Symptoms of schizophrenia and regularity in treatment: a stochastic analysis

Background: The alarming rise of mental disorders worldwide stimulates the need to study them from a statistical viewpoint. Schizophrenia is one of the most prevalent mental illness which is characterised by various symptoms, the presence of a cluster of which leads to its diagnosis. Regular treatment leads to a remission of the illness which might relapse on discontinuity of medicines. There have been numerous epidemiological studies and clinical trials on the illness. However, schizophrenia also poses a challenge to statisticians in theorising and statistically modeling its different aspects. Aim: This is an attempt to study, by developing suitable stochastic models, the behaviour of the symptoms of schizophrenia manifested in a patient in relation to the successive visits to the doctor. Methods: The concepts of probability theory, structure functions, binomial distribution, Markov chain, and transition probabilities are the statistical tools used to model the medical facts regarding schizophrenia. Results: By developing probabilistic and stochastic models, a relationship between the number of symptoms at the time of diagnosis and the number of revisits to the doctor has been developed and thereby an important result regarding the expected number of symptoms present at a particular visit to the doctor has been established. A Markovian model studying the pattern of the symptoms in the course to recovery has been presented and its application in the behaviour of the symptoms of schizophrenia has been verified. Conclusions: It is expected that the above results might help doctors in planning out the treatment schedule in advance. It can also lead to a further study on cost benefit analysis of the treatment process.

A Short Report on the Markov Property of DNA Sequences on 200-bp Genomic Units of ENCODE/Broad ChromHMM Annotations: A Computational Perspective

The non-coding DNA in eukaryotic genomes encodes a language which programs chromatin accessibility, transcription factor binding, and various other activities. The objective of this short report was to determine the impact of primary DNA sequence on the epigenomic landscape across 200-base pair genomic units by integrating nine publicly available ChromHMM Browser Extensible Data files of the Encyclopedia of DNA Elements (ENCODE) project. The nucleotide frequency profiles of nine chromatin annotations with the units of 200 bp were analyzed and integrative Markov chains were built to detect the Markov properties of the DNA sequences in some of the active chromatin states of different ChromHMM regions. Our aim was to identify the possible relationship between DNA sequences and the newly built chromatin states based on the integrated ChromHMM datasets of different cells and tissue types.

Study of medical equipment configuration based on Markov-process / 医疗卫生装备

Objective To explore medical equipment allocation with considerations on randomly distributed and dynamic injury conditions by analyzing injury conditions transition and medical equipment stochastic service process.Methods A casualty array change model was established by injury conditions evolution analysis,Poisson process and Markov chain.Medical equipment stochastic service processes in medical facilities were probed,and the service rules were constructed.Expert investigation was carried out to acquire conditions transition indexes and to determine the vectors for conditions transition without manual intervention and their changes after treatment,then simulation tools were used to optimize medical equipment allocation.Results The emergency treatment table in some field medical station was considered as the subject,and the optimum allocation was proposed for emergency treatment table with practical data and simulation calculation.Conclusion The emergency treatment table allocation proposed was similar to the actual one in the medical station.Markov-process-based medical equipment allocation responses injury conditions changes and the fluctuation of treatment sequence,which has the result reliable and the method versatile and practical,and lays a foundation for medical equipment allocation and optimization.

Comparison of different methods in dealing with HIV viral load data with diversified missing value mechanism on HIV positive MSM / 中华流行病学杂志

Objective To compare results of different methods in organizing HIV viral load (VL) data with missing values mechanism. Methods We used software SPSS 17.0 to simulate complete and missing data with different missing value mechanism from HIV viral loading data collected from MSM in 16 cities in China in 2013. Maximum Likelihood Methods Using the Expectation and Maximization Algorithm (EM), regressive method, mean imputation, delete method, and Markov Chain Monte Carlo (MCMC) were used to supplement missing data respectively. The results of different methods were compared according to distribution characteristics, accuracy and precision. Results HIV VL data could not be transferred into a normal distribution. All the methods showed good results in iterating data which is Missing Completely at Random Mechanism (MCAR). For the other types of missing data, regressive and MCMC methods were used to keep the main characteristic of the original data. The means of iterating database with different methods were all close to the original one. The EM, regressive method, mean imputation, and delete method under-estimate VL while MCMC overestimates it. Conclusion MCMC can be used as the main imputation method for HIV virus loading missing data. The iterated data can be used as a reference for mean HIV VL estimation among the investigated population.

Comparison of different methods in dealing with HIV viral load data with diversified missing value mechanism on HIV positive MSM / 中华流行病学杂志

Objective To compare results of different methods in organizing HIV viral load (VL) data with missing values mechanism. Methods We used software SPSS 17.0 to simulate complete and missing data with different missing value mechanism from HIV viral loading data collected from MSM in 16 cities in China in 2013. Maximum Likelihood Methods Using the Expectation and Maximization Algorithm (EM), regressive method, mean imputation, delete method, and Markov Chain Monte Carlo (MCMC) were used to supplement missing data respectively. The results of different methods were compared according to distribution characteristics, accuracy and precision. Results HIV VL data could not be transferred into a normal distribution. All the methods showed good results in iterating data which is Missing Completely at Random Mechanism (MCAR). For the other types of missing data, regressive and MCMC methods were used to keep the main characteristic of the original data. The means of iterating database with different methods were all close to the original one. The EM, regressive method, mean imputation, and delete method under-estimate VL while MCMC overestimates it. Conclusion MCMC can be used as the main imputation method for HIV virus loading missing data. The iterated data can be used as a reference for mean HIV VL estimation among the investigated population.

Modeling and analysis of triage in disaster rescue action executed by mobile medical unit using stochastic Petri net / 军事医学

Objective To analyze the process of triage in disaster rescue action performed by a mobile medical unit so that the rescue process can be improved , the efficiency of rescue enhanced , and the decision on health service in rescue action is supported.Methods The process of triage in disaster rescue action was modeled based on stochastic Petri net while the performance of the model was analyzed quantitatively .Results and Conclusion The critical factor which affects the efficiency of rescue work is obtained by analyzing the performance of the model .

Population Forecasts for Bangladesh, Using a Bayesian Methodology.

Population projection for many developing countries could be quite a challenging task for the demographers mostly due to lack of availability of enough reliable data. The objective of this paper is to present an overview of the existing methods for population forecasting and to propose an alternative based on the Bayesian statistics, combining the formality of inference. The analysis has been made using Markov Chain Monte Carlo (MCMC) technique for Bayesian methodology available with the software WinBUGS. Convergence diagnostic techniques available with the WinBUGS software have been applied to ensure the convergence of the chains necessary for the implementation of MCMC. The Bayesian approach allows for the use of observed data and expert judgements by means of appropriate priors, and a more realistic population forecasts, along with associated uncertainty, has been possible.

Modelaje Bayesiano espacio-temporal de factores asociados con la incidencia del dengue en el área metropolitana de Maracay, Venezuela / Spatio-temporal Bayesian hierarchical modeling of Dengue incidence in the metropolitan area of Maracay, Venezuela

El dengue es uno de los mayores problemas de salud pública en el estado Aragua. La situación se ha deteriorado en los últimos años, reportándose la mayor epidemia durante el año 2001. En los años 2002 y 2003 las tasas de exposición y riesgos relativos en municipios que conforman al estado Aragua, muestran que el área metropolitana de Maracay concentra riesgos importantes. Los municipios Girardot (capital), Francisco Linares Alcántara y Santiago Mariño, son los que concentraron los mayores riesgos. Durante ese período el número de nuevos casos de dengue aumentó especialmente durante la época de lluvias, evidenciándose la existencia de un patrón estacional. Este trabajo propone Modelos Bayesianos Jerárquicos con estructura espacio temporal que incluye variables climáticas y socio-demográficas con las cuales se identificaron factores de mayor influencia en la incidencia del dengue y se determinaron las parroquias con mayores riesgos.Los ajustes de los modelos resultantes se obtuvieron mediante técnicas con cadenas Markov Monte Carlo (MCMC) y se compararon con el criterio de información de deviancia (DIC). Estos modelos constituyen una herramienta importante que expertos en epidemiología y miembros del sector de salud pública deben considerar para el control del vector Aedes aegypti Linnaeus en el estado Aragua.

Dengue fever is a major public health problem in Aragua State, Venezuela. The situation has worsened in recent years, with a major epidemic during 2001. During 2002 and 2003 the exposition rates and relative risks of the municipalities that encompass Aragua State showed the highest relative risk of infection in the metropolitan area of Maracay. The municipalities of Girardot (capital), Francisco Linares Alcántara and Santiago Mariño concentrated the highest risk. During 2002 and 2003 the number of new dengue cases increased especially during the rainy season, showing the existence of a seasonal pattern. The present work presents Bayesian Hierarchical Models with spatio-temporal structure that included climatic and socioeconomic explanatory variables used to identify factors of major influence on dengue incidence and determined the municipalities with higher risks. Models were fitted using Markov Chain Monte Carlo (MCMC) methods and selected using the deviance information criteria (DIC), respectively. These models constitute an important tool that epidemiologists and public health officers in Aragua State have to consider for the control of the vector Aedes aegypti Linnaeus.

Projeção da distribuição diamétrica de uma floresta explorada seletivamente na Amazônia Ocidental / Projection of the diameter distribution in a selective logging forest in the western Amazon

Utilizando um modelo estocástico, foi projetada a distribuição diamétrica futura de uma floresta submetida à exploração seletiva de madeira na Amazônia Ocidental. Foram utilizados dados de cinco parcelas permanentes localizadas no PC Pedro Peixoto, no Acre. A primeira medição das parcelas ocorreu em 1996, a exploração florestal em 1997 e as re-medições em 1999 e 2001. A principal variável utilizada foi o diâmetro à altura do peito (DAP). A matriz de transição probabilística (Cadeia de Markov) foi utilizada para fazer a projeção da distribuição diamétrica do número de árvores sobreviventes nas classes diamétricas. O modelo foi primeiramente testado para fazer a projeção para 2001, tendo como base as observações de 1999 e seu passado imediato (1997). Quando comparadas às projeções feitas para 2001 e as medições de campo (2001), o teste Qui-quadrado mostrou que não houve diferença significativa entre freqüências esperadas e observadas na distribuição diamétrica (p=0,05). A projeção para 2005 indica que a taxa de mortalidade será próxima a de 2001, e se repetida a taxa de recrutamento em 2005 o total de árvores será maior que o observado em 2001. Esse comportamento da floresta indica que não existe um padrão definido para a dinâmica nas classes diamétricas em termos de mortalidade ou crescimento, apresentando um comportamento aleatório ou probabilístico, justificando a eficiência da Cadeia de Markov para projetar a dinâmica da floresta estudada, podendo auxiliar na determinação do ciclo de corte ou mostrando as tendências que a floresta de hoje apresentará em um futuro próximo.

The diameter distribution of an experimental forest stand in the Western Amazon was projected using a stochastic model after selective logging. The study was developed using data from five permanent plots located in the colonization project Pedro Peixoto, in the state of Acre. Initial measurements of diameter at breast height (DBH) were taken in 1996. The forest was selectively logged in 1997 and DBHs were re-measured in two different occasions, 1999 and 2001. A probabilistic transition matrix (Markov Chain) was used to project the diameter distribution of the number of surviving trees in each diameter class. The model was first tested to project the diameter distribution in 2001, based on DBH measurements from 1997 and 1999. When the projected diameter distribution for 2001 was compared with the field data from the same year, a Chi-squared test (á = 0.05) showed that there was not significant difference between the expected and observed diameter distribution. After that, a projection for 2005 (four years in the future) was run using DBH measurements from 1997 to 2001, indicating that mortality rate was similar to 2001. If repeated the rate of recruitment of 2005, the total number of trees will be higher than observed in 2001. The dynamics of the studied forest suggests that there is not a definitive pattern to changes in diameter distribution and mortality, which indicates a stochastic or probabilistic pattern. This pattern is better modeled by the Markov Chain to project the forest dynamics of studied area, and can help on determination of timber harvesting or the tendencies of forest dynamics in a near future.

Análise Bayesiana no estudo do tempo de retorno das precipitações pluviais máximas em Jaboticabal (SP) / Bayesian analysis for estimating the return period of maximum precipitation at Jaboticabal São Paulo state, Brazil

Dados históricos de precipitação máxima são utilizados para realizar previsões de chuvas extremas, cujo conhecimento é de grande importância na elaboração de projetos agrícolas e de engenharia hidráulica. A distribuição generalizada de valores extremos (GEV) tem sido aplicada com freqüência nesses tipos de estudos, porém, algumas dificuldades na obtenção de estimativas confiáveis sobre alguma medida dos dados têm ocorrido devido ao fato de que, na maioria das situações, tem-se uma quantidade escassa de dados. Uma alternativa para obter melhorias na qualidade das estimativas seria utilizar informações dos especialistas de determinada área em estudo. Sendo assim, objetiva-se neste trabalho analisar a aplicação da Inferência Bayesiana com uma distribuição a priori baseada em quantis extremos, que facilite a incorporação dos conhecimentos fornecidos por especialistas, para obter as estimativas de precipitação máxima para os tempos de retorno de 10 e 20 anos e seus respectivos limites superiores de 95 por cento, para o período anual e para os meses da estação chuvosa em Jaboticabal (SP). A técnica Monte Carlo, via Cadeias de Markov (MCMC), foi empregada para inferência a posteriori de cada parâmetro. A metodologia Bayesiana apresentou resultados mais acurados e precisos, tanto na estimação dos parâmetros da distribuição GEV, como na obtenção dos valores de precipitação máxima provável para a região de Jaboticabal, apresentando-se como uma boa alternativa na incorporação de conhecimentos a priori no estudo de dados extremos.

Historical maximum rainfall data are used to forecast extreme rainfall, which is important to elaborate agricultural and hydraulic engineering projects. Generalized Extreme Value Distribution (GEV) has been applied in such type of studies. Since those values are extracted from the upper (or lower) tail of the original distribution, a scarce amount of data is obtained in most cases, which may be a problem acquiring reliable estimates about some measure of interest. An alternative to overcome this potential problem would be the use of information available from experts in the area. Therefore, this paper intended to analyze the application of the Bayesian Inference using a priori distribution based on extreme quantiles, which facilitates the incorporation of the information supplied by the experts in order to determine the punctual and the 95 percent upper limit estimates of the probable maximum precipitation for return periods of 10 and 20 years, yearly and monthly in Jaboticabal, São Paulo State, Brazil. Markov Chain Monte Carlo (MCMC) methods were used to a posterior inference of each parameter. Bayesian inference yielded more suitable and accurate results in the estimation of the parameters of the GEV distribution as well as in the determination of the values of the probable maximum precipitation estimates for Jaboticabal. It turned out as an interesting way of incorporating prior knowledge to the study of extreme data.

A Statistical Analysis of SNPs, In-Dels, and Their Flanking Sequences in Human Genomic Regions

Due to the increasing interest in SNPs and mutational hot spots for disease traits, it is becoming more important to define and understand the relationship between SNPs and their flanking sequences. To study the effects of flanking sequences on SNPs, statistical approaches are necessary to assess bias in SNP data. In this study we mainly applied Markov chains for SNP sequences, particularly those located in intronic regions, and for analysis of in-del data. All of the pertaining sequences showed a significant tendency to generate particular SNP types. Most sequences flanking SNPs had lower complexities than average sequences, and some of them were associated with microsatellites. Moreover, many Alu repeats were found in the flanking sequences. We observed an elevated frequency of single-base-pair repeat-like sequences, mirror repeats, and palindromes in the SNP flanking sequence data. Alu repeats are hypothesized to be associated with C-to-T transition mutations or A-to-I RNA editing. In particular, the in-del data revealed an association between particular changes such as palindromes or mirror repeats. Results indicate that the mechanism of induction of in-del transitions is probably very different from that which is responsible for other SNPs. From a statistical perspective, frequent DNA lesions in some regions probably have effects on the occurrence of SNPs.