicians in devising individualized treatment plans and facilitating cost-effective analyses in the context of endometrial cancer care.

Fast, approximation-free molecular simulation of the SPC/Fw water model using non-reversible Markov chains.

In a world made of atoms, computer simulations of molecular systems such as proteins in water play an enormous role in science. Software packages for molecular simulation have been developed for decades. They all discretize Hamilton's equations of motion and treat long-range potentials through cutoffs or discretization of reciprocal space. This introduces severe approximations and artifacts that must be controlled algorithmically. Here, we bring to fruition a paradigm for molecular simulation that relies on modern concepts in statistics to explore the thermodynamic equilibrium with an exact and efficient non-reversible Markov process. It is free of all discretizations, approximations, and cutoffs. We explicitly demonstrate that this approach reaches a break-even point with traditional molecular simulation performed at high precision, but without any of its approximations. We stress the potential of our paradigm for crucial applications in biophysics and other fields, and as a practical approach to molecular simulation. We set out a strategy to reach our goal of rigorous molecular simulation.

Modeling metastatic progression from cross-sectional cancer genomics data.

MOTIVATION: Metastasis formation is a hallmark of cancer lethality. Yet, metastases are generally unobservable during their early stages of dissemination and spread to distant organs. Genomic datasets of matched primary tumors and metastases may offer insights into the underpinnings and the dynamics of metastasis formation. RESULTS: We present metMHN, a cancer progression model designed to deduce the joint progression of primary tumors and metastases using cross-sectional cancer genomics data. The model elucidates the statistical dependencies among genomic events, the formation of metastasis, and the clinical emergence of both primary tumors and their metastatic counterparts. metMHN enables the chronological reconstruction of mutational sequences and facilitates estimation of the timing of metastatic seeding. In a study of nearly 5000 lung adenocarcinomas, metMHN pinpointed TP53 and EGFR as mediators of metastasis formation. Furthermore, the study revealed that post-seeding adaptation is predominantly influenced by frequent copy number alterations. AVAILABILITY AND IMPLEMENTATION: All datasets and code are available on GitHub at https://github.com/cbg-ethz/metMHN.

Identifying Effective Connectivity between Stochastic Neurons with Variable-Length Memory Using a Transfer Entropy Rate Estimator.

Information theory explains how systems encode and transmit information. This article examines the neuronal system, which processes information via neurons that react to stimuli and transmit electrical signals. Specifically, we focus on transfer entropy to measure the flow of information between sequences and explore its use in determining effective neuronal connectivity. We analyze the causal relationships between two discrete time series, X:=Xt:t∈Z and Y:=Yt:t∈Z, which take values in binary alphabets. When the bivariate process (X,Y) is a jointly stationary ergodic variable-length Markov chain with memory no larger than k, we demonstrate that the null hypothesis of the test-no causal influence-requires a zero transfer entropy rate. The plug-in estimator for this function is identified with the test statistic of the log-likelihood ratios. Since under the null hypothesis, this estimator follows an asymptotic chi-squared distribution, it facilitates the calculation of p-values when applied to empirical data. The efficacy of the hypothesis test is illustrated with data simulated from a neuronal network model, characterized by stochastic neurons with variable-length memory. The test results identify biologically relevant information, validating the underlying theory and highlighting the applicability of the method in understanding effective connectivity between neurons.

Multicriteria optimization of the composition, thermodynamic and strength properties of fly-ash as an additive in metakaolin-based geopolymer composites.

This paper presents the construction of intelligent systems for selecting the optimum concentration of geopolymer matrix components based on ranking optimality criteria. A peculiarity of the methodology is replacing discrete time intervals with a sequence of states. Markov chains represent a synthetic property accumulating heterogeneous factors. The computational basis for the calculations was the digitization of experimental data on the strength properties of fly ashes collected from thermal power plants in the Czech Republic and used as additives in geopolymers. A database and a conceptual model of priority ranking have been developed, that are suitable for determining the structure of relations of the main factors. Computational results are presented by studying geopolymer matrix structure formation kinetics under changing component concentrations in real- time. Multicriteria optimization results for fly-ash as an additive on metakaolin-based geopolymer composites show that the optimal composition of the geopolymer matrix within the selected variation range includes 100 g metakaolin, 90 g potassium activator, 8 g silica fume, 2 g basalt fibers and 50 g fly ash by ratio weight. This ratio gives the best mechanical, thermal, and technological properties.

Representing and extracting knowledge from single-cell data.

Single-cell analysis is currently one of the most high-resolution techniques to study biology. The large complex datasets that have been generated have spurred numerous developments in computational biology, in particular the use of advanced statistics and machine learning. This review attempts to explain the deeper theoretical concepts that underpin current state-of-the-art analysis methods. Single-cell analysis is covered from cell, through instruments, to current and upcoming models. The aim of this review is to spread concepts which are not yet in common use, especially from topology and generative processes, and how new statistical models can be developed to capture more of biology. This opens epistemological questions regarding our ontology and models, and some pointers will be given to how natural language processing (NLP) may help overcome our cognitive limitations for understanding single-cell data.

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.

On the surprising effectiveness of a simple matrix exponential derivative approximation, with application to global SARS-CoV-2.

The continuous-time Markov chain (CTMC) is the mathematical workhorse of evolutionary biology. Learning CTMC model parameters using modern, gradient-based methods requires the derivative of the matrix exponential evaluated at the CTMC's infinitesimal generator (rate) matrix. Motivated by the derivative's extreme computational complexity as a function of state space cardinality, recent work demonstrates the surprising effectiveness of a naive, first-order approximation for a host of problems in computational biology. In response to this empirical success, we obtain rigorous deterministic and probabilistic bounds for the error accrued by the naive approximation and establish a "blessing of dimensionality" result that is universal for a large class of rate matrices with random entries. Finally, we apply the first-order approximation within surrogate-trajectory Hamiltonian Monte Carlo for the analysis of the early spread of Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) across 44 geographic regions that comprise a state space of unprecedented dimensionality for unstructured (flexible) CTMC models within evolutionary biology.

Simulating conversations: A Markov chain model of a central speaker's mnemonic influence over a group of communicating listeners.

Through their selective rehearsal, Central Speakers can reshape collective memory in a group of listeners, both by increasing accessibility for mentioned items (shared practice effects) and by decreasing relative accessibility for related but unmentioned items (socially shared retrieval induced forgetting, i.e., SSRIF). Subsequent networked communication in the group can further modify these mnemonic influences. Extant empirical work has tended to examine such downstream influences on a Central Speaker's mnemonic influence following a relatively limited number of interactions - often only two or three conversations. We develop a set of Markov chain simulations to model the long-term dynamics of such conversational remembering across a variety of group types, based on reported empirical data. These models indicate that some previously reported effects will stabilize in the long-term collective memory following repeated rounds of conversation. Notably, both shared practice effects and SSRIF persist into future steady states. However, other projected future states differ from those described so far in the empirical literature, specifically: the amplification of shared practice effects in communicational versus solo remembering non-conversational groups, the relatively transient impact of social (dis)identification with a Central Speaker, and the sensitivity of communicating networks to much smaller mnemonic biases introduced by the Central Speaker than groups of individual rememberers. Together, these simulations contribute insights into the long-term temporal dynamics of collective memory by addressing questions difficult to tackle using extant laboratory methods, and provide concrete suggestions for future empirical work.

Characterization of sleep efficiency transitions in family caregivers.

Family caregivers are at high risk of psychological distress and low sleep efficiency resulting from their caregiving responsibilities. Although psychological symptoms are associated with sleep efficiency, there is limited knowledge about the association of psychological distress with variations in sleep efficiency. We aimed to characterize the short- and long-term patterns of caregivers' sleep efficiency using Markov chain models and compare these patterns between groups with high and low psychological symptoms (i.e., depression, anxiety, and caregiving stress). Based on 7-day actigraphy data from 33 caregivers, we categorized sleep efficiency into three states, < 75% (S1), 75-84% (S2), and ≥ 85% (S3), and developed Markov chain models. Caregivers were likely to maintain a consistent sleep efficiency state from one night to the next without returning efficiently to a normal state. On average, it took 3.6-5.1 days to return to a night of normal sleep efficiency (S3) from lower states, and the long-term probability of achieving normal sleep was 42%. We observed lower probabilities of transitioning to or remaining in a normal sleep efficiency state (S3) in the high depression and anxiety groups compared to the low symptom groups. The differences in the time required to return to a normal state were inconsistent by symptom levels. The long-term probability of achieving normal sleep efficiency was significantly lower for caregivers with high depression and anxiety compared to the low symptom groups. Caregivers' sleep efficiency appears to remain relatively consistent over time and does not show rapid recovery. Caregivers with higher levels of depression and anxiety may be more vulnerable to sustained suboptimal sleep efficiency.

Early surgery compared to nonoperative management for mild degenerative cervical myelopathy: a cost-utility analysis.

BACKGROUND CONTEXT: Degenerative cervical myelopathy (DCM) is a form of acquired spinal cord compression and contributes to reduced quality of life secondary to neurological dysfunction and pain. There remains uncertainty regarding optimal management for individuals with mild myelopathy. Specifically, owing to lacking long-term natural history studies in this population, we do not know whether these individuals should be treated with initial surgery or observation. PURPOSE: We sought to perform a cost-utility analysis to examine early surgery for mild degenerative cervical myelopathy from the healthcare payer perspective. STUDY DESIGN/SETTING: We utilized data from the prospective observational cohorts included in the Cervical Spondylotic Myelopathy AO Spine International and North America studies to determine health related quality of life estimates and clinical myelopathy outcomes. PATIENT SAMPLE: We recruited all patients that underwent surgery for DCM enrolled in the Cervical Spondylotic Myelopathy AO Spine International and North America studies between December 2005 and January 2011. OUTCOME MEASURES: Clinical assessment measures were obtained using the Modified Japanese Orthopedic Association scale and health-related quality of life measures were obtained using the Short Form-6D utility score at baseline (preoperative), 6 months, 12 months and 24 months postsurgery. Cost measures inflated to January 2015 values were obtained using pooled estimates from the hospital payer perspective for surgical patients. METHODS: We employed a Markov state transition model with Monte Carlo microsimulation using a lifetime horizon to obtain an incremental cost utility ratio associated with early surgery for mild myelopathy. Parameter uncertainty was assessed through deterministic means using one-way and two-way sensitivity analyses and probabilistically using parameter estimate distributions with microsimulation (10,000 trials). Costs and utilities were discounted at 3% per annum. RESULTS: Initial surgery for mild degenerative cervical myelopathy was associated with an incremental lifetime increase of 1.26 quality-adjusted life years (QALY) compared to observation. The associated cost incurred to the healthcare payer over a lifetime horizon was $12,894.56, resulting in a lifetime incremental cost-utility ratio of $10,250.71/QALY. Utilizing a willingness to pay threshold in keeping with the World Health Organization definition of "very cost-effective" ($54,000 CDN), the probabilistic sensitivity analysis demonstrated that 100% of cases were cost-effective. CONCLUSIONS: Surgery compared to initial observation for mild degenerative cervical myelopathy was cost-effective from the Canadian healthcare payer perspective and was associated with lifetime gains in health-related quality of life.

Dynamic functional network connectivity based on spatial source phase maps of complex-valued fMRI data: Application to schizophrenia.

BACKGROUND: Dynamic spatial functional network connectivity (dsFNC) has shown advantages in detecting functional alterations impacted by mental disorders using magnitude-only fMRI data. However, complete fMRI data are complex-valued with unique and useful phase information. METHODS: We propose dsFNC of spatial source phase (SSP) maps, derived from complex-valued fMRI data (named SSP-dsFNC), to capture the dynamics elicited by the phase. We compute mutual information for connectivity quantification, employ statistical analysis and Markov chains to assess dynamics, ultimately classifying schizophrenia patients (SZs) and healthy controls (HCs) based on connectivity variance and Markov chain state transitions across windows. RESULTS: SSP-dsFNC yielded greater dynamics and more significant HC-SZ differences, due to the use of complete brain information from complex-valued fMRI data. COMPARISON WITH EXISTING METHODS: Compared with magnitude-dsFNC, SSP-dsFNC detected additional and meaningful connections across windows (e.g., for right frontal parietal) and achieved 14.6% higher accuracy for classifying HCs and SZs. CONCLUSIONS: This work provides new evidence about how SSP-dsFNC could be impacted by schizophrenia, and this information could be used to identify potential imaging biomarkers for psychotic diagnosis.

Custo-utilidade da utilização de teste farmacogenético como guia para o tratamento de depressão sob a perspectiva do Sistema de Saúde Suplementar / Cost-utility of pharmacogenetic testing as a guide for the treatment of depression from the Brazilian Supplementary Health System perspective

Objetivo: Desenvolver uma análise de custo-utilidade da implementação do teste farmacogenético como uma ferramenta adicional para orientar a escolha do melhor tratamento medicamentoso para indivíduos com depressão. Métodos: Para a realização desta análise, criou-se um modelo analítico de decisão baseado em um modelo de Markov. A avaliação foi realizada sob a perspectiva do Sistema de Saúde Suplementar brasileiro, com horizonte temporal de 10 anos, incluindo custos médicos diretos e custos da tecnologia utilizada, além de ter como comparador o tratamento empírico tradicional para a depressão. As probabilidades de transição foram obtidas por meio de análise da literatura disponível. Também foram realizadas análises de sensibilidade probabilística e univariada. Adicionalmente, foi realizada uma avaliação sob a perspectiva da sociedade, incluindo os custos de tratamento medicamentoso realizados pelos pacientes. Resultados: De acordo com a análise realizada, o emprego do teste farmacogenético como guia do tratamento para depressão mostrou-se favorável, proporcionando economia de -R$ 3.439,97 por paciente e aumento de 0,39 QALY ao longo do horizonte temporal. Assim, evidencia-se uma economia significativa a favor do teste farmacogenético, correspondendo a -R$ 8.776,78 por QALY salvo. Além disso, a robustez do modelo foi comprovada por meio das análises de sensibilidade. No cenário sob perspectiva da sociedade, o resultado foi ainda mais favorável, proporcionando economia de -R$ 9.381,49 por paciente e aumento de 0,39 QALY, correspondendo a -R$ 23.936,05 por QALY salvo. Conclusão: Os resultados encontrados neste estudo demonstraram que o uso de testes farmacogenéticos no tratamento da depressão é economicamente vantajoso, com aumento no valor de QALY e redução nos custos médicos diretos, em comparação ao tratamento empírico tradicional. Essa descoberta alinha-se à tendência atual de personalização no cuidado da saúde mental, sugerindo implicações práticas na reavaliação de protocolos, com potencial incorporação dos testes farmacogenéticos como padrão de cuidado.

Objective: To evaluate the cost-utility of pharmacogenetic testing incorporation as an additional tool in guiding the selection of optimal drug treatments for individuals with depression. Methods: A decision analytical model was created based on the Markov model for this analysis. The evaluation was conducted from the perspective of the Brazilian Supplementary Health System, with a time horizon of 10 years. The study included direct medical and technology costs and a comparison with traditional empirical treatment for depression was performed. Transition probabilities were derived from an analysis of available literature. Probabilistic and univariate sensitivity analyses were also carried out. Additionally, an evaluation was conducted from the perspective of Society, including the costs of drug treatment carried out by patients. Results: The application of pharmacogenetic testing as a guide for depression treatment demonstrated favorable outcomes, yielding savings of -R$ 3,439.97 per patient and an increase of 0.39 QALY over the specified time frame. Thus, significant savings were evident, corresponding to -R$ 8,776.78 per QALY saved. The sensitivity analyses confirmed the model's robustness. In the Society's perspective scenario, the outcome was even more favorable, resulting in savings of -R$ 9,381.49 per patient and a 0.39 increase in QALYs, equivalent to -R$ 23,936.05 per QALY saved. Conclusion: The study findings reveal that incorporating harmacogenetic tests in depression treatment offers economic benefits, evidenced by an increase in QALY value and a decrease in direct medical costs compared to conventional empirical treatment. This aligns with the ongoing trend towards personalized mental health care, implying practical considerations for protocol reassessment and the possible integration of pharmacogenetic tests as a standard of care.

Asymptotic behavior of mean fixation times in the Moran process with frequency-independent fitnesses.

We derive asymptotic formulae in the limit when population size N tends to infinity for mean fixation times (conditional and unconditional) in a population with two types of individuals, A and B, governed by the Moran process. We consider only the case in which the fitness of the two types do not depend on the population frequencies. Our results start with the important cases in which the initial condition is a single individual of any type, but we also consider the initial condition of a fraction [Formula: see text] of A individuals, where x is kept fixed and the total population size tends to infinity. In the cases covered by Antal and Scheuring (Bull Math Biol 68(8):1923-1944, 2006), i.e. conditional fixation times for a single individual of any type, it will turn out that our formulae are much more accurate than the ones they found. As quoted, our results include other situations not treated by them. An interesting and counterintuitive consequence of our results on mean conditional fixation times is the following. Suppose that a population consists initially of fitter individuals at fraction x and less fit individuals at a fraction [Formula: see text]. If population size N is large enough, then in the average the fixation of the less fit individuals is faster (provided it occurs) than fixation of the fitter individuals, even if x is close to 1, i.e. fitter individuals are the majority.

Covariate dependent Markov chains constructed with gradient boost modeling can effectively generate long-term predictions of obesity trends.

IMPORTANCE: The prevalence of obesity among United States adults has increased from 30.5% in 1999 to 41.9% in 2020. However, despite the recognition of long-term weight gain as an important public health issue, there is a paucity of studies studying the long-term weight gain and building models for long-term projection. METHODS: A retrospective, cross-sectional cohort study using the publicly available National Health and Nutrition Examination Survey (NHANES 2017-2020) was conducted in patients who completed the weight questionnaire and had accurate data for both weight at time of survey and weight ten years ago. Multistate gradient boost modeling classifiers were used to generate covariate dependent transition matrices and Markov chains were utilized for multistate modeling. RESULTS: Of the 6146 patients that met the inclusion criteria, 3024 (49%) of patients were male and 3122 (51%) of patients were female. There were 2252 (37%) White patients, 1257 (20%) Hispanic patients, 1636 (37%) Black patients, and 739 (12%) Asian patients. The average BMI was 30.16 (SD = 7.15), the average weight was 83.67 kilos (SD = 22.04), and the average weight change was a 3.27 kg (SD = 14.97) increase in body weight (Fig. 1). A total of 2411 (39%) patients lost weight, and 3735 (61%) patients gained weight (Table 1). We observed that 87 (1%) of patients were underweight (BMI < 18.5), 2058 (33%) were normal weight (18.5 ≤ BMI < 25), 1376 (22%) were overweight (25 ≤ BMI < 30) and 2625 (43%) were obese (BMI > 30). From analysis of the transitions between normal/underweight, overweight, and obese, we observed that after 10 years, of the patients who were underweight, 65% stayed underweight, 32% became normal weight, 2% became overweight, and 2% became obese. After 10 years, of the patients who were normal weight, 3% became underweight, 78% stayed normal weight, 17% became overweight, and 2% became obese. Of the patients who were overweight, 71% stayed overweight, 0% became underweight, 14% became normal weight, and 15% became obese. Of the patients who were obese, 84% stayed obese, 0% became underweight, 1% became normal weight, and 14% became overweight. CONCLUSIONS: United States adults are at risk of transitioning from normal weight to becoming overweight or obese. Covariate dependent Markov chains constructed with gradient boost modeling can effectively generate long-term predictions.

Modelling a Consultant Workforce for the United Kingdom: needs-based planning for Dental Public Health.

OBJECTIVE: To develop a needs-based workforce planning model to explore specialist workforce capacity and capability for the effective, efficient, and safe provision of services in the United Kingdom (UK); and test the model using Dental Public Health (DPH). BASIC RESEARCH DESIGN: Data from a national workforce survey, national audit, and specialty workshops in 2020 and 2021 set the parameters for a safe effective DPH workforce. A working group drawing on external expertise, developed a conceptual workforce model which informed the mathematical modelling, taking a Markovian approach. The latter enabled the consideration of possible scenarios relating to workforce development. It involved exploration of capacity within each career stage in DPH across a time horizon of 15 years. Workforce capacity requirements were calculated, informed by past principles. RESULTS: Currently an estimated 100 whole time equivalent (WTE) specialists are required to provide a realistic basic capacity nationally for DPH across the UK given the range of organisations, population growth, complexity and diversity of specialty roles. In February 2022 the specialty had 53.55 WTE academic/service consultants, thus a significant gap. The modelling evidence suggests a reduction in DPH specialist capacity towards a steady state in line with the current rate of training, recruitment and retention. The scenario involving increasing training numbers and drawing on other sources of public health trained dentists whilst retaining expertise within DPH has the potential to build workforce capacity. CONCLUSIONS: Current capacity is below basic requirements and approaching 'steady state'. Retention and innovative capacity building are required to secure and safeguard the provision of specialist DPH services to meet the needs of the UK health and care systems.