This document proposes a stochastic model to describe the progression of chronic kidney disease (CKD) using a continuous-time Markov chain. The model has 5 states representing different stages of CKD severity and death. Explicit expressions are derived for the transition probabilities by solving the Kolmogorov differential equations. The mean time spent in each CKD stage and life expectancy of CKD patients can be estimated using the model. A numerical example is provided to illustrate the model.
This study examined trends in living donor liver transplantation (LDLT) for patients with primary sclerosing cholangitis (PSC) in the era before and after the introduction of the MELD scoring system for organ allocation. The results found that both before and after MELD, patients with PSC were more likely to receive LDLTs than those without PSC. Additionally, the difference increased significantly after MELD, suggesting that MELD may have reduced access to deceased donor livers for PSC patients and led clinicians to refer PSC patients for LDLTs more often to compensate. The findings raise concerns that PSC patients may be disadvantaged if LDLT availability further declines.
PREDICTIVE MODEL FOR LIKELIHOOD OF DETECTING CHRONIC KIDNEY FAILURE AND DISEA...ijcsitcejournal
Fuzzy logic is highly appropriate and valid basis for developing knowledge-based systems in medicine for different tasks and it has been known to produce highly accurate results. Examples of such tasks include syndrome differentiation, likelihood survival for sickle cell anaemia among paediatric patients, diagnosis and optimal selection of medical treatments and real time monitoring of patients. For this paper, a Fuzzy logic-based system is untaken used to provide a comprehensive simulation of a prediction model for determining the likelihood of detecting Chronic Kidney failure/diseases in humans. The Fuzzy-based system uses a 4-tuple record comprising of the following test taken: Blood Urea Test, Urea Clearance Test, Creatinine Clearance test and Estimated Glomerular Filtrate
ate(eGFR).Understanding of the test was elicited from a private hospital in Ibadan through the help of an experienced and qualified nurse which also follows same test according to National Kidney Foundation. This knowledge was then used in the developing the simulated and rule-base prediction model using MATLAB software. The paper also follows the 3 major stages of Fuzzy logic. The results of fuzzification of variables, inference, model testing and defuzzification of variables was also presented. This in turn simplifies the complication involved in detecting Chronic Kidney failure/disease using Fuzzy logic based model.
This document presents a Bayesian semiparametric framework for analyzing semicompeting risks data where the observation of time to a non-terminal event (e.g. hospital readmission) is subject to a terminal event (e.g. death). The framework models the hazards of the non-terminal and terminal events using a shared frailty illness-death model, accounting for dependence between events. It allows researchers to estimate regression parameters, characterize event dependence, and predict outcomes. The framework is applied to Medicare data on pancreatic cancer patients to investigate risks of readmission and death.
This study aimed to develop a predictive model for the costs and life expectancy of patients with diffuse large B-cell lymphoma (DLBCL) in the UK. The study used a discrete event simulation model based on data from 4880 DLBCL patients. The model predicted 5-year and lifetime medical costs and survival for patients based on their characteristics, treatment responses, and costs derived from the data. The results were validated against empirical data and literature. Younger patients had higher costs but better survival, while treatment provided higher costs and longer survival than no treatment. Total annual costs of treating DLBCL in the UK were estimated to be £95-99 million.
This study developed a preoperative risk model to predict the occurrence of postoperative pneumonia in patients undergoing coronary artery bypass grafting (CABG). Researchers analyzed data on over 16,000 CABG patients from 33 hospitals. Postoperative pneumonia occurred in 3.3% of patients. The final model identified 17 preoperative factors that were significantly associated with increased risk of pneumonia, including demographics, laboratory values, comorbid diseases, pulmonary function, and cardiac function/anatomy. The model had good discrimination (C-statistic of 0.74) and performed well in validation analyses. This risk model can help provide individualized risk estimates and identify opportunities to reduce preoperative pneumonia risk.
This document discusses estimating blood volume flow in precapillary microvessels in the rabbit mesentery based on axial erythrocyte velocity measurements. It summarizes:
1) Volume flow was estimated in 30 microvessels with diameters between 5.6-12 μm by measuring instantaneous axial blood velocity throughout the cardiac cycle and averaging. The effect of velocity profile variation with diameter was also taken into account.
2) According to Murray's law, volume flow should be proportional to diameter to the fourth power. Curve fitting to the volume flow and diameter data supported this relationship, validating the hypothesis that the principle of constant longitudinal pressure gradient applies in the precapillary microvasculature.
3) A
Modeling Algorithm of Estimation Of Renal Function by the Cockcroft and M...hiij
The purpose of this study was to determine the concordance between two equations used for estimating
glomerular filtration rate, in order to verify the possibility to be used interchangeably in the clinical
practice. The two equations are of Cockcroft & Gault (CG) (1976) formula and MDRD (modification of
Diet in Renal Disease) (1999) formula, these two models allow the assessment of glomerular filtration rate
(GFR) by calculating creatinine clearance (CLCR).To make a comparison between these two formulas
different models were examined for Subjects with normal renal function, Patients with renal impairment,
Diabetic patients, Age and sex, finally lean and obese patients by modeling two algorithms with the two
functions. Results show that the formula of Cockcroft & Gault remains the method of choice for estimating
renal function in clinical practice.
An illustration of the usefulness of the multi-state model survival analysis ...cheweb1
This seminar will demonstrate the potential of multi-state survival modeling (MSM) as a tool for decision analytic modelling and compare it to the usual Markov transition modelling approach. After briefly reviewing examples of MSM in the health economics literature, a technology appraisal submitted to NICE evaluating the cost effectiveness of Rituximab for first line treatment of chronic lymphocytic leukaemia will be used for illustration purposes. Finally, areas of future research will be outlined.
This study examined trends in living donor liver transplantation (LDLT) for patients with primary sclerosing cholangitis (PSC) in the era before and after the introduction of the MELD scoring system for organ allocation. The results found that both before and after MELD, patients with PSC were more likely to receive LDLTs than those without PSC. Additionally, the difference increased significantly after MELD, suggesting that MELD may have reduced access to deceased donor livers for PSC patients and led clinicians to refer PSC patients for LDLTs more often to compensate. The findings raise concerns that PSC patients may be disadvantaged if LDLT availability further declines.
PREDICTIVE MODEL FOR LIKELIHOOD OF DETECTING CHRONIC KIDNEY FAILURE AND DISEA...ijcsitcejournal
Fuzzy logic is highly appropriate and valid basis for developing knowledge-based systems in medicine for different tasks and it has been known to produce highly accurate results. Examples of such tasks include syndrome differentiation, likelihood survival for sickle cell anaemia among paediatric patients, diagnosis and optimal selection of medical treatments and real time monitoring of patients. For this paper, a Fuzzy logic-based system is untaken used to provide a comprehensive simulation of a prediction model for determining the likelihood of detecting Chronic Kidney failure/diseases in humans. The Fuzzy-based system uses a 4-tuple record comprising of the following test taken: Blood Urea Test, Urea Clearance Test, Creatinine Clearance test and Estimated Glomerular Filtrate
ate(eGFR).Understanding of the test was elicited from a private hospital in Ibadan through the help of an experienced and qualified nurse which also follows same test according to National Kidney Foundation. This knowledge was then used in the developing the simulated and rule-base prediction model using MATLAB software. The paper also follows the 3 major stages of Fuzzy logic. The results of fuzzification of variables, inference, model testing and defuzzification of variables was also presented. This in turn simplifies the complication involved in detecting Chronic Kidney failure/disease using Fuzzy logic based model.
This document presents a Bayesian semiparametric framework for analyzing semicompeting risks data where the observation of time to a non-terminal event (e.g. hospital readmission) is subject to a terminal event (e.g. death). The framework models the hazards of the non-terminal and terminal events using a shared frailty illness-death model, accounting for dependence between events. It allows researchers to estimate regression parameters, characterize event dependence, and predict outcomes. The framework is applied to Medicare data on pancreatic cancer patients to investigate risks of readmission and death.
This study aimed to develop a predictive model for the costs and life expectancy of patients with diffuse large B-cell lymphoma (DLBCL) in the UK. The study used a discrete event simulation model based on data from 4880 DLBCL patients. The model predicted 5-year and lifetime medical costs and survival for patients based on their characteristics, treatment responses, and costs derived from the data. The results were validated against empirical data and literature. Younger patients had higher costs but better survival, while treatment provided higher costs and longer survival than no treatment. Total annual costs of treating DLBCL in the UK were estimated to be £95-99 million.
This study developed a preoperative risk model to predict the occurrence of postoperative pneumonia in patients undergoing coronary artery bypass grafting (CABG). Researchers analyzed data on over 16,000 CABG patients from 33 hospitals. Postoperative pneumonia occurred in 3.3% of patients. The final model identified 17 preoperative factors that were significantly associated with increased risk of pneumonia, including demographics, laboratory values, comorbid diseases, pulmonary function, and cardiac function/anatomy. The model had good discrimination (C-statistic of 0.74) and performed well in validation analyses. This risk model can help provide individualized risk estimates and identify opportunities to reduce preoperative pneumonia risk.
This document discusses estimating blood volume flow in precapillary microvessels in the rabbit mesentery based on axial erythrocyte velocity measurements. It summarizes:
1) Volume flow was estimated in 30 microvessels with diameters between 5.6-12 μm by measuring instantaneous axial blood velocity throughout the cardiac cycle and averaging. The effect of velocity profile variation with diameter was also taken into account.
2) According to Murray's law, volume flow should be proportional to diameter to the fourth power. Curve fitting to the volume flow and diameter data supported this relationship, validating the hypothesis that the principle of constant longitudinal pressure gradient applies in the precapillary microvasculature.
3) A
Modeling Algorithm of Estimation Of Renal Function by the Cockcroft and M...hiij
The purpose of this study was to determine the concordance between two equations used for estimating
glomerular filtration rate, in order to verify the possibility to be used interchangeably in the clinical
practice. The two equations are of Cockcroft & Gault (CG) (1976) formula and MDRD (modification of
Diet in Renal Disease) (1999) formula, these two models allow the assessment of glomerular filtration rate
(GFR) by calculating creatinine clearance (CLCR).To make a comparison between these two formulas
different models were examined for Subjects with normal renal function, Patients with renal impairment,
Diabetic patients, Age and sex, finally lean and obese patients by modeling two algorithms with the two
functions. Results show that the formula of Cockcroft & Gault remains the method of choice for estimating
renal function in clinical practice.
An illustration of the usefulness of the multi-state model survival analysis ...cheweb1
This seminar will demonstrate the potential of multi-state survival modeling (MSM) as a tool for decision analytic modelling and compare it to the usual Markov transition modelling approach. After briefly reviewing examples of MSM in the health economics literature, a technology appraisal submitted to NICE evaluating the cost effectiveness of Rituximab for first line treatment of chronic lymphocytic leukaemia will be used for illustration purposes. Finally, areas of future research will be outlined.
This study analyzed data from 2467 lung cancer cases diagnosed between 1996-2010 in southern Switzerland to assess the impact of immunohistochemical (IHC) studies on lung cancer subtypes. The four main histotypes were adenocarcinoma (AC), large cell carcinoma/non-small cell lung cancer (LCC/NSCLC), small cell carcinoma (SmCC), and squamous cell carcinoma (SqCC). Trend analysis showed a significant increase in AC incidence and decrease in LCC/NSCLC incidence beginning in 2003, coinciding with the introduction of IHC studies. Improved two-year survival was seen in SqCC while survival decreased in LCC/NSCLC. The results highlight that IHC studies impact
This document summarizes a retrospective study examining the physiological changes in patients with maxillofacial trauma compared to a control group. The study found several significant differences in complete blood counts and vital signs between the two groups within 24 hours of injury. Specifically, trauma patients had higher hemoglobin, red blood cell count, and white blood cell count levels. They also had lower diastolic blood pressure, oxygen saturation, and higher temperature and pulse rate compared to controls. The authors conclude that while the changes were within normal ranges, they reflect the body's compensatory mechanisms to stabilize after injury and extrapolate these findings to better understand the metabolic response to trauma.
Use Proportional Hazards Regression Method To Analyze The Survival of Patient...Waqas Tariq
The Kaplan Meier method is used to analyze data based on the survival time. In this paper used Kaplan Meier procedure and Cox regression with these objectives. The objectives are finding the percentage of survival at any time of interest, comparing the survival time of two studied groups and examining the effect of continuous covariates with the relationship between an event and possible explanatory variables. The variables (Age, Gender, Weight, Drinking, Smoking, District, Employer, Blood Group) are used to study the survival patients with cancer stomach. The data in this study taken from Hiwa/Hospital in Sualamaniyah governorate during the period of (48) months starting from (1/1/2010) to (31/12/2013) .After Appling the Cox model and achieve the hypothesis we estimated the parameters of the model by using (Partial Likelihood) method and then test the variables by using (Wald test) the result show that the variables age and weight are influential at the survival of time.
Background: Resectability Criteria for Colorectal Liver Metastases (CRLM) have expanded, and advances in liver surgery have increased the number of patients eligible for resection. Identifying risk factors for early recurrence to help stratify CRLM patients will contribute to targeted management of these patients, including surveillance follow-up.Objectives: To identify risk factors for early recurrence post-resection for CRLM in a contemporary cohort of patients. Early recurrence was defi ned based on unit protocol as evidence of recurrent disease on follow-up imaging within one year of surgery.Methods: From January 2012 to December 2016, 133 patients with CRLM underwent liver resection in our Unit; 115 patients followed up for at least a year were eligible. We analysed pre-operative variables (sex, age, BMI, comorbidities, CEA and Liver function tests (LFTs), lesion number, size of largest liver lesion, neoadjuvant chemotherapy), operative variables (anatomical vs non-anatomical, major vs minor, redo liver surgery, concomitant use of ablation techniques, blood loss, blood transfusions, Pringle’s manoeuvre), and post-operative variables (complications, length of hospital stay, histological parameters) were analysed.
Clustering Cardiovascular Risk Trajectories of Patients with Type 2 Diabetes ...anmarmil
Presentation done in the 41st International Engineering in Medicine and Biology Conference, to be held in Berlin, Germany from July 23–27, 2019.
Author version of the full paper available in https://www.researchgate.net/publication/334647238_Clustering_Cardiovascular_Risk_Trajectories_of_Patients_with_Type_2_Diabetes_Using_Process_Mining
This meta-analysis combines data from 5 randomized controlled trials investigating adjuvant chemotherapy and chemoradiation for pancreatic cancer. It includes individual patient data from 875 patients across 4 trials, as well as previously unpublished updated follow-up data from 261 additional patients in the ESPAC1 trial. The analysis found that chemotherapy significantly reduced the risk of death, with median survival of 19 months with chemotherapy versus 13.5 months without. However, chemoradiation did not significantly reduce the risk of death compared to no adjuvant treatment, with median survivals of 15.8 months and 15.2 months respectively. Subgroup analyses suggested chemoradiation may be more effective for patients with positive resection margins, while chemotherapy was less effective for this
Week12sampling and feature selection technique to solve imbalanced datasetMusTapha KaMal FaSya
The document describes a study that aimed to improve predictions of breast cancer patient survivability by addressing the issue of imbalanced data. The study used various machine learning techniques including logistic regression, decision trees, SMOTE oversampling, and cost-sensitive learning on a dataset of 215,221 breast cancer patients obtained from the SEER database. Experimental results found that decision tree and logistic regression models combined with SMOTE and cost-sensitive learning had higher predictive performance than the original models. Logistic regression was also found to have better statistical power than decision trees in predicting five-year survivability.
The Prognostic Value of Nucleolar Organiser Regions in Colorectal CancerMichelle Fynes
Nucleolar organiser regions (AgNORs) are loops of ribosomal DNA which reflect the cellular activity or malignant potential of the cell and are identified by a specific staining technique. The purpose of this study was to assess the prognostic value of AgNORs in colorectal cancer and to compare it with other accepted prognostic methods.
The Texas Supreme Court held that a forfeiture clause in ExxonMobil's non-contributory profit sharing plan that allowed forfeiture of stock awards if an employee worked for a competitor was not an unenforceable non-compete agreement under Texas law. The court conducted a conflict-of-law analysis and determined that New York law, as chosen in the plan, should apply. Under New York law, the forfeiture clause was enforceable because the employee, Drennen, voluntarily left ExxonMobil to work for a competitor and forfeited his stock awards by doing so. However, the court reserved judgment on whether such forfeiture clauses would be enforceable restraints of trade under Texas law.
A Review: Significant Research on Time And Frequency Synchronization In MIMO ...IJERA Editor
This paper proposes a fast and dependable procedure for timing and frequency synchronization of multiple-input
multiple- output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. Orthogonal frequency
division multiplexing (OFDM) could be a outstanding technique for high info rate remote transmission. The
execution of OFDM framework is exceptionally touchy to transporter repeat Offset (CFO) that presents between
bearer electric resistances (ICI). Multi data multi yield frame work used for increasing various qualities increase
and limit of the framework. During this space repeat synchronization in associate OFDM framework is
contemplated and gave past work OFDM framework.
The document discusses rejecting "busyness" in business and leadership. It argues that being overly busy prevents leaders from doing deeper work and focusing on important issues. It advocates for slowing down and creating space for reflection, which allows for more meaningful problem solving and creation of purpose-driven visions to guide an organization. The unconventional leader protects time for quiet reflection and avoids being swept up in constant activity and distraction.
An advisory firm delivering services to the investors may help you in this sector. They use to provide such professionals who give such tips and hints which benefits the traders and help them to achieve the desired success.
An automatic filtering task in osn using content based approachIAEME Publication
This document summarizes an academic paper on developing an automatic filtering system for online social networks using content-based approaches. It describes a three-tier architecture for the filtering system, with the lowest layer managing social networks, a middle layer performing message categorization and blacklisting, and a top layer providing a graphical user interface. The system works by intercepting messages, extracting metadata using machine learning classification, applying filtering and blacklisting rules, and publishing approved messages while filtering unwanted ones based on content and creator. It aims to allow users more control over messages on their walls by blocking offensive, political, or other undesirable content in an automatic way.
Kisah Abu Nawas, tokoh Persia yang hidup pada abad ke-8 M yang dikenal karena humor dan kecerdasannya. Abu Nawas berpura-pura menjadi orang gila setelah ayahnya meninggal agar tidak diangkat menjadi hakim menggantikan ayahnya, meskipun akhirnya diangkat menjadi hakim.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
This study analyzed data from 2467 lung cancer cases diagnosed between 1996-2010 in southern Switzerland to assess the impact of immunohistochemical (IHC) studies on lung cancer subtypes. The four main histotypes were adenocarcinoma (AC), large cell carcinoma/non-small cell lung cancer (LCC/NSCLC), small cell carcinoma (SmCC), and squamous cell carcinoma (SqCC). Trend analysis showed a significant increase in AC incidence and decrease in LCC/NSCLC incidence beginning in 2003, coinciding with the introduction of IHC studies. Improved two-year survival was seen in SqCC while survival decreased in LCC/NSCLC. The results highlight that IHC studies impact
This document summarizes a retrospective study examining the physiological changes in patients with maxillofacial trauma compared to a control group. The study found several significant differences in complete blood counts and vital signs between the two groups within 24 hours of injury. Specifically, trauma patients had higher hemoglobin, red blood cell count, and white blood cell count levels. They also had lower diastolic blood pressure, oxygen saturation, and higher temperature and pulse rate compared to controls. The authors conclude that while the changes were within normal ranges, they reflect the body's compensatory mechanisms to stabilize after injury and extrapolate these findings to better understand the metabolic response to trauma.
Use Proportional Hazards Regression Method To Analyze The Survival of Patient...Waqas Tariq
The Kaplan Meier method is used to analyze data based on the survival time. In this paper used Kaplan Meier procedure and Cox regression with these objectives. The objectives are finding the percentage of survival at any time of interest, comparing the survival time of two studied groups and examining the effect of continuous covariates with the relationship between an event and possible explanatory variables. The variables (Age, Gender, Weight, Drinking, Smoking, District, Employer, Blood Group) are used to study the survival patients with cancer stomach. The data in this study taken from Hiwa/Hospital in Sualamaniyah governorate during the period of (48) months starting from (1/1/2010) to (31/12/2013) .After Appling the Cox model and achieve the hypothesis we estimated the parameters of the model by using (Partial Likelihood) method and then test the variables by using (Wald test) the result show that the variables age and weight are influential at the survival of time.
Background: Resectability Criteria for Colorectal Liver Metastases (CRLM) have expanded, and advances in liver surgery have increased the number of patients eligible for resection. Identifying risk factors for early recurrence to help stratify CRLM patients will contribute to targeted management of these patients, including surveillance follow-up.Objectives: To identify risk factors for early recurrence post-resection for CRLM in a contemporary cohort of patients. Early recurrence was defi ned based on unit protocol as evidence of recurrent disease on follow-up imaging within one year of surgery.Methods: From January 2012 to December 2016, 133 patients with CRLM underwent liver resection in our Unit; 115 patients followed up for at least a year were eligible. We analysed pre-operative variables (sex, age, BMI, comorbidities, CEA and Liver function tests (LFTs), lesion number, size of largest liver lesion, neoadjuvant chemotherapy), operative variables (anatomical vs non-anatomical, major vs minor, redo liver surgery, concomitant use of ablation techniques, blood loss, blood transfusions, Pringle’s manoeuvre), and post-operative variables (complications, length of hospital stay, histological parameters) were analysed.
Clustering Cardiovascular Risk Trajectories of Patients with Type 2 Diabetes ...anmarmil
Presentation done in the 41st International Engineering in Medicine and Biology Conference, to be held in Berlin, Germany from July 23–27, 2019.
Author version of the full paper available in https://www.researchgate.net/publication/334647238_Clustering_Cardiovascular_Risk_Trajectories_of_Patients_with_Type_2_Diabetes_Using_Process_Mining
This meta-analysis combines data from 5 randomized controlled trials investigating adjuvant chemotherapy and chemoradiation for pancreatic cancer. It includes individual patient data from 875 patients across 4 trials, as well as previously unpublished updated follow-up data from 261 additional patients in the ESPAC1 trial. The analysis found that chemotherapy significantly reduced the risk of death, with median survival of 19 months with chemotherapy versus 13.5 months without. However, chemoradiation did not significantly reduce the risk of death compared to no adjuvant treatment, with median survivals of 15.8 months and 15.2 months respectively. Subgroup analyses suggested chemoradiation may be more effective for patients with positive resection margins, while chemotherapy was less effective for this
Week12sampling and feature selection technique to solve imbalanced datasetMusTapha KaMal FaSya
The document describes a study that aimed to improve predictions of breast cancer patient survivability by addressing the issue of imbalanced data. The study used various machine learning techniques including logistic regression, decision trees, SMOTE oversampling, and cost-sensitive learning on a dataset of 215,221 breast cancer patients obtained from the SEER database. Experimental results found that decision tree and logistic regression models combined with SMOTE and cost-sensitive learning had higher predictive performance than the original models. Logistic regression was also found to have better statistical power than decision trees in predicting five-year survivability.
The Prognostic Value of Nucleolar Organiser Regions in Colorectal CancerMichelle Fynes
Nucleolar organiser regions (AgNORs) are loops of ribosomal DNA which reflect the cellular activity or malignant potential of the cell and are identified by a specific staining technique. The purpose of this study was to assess the prognostic value of AgNORs in colorectal cancer and to compare it with other accepted prognostic methods.
The Texas Supreme Court held that a forfeiture clause in ExxonMobil's non-contributory profit sharing plan that allowed forfeiture of stock awards if an employee worked for a competitor was not an unenforceable non-compete agreement under Texas law. The court conducted a conflict-of-law analysis and determined that New York law, as chosen in the plan, should apply. Under New York law, the forfeiture clause was enforceable because the employee, Drennen, voluntarily left ExxonMobil to work for a competitor and forfeited his stock awards by doing so. However, the court reserved judgment on whether such forfeiture clauses would be enforceable restraints of trade under Texas law.
A Review: Significant Research on Time And Frequency Synchronization In MIMO ...IJERA Editor
This paper proposes a fast and dependable procedure for timing and frequency synchronization of multiple-input
multiple- output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. Orthogonal frequency
division multiplexing (OFDM) could be a outstanding technique for high info rate remote transmission. The
execution of OFDM framework is exceptionally touchy to transporter repeat Offset (CFO) that presents between
bearer electric resistances (ICI). Multi data multi yield frame work used for increasing various qualities increase
and limit of the framework. During this space repeat synchronization in associate OFDM framework is
contemplated and gave past work OFDM framework.
The document discusses rejecting "busyness" in business and leadership. It argues that being overly busy prevents leaders from doing deeper work and focusing on important issues. It advocates for slowing down and creating space for reflection, which allows for more meaningful problem solving and creation of purpose-driven visions to guide an organization. The unconventional leader protects time for quiet reflection and avoids being swept up in constant activity and distraction.
An advisory firm delivering services to the investors may help you in this sector. They use to provide such professionals who give such tips and hints which benefits the traders and help them to achieve the desired success.
An automatic filtering task in osn using content based approachIAEME Publication
This document summarizes an academic paper on developing an automatic filtering system for online social networks using content-based approaches. It describes a three-tier architecture for the filtering system, with the lowest layer managing social networks, a middle layer performing message categorization and blacklisting, and a top layer providing a graphical user interface. The system works by intercepting messages, extracting metadata using machine learning classification, applying filtering and blacklisting rules, and publishing approved messages while filtering unwanted ones based on content and creator. It aims to allow users more control over messages on their walls by blocking offensive, political, or other undesirable content in an automatic way.
Kisah Abu Nawas, tokoh Persia yang hidup pada abad ke-8 M yang dikenal karena humor dan kecerdasannya. Abu Nawas berpura-pura menjadi orang gila setelah ayahnya meninggal agar tidak diangkat menjadi hakim menggantikan ayahnya, meskipun akhirnya diangkat menjadi hakim.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
Launching google classroom in your schoolCraig Hansen
This document provides an overview of launching Google Classroom in a school. It discusses what Google Classroom (GC) is and is not, how the presenter has launched it at their school, and 31 things teachers can do on GC. GC is introduced as a learning management system with minimal gradebook functionality that automatically saves all files to Google Drive. Teachers are then guided through live steps to set up a class, add teachers, load assignments, share files, and receive assignments on GC.
To find effects of GMAW parameters on Mechanical Properties of Aluminum AlloysIJERA Editor
The present research aims to investigate the effects of Gas Metal Arc Welding (GMAW) on the mechanical
properties of different grades of aluminum alloys. GMAW is the most common method of joining aluminum
alloys used in various industrial processes. It replaces the Tungsten Inert Gas (TIG) method of providing equally
high quality of joints with a much higher performance. Aluminum alloys under consideration for this
experiment will be from 6XXX series, consisting of Silicon and Magnesium as main alloying elements. Weld
joints Will be produced with the help of a Gas Metal Arc Welding (GMAW) process. The Hardness, Tensile
strength, yield stresses and elongation will be the mechanical properties to be obtained. As aluminum alloys
show large micro structural changes after welding it is necessary to know about the effect of welding parameters
on the mechanical properties of weldements as too high welding current and too high welding speed will result
in high heat input and weakening of weld profile so a balance is need to be struck between welding parameters
and mechanical properties. Scattering Electron Microscopy (SEM) technique will be used to analyze micro
Controlling and Reducing of Speed for Vehicles Automatically By Using Rf Tech...IJERA Editor
This document describes a system to automatically control and reduce vehicle speed using RF technology. The system uses RF transmitters mounted in areas like curves to transmit a signal when a vehicle enters that area. Receivers in the vehicle detect this signal and send it to a microcontroller which reduces the fuel flow, slowing the vehicle. This prevents accidents by reducing speed in hazardous areas. The document provides details on the system components, working, applications, advantages and conclusions.
This study evaluated the predictive value of red cell distribution width (RDW) on the development of anastomotic leak or readmission within 30 days following colectomy. The study reviewed 118 patients who underwent colectomy and found that an elevated RDW (greater than or equal to 14.0) had a sensitivity of 89.8% for predicting readmission or leak. A normal RDW below 14.0 had a negative predictive value of 87.7% for predicting an uncomplicated postoperative course without readmission or leak. The RDW test was found to be a readily available and effective criterion for predicting readmissions and leaks following colectomy.
This study examined trends in living donor liver transplantation (LDLT) for patients with primary sclerosing cholangitis (PSC) in the era before and after the introduction of the MELD scoring system for organ allocation. The results found that both before and after MELD, patients with PSC were more likely to receive LDLTs than those without PSC. Additionally, the difference increased significantly after MELD, suggesting that MELD may have reduced access to deceased donor livers for PSC patients and increased their rates of LDLT. The authors conclude that MELD could be unintentionally disadvantaging PSC patients and modifications may be needed if LDLT availability further declines.
This study examined trends in living donor liver transplantation (LDLT) for patients with primary sclerosing cholangitis (PSC) in the era before and after the implementation of the Model for End-Stage Liver Disease (MELD) score for organ allocation. The results found that patients with PSC were more likely to receive LDLTs than patients without PSC both before and after MELD. Additionally, the likelihood of PSC patients receiving an LDLT increased to a greater degree after MELD compared to before. This raises the possibility that MELD reduced access to deceased donor livers for PSC patients, leading clinicians to refer them more often for LDLTs. Future research is needed to determine if LDLTs impact outcomes
Analysis of chronic diseases progression using stochastic models.pdfiman773407
This is my Master thesis in statistics from Cairo university. It is about using a continuous time Markov chains in the analysis of non-alcoholic fatty liver disease or the newly proposed name (metabolic associates fatty liver disease) .
- The document describes two Markov models (Muenz-Rubinstein and Azzalini) for analyzing health condition data from the Health and Retirement Survey (HRS)
- It fits both models to HRS data to predict health conditions (dependent variable) based on age, gender, and BMI (independent variables)
- Results show Azzalini's model was more efficient at predicting health conditions compared to Muenz-Rubinstein based on the estimated efficiencies of each model
Living Donor Liver Transplantation in Hepatocellular Carcinoma: How Far Can W...semualkaira
The expansion in Liver Transplantation (LT) selection criteria for
Hepatocellular Carcinoma (HCC) has shown acceptable results in
survival rate and tumor recurrence. Historical analysis of the results shows that the path taken so far is correct; however, there
are still doubts about the limit of this expansion. The acquisition
of new selection tools that measure the biological behavior of the
tumor, instead of the historic and simple preoperative morphological analysis, has been gaining strength in this expansion. In this
context, analyzing the ethical perspective in the use of grafts from
living donors is essential in order to seek a risk vs. benefit balance
for both donor and recipient.
Research Progress in Chronic Lymphocytic Leukemiadaranisaha
Cancer is an uncontrolled division of cell occurs due to genetic alterations and mutation. Chronic lymphocytic leukemia is the heterogeneous lymphocytic malignancy worldwide that leads to death. The advancement of genetic analysis techniques and the identification of suitable biomarkers show significant differences in the treatment period. In this paper will discuss the microRNA that is small Non-coding RNAs and is involved in CLL beginning, development, and resistance to therapy and also will explain the stages of CLL.
Research Progress in Chronic Lymphocytic Leukemiasemualkaira
Cancer is an uncontrolled division of cell occurs due
to genetic alterations and mutation. Chronic lymphocytic leukemia is the heterogeneous lymphocytic malignancy worldwide that
leads to death. The advancement of genetic analysis techniques
and the identification of suitable biomarkers show significant differences in the treatment period. In this paper will discuss the microRNA that is small Non-coding RNAs and is involved in CLL
beginning, development, and resistance to therapy and also will
explain the stages of CLL. Moreover, we will also discuss the fluorescent in-situ hybridization FISH-based prognostic factors common genetic aberrations or mutations in CLL. In this paper we will
also discuss about the methods for the treatment of lymphomas
Research Progress in Chronic Lymphocytic Leukemiasemualkaira
Cancer is an uncontrolled division of cell occurs due
to genetic alterations and mutation. Chronic lymphocytic leukemia is the heterogeneous lymphocytic malignancy worldwide that
leads to death. The advancement of genetic analysis techniques
and the identification of suitable biomarkers show significant differences in the treatment period. In this paper will discuss the microRNA that is small Non-coding RNAs and is involved in CLL
beginning, development, and resistance to therapy and also will
explain the stages of CLL. Moreover, we will also discuss the fluorescent in-situ hybridization FISH-based prognostic factors common genetic aberrations or mutations in CLL. In this paper we will
also discuss about the methods for the treatment of lymphomas
Research Progress in Chronic Lymphocytic Leukemiasemualkaira
Cancer is an uncontrolled division of cell occurs due to genetic alterations and mutation. Chronic lymphocytic leukemia is the heterogeneous lymphocytic malignancy worldwide that leads to death. The advancement of genetic analysis techniques and the identification of suitable biomarkers show significant differences in the treatment period. In this paper will discuss the microRNA that is small Non-coding RNAs and is involved in CLL beginning, development, and resistance to therapy and also will explain the stages of CLL.
Research Progress in Chronic Lymphocytic Leukemiasemualkaira
Cancer is an uncontrolled division of cell occurs due
to genetic alterations and mutation. Chronic lymphocytic leukemia is the heterogeneous lymphocytic malignancy worldwide that
leads to death. The advancement of genetic analysis techniques
and the identification of suitable biomarkers show significant differences in the treatment period. In this paper will discuss the microRNA that is small Non-coding RNAs and is involved in CLL
beginning, development, and resistance to therapy and also will
explain the stages of CLL. Moreover, we will also discuss the fluorescent in-situ hybridization FISH-based prognostic factors common genetic aberrations or mutations in CLL. In this paper we will
also discuss about the methods for the treatment of lymphomas.
Research Progress in Chronic Lymphocytic Leukemiasemualkaira
Cancer is an uncontrolled division of cell occurs due
to genetic alterations and mutation. Chronic lymphocytic leukemia is the heterogeneous lymphocytic malignancy worldwide that
leads to death. The advancement of genetic analysis techniques
and the identification of suitable biomarkers show significant differences in the treatment period. In this paper will discuss the microRNA that is small Non-coding RNAs and is involved in CLL
beginning, development, and resistance to therapy and also will
explain the stages of CLL. Moreover, we will also discuss the fluorescent in-situ hybridization FISH-based prognostic factors common genetic aberrations or mutations in CLL. In this paper we will
also discuss about the methods for the treatment of lymphomas
Research Progress in Chronic Lymphocytic LeukemiaAnonIshanvi
Cancer is an uncontrolled division of cell occurs due to genetic alterations and mutation. Chronic lymphocytic leukemia is the heterogeneous lymphocytic malignancy worldwide that leads to death.
Research Progress in Chronic Lymphocytic LeukemiaJohnJulie1
This document summarizes recent research progress in chronic lymphocytic leukemia (CLL). It discusses microRNAs that are involved in the initiation and development of CLL as well as resistance to therapy. It also examines prognostic genetic mutations and abnormalities detected by fluorescent in situ hybridization that can provide information to guide treatment. The document reviews current treatment approaches for CLL including chemotherapy, immunotherapy, targeted therapies, and stem cell transplantation based on disease stage and other risk factors.
Research Progress in Chronic Lymphocytic LeukemiaEditorSara
Cancer is an uncontrolled division of cell occurs due to genetic alterations and mutation. Chronic lymphocytic leukemia is the heterogeneous lymphocytic malignancy worldwide that leads to death. The advancement of genetic analysis techniques and the identification of suitable biomarkers show significant differences in the treatment period. In this paper will discuss the microRNA that is small Non-coding RNAs and is involved in CLL beginning, development, and resistance to therapy and also will explain the stages of CLL.
Research Progress in Chronic Lymphocytic LeukemiaNainaAnon
Cancer is an uncontrolled division of cell occurs due to genetic alterations and mutation. Chronic lymphocytic leukemia is the heterogeneous lymphocytic malignancy worldwide that leads to death. The advancement of genetic analysis techniques and the identification of suitable biomarkers show significant differences in the treatment period. In this paper will discuss the microRNA that is small Non-coding RNAs and is involved in CLL beginning, development, and resistance to therapy and also will explain the stages of CLL.
Research Progress in Chronic Lymphocytic LeukemiaEditorSara
Cancer is an uncontrolled division of cell occurs due to genetic alterations and mutation. Chronic lymphocytic leukemia is the heterogeneous lymphocytic malignancy worldwide that leads to death. The advancement of genetic analysis techniques and the identification of suitable biomarkers show significant differences in the treatment period. In this paper will discuss the microRNA that is small Non-coding RNAs and is involved in CLL beginning, development, and resistance to therapy and also will explain the stages of CLL
The study examined waitlist survival of patients with primary sclerosing cholangitis (PSC) following implementation of the MELD allocation score for liver transplantation. Over an eight-year period, fewer PSC patients (13.6%) died or were removed from the waitlist compared to non-PSC patients (20.5%). Adjusted analysis found PSC patients had a lower risk of waitlist mortality. This difference was partly explained by lower rates of portal hypertension complications in PSC patients. The results suggest practices to increase PSC patient access, such as exception points or living donor transplants, may be unnecessary as PSC patients have better waitlist survival than patients with other liver diseases.
Kshivets O. Synergetics and Survival of Lung Cancer PatientsOleg Kshivets
1. The document analyzes factors that may predict 5-year survival rates of lung cancer patients who underwent lobectomies or pneumonectomies, including phase transitions in the cancer-human system and ratios of cancer and blood cell populations.
2. Data was collected from 490 lung cancer patients undergoing surgery between 1985-2016. Statistical analyses including Cox regression and neural networks were used to identify relationships between survival rates and factors like cancer stage, cell ratios, and phase transitions between early-stage and invasive cancer.
3. The results found that 5-year survival rates were significantly impacted by phase transitions between early and invasive cancer stages, cancer node status, and cell ratio factors. Neural networks analysis correctly predicted 5
The Impact of Lymph Node Dissection on Survival in Intermediate- and High-Ris...semualkaira
Aimed to evaluate the therapeutic effect of pelvic lymph node dissection (PLND) on survival and determine the predictors of lymph node involvement (LNI) in patients with intermediate- or high-risk prostate cancer (PCa) treated with Radical Prostatectomy
The Impact of Lymph Node Dissection on Survival in Intermediate- and High-Ris...
B411010819
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A Stochastic Model for the Progression of Chronic Kidney Disease Noura Anwar*, Mahmoud Riad Mahmoud** *(ISSR, Cairo University) **(ISSR, Cairo University) ABSTRACT Multistate Markov models are well-established methods for estimating rates of transition between stages of chronic diseases. The objective of this study is to propose a stochastic model that describes the progression process of chronic kidney disease; CKD, estimate the mean time spent in each stage of disease stages that precedes developing end-stage renal failure and to estimate the life expectancy of a CKD patient. Continuous- time Markov Chain is appropriate to model CKD. Explicit expressions of transition probability functions are derived by solving system of forward Kolmogorov differential equations. Besides, the mean sojourn time, the state probability distribution, life expectancy of a CKD patient and expected number of patients in each state of the system are presented in the study. A numerical example is provided. Finally, concluding remarks and discussion are presented. Keywords-Chronic Kidney Disease , Continuous-Time Markov Chain , Kolmogorov Differential Equations , Expected Time to Absorption, Stochastic Processes .
I. INTRODUCTION
Recently,non-communicableand chronic diseases have become the major causes of morbidity and mortality around the world[1]. One of these diseases is Chronic Kidney Disease which is defined according to the presence or absence of kidney damage and level of kidney function, irrespective of the etiology of kidney disease. Chronic Kidney Disease “CKD” is a worldwide public health problem. It forms a substantial burden for developed societies [21, 11, 22]as well as in developing countries [2, 3, 4, 26, 15, 23]. For example, in Egypt, there are more than 25000 patients with End-Stage Renal Disease “ESRD” and this number have drastically increased over the latest decades [12]. One of the strategies of defeating any chronic disease is to detect it early side by side with the national planning for insuring sufficient treatment of patients. The earlier the CKD is detected the easier to keep the patients in their primary stages and delaying their transition to more severe stages using suitable treatments and suitable lifestyle regime. Multistate models based on Markov processes are solid methods for estimating rates of transition between stages of diseases. Covariates like age, sex, occupation, previous residence, other chronic diseases, effect of a given intervention …etc. can be fitted to the transition rates. The expected output of these models help in enhancing the national health policies and forming any preventative strategies of CKD and exploring it in earlier stages where the development of the disease can be revised or prevented. For example, the mean sojourn time that the patient spends in the various states of the process,an important concept of multistate Markov models, may be weighted by cost or utility of a given intervention, then it is used to calculate expected costs and outcomes, thus it allows for comparisons between competing alternatives.
Stochastic models help in understanding the mechanism of diseases in terms of explaining relationships between developing and progressing in disease stages and other relevant covariates. Applications of stochastic processesin medicine and their use in controlling disease-related morbidity and mortality have been attempted by number of authors[13, 18, 14, 5, 27, 25]. The objective of stochastic modeling of diseases vary between research. Number of authorswho modeled diseases in order to assess the cost-effectiveness of a new intervention or new technology [6].Another objective of stochastic models is calculate disease progression and use them in controlling diseases-related mortality. It was used in controlling Cancer-related mortality [18]. Jackson et al.(2003) presented a general Hidden Markov model for simultaneously estimating transition rates and probabilities of stage misclassification when diagnosis of disease stages are subject to error.Later in 2007, Shih and others proposed a method for estimating progression of a chronic disease with multistate properties -Type 2 Diabetes- by unifying the prevalence pool concept with the Markov Process Model. Recently, Begun et al.(2012) proposed a multistate continuous-time nonhomogeneous Markov model for describing patients with
RESEARCH ARTICLE OPEN ACCESS
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decreased renal function in order to quantify disease progression and its predictor covariates using observable data.
The main goal of this study is to propose a stochastic model that describes the progression process of CKD, to estimate the mean time spent in each stage of the disease stagesand to estimate the life expectancy of a CKD patient.
II. Methods
Stochastic processes modeling approach is utilized to develop a model of the progression of CKD.General model of disease progression proposed by Jackson et al.(2003). Their general model is consisting of a varying number of transient states and an absorbing state. Themodel allows for moving progressively from milder to more severe disease stages and vice versa.At the same time it allows moving from any of the disease stage to an absorbing stage. The general model of disease progression of Jackson et al. (2003)can be used to describe the progression of CKD which is defined, according to the Kidney Disease Outcomes Quality Initiative (KDOQI) classification for CKD , in terms of staged progressive irreversible deterioration of kidney function. CKD processis illustrated graphically in Fig.1. It is noticed from Fig.1 and from the definition of CKD as a staged progressive irreversible disease that the state space of the progression process is discrete, but the process is continuous with respect to time. The states of CKD that will be considered in the study are defined in Table .1.
Continuous-time Markov chain, “CTMC” is appropriate to model CKD since the patient condition deterioration is continuous in time. A CTMC is said to be homogenous in time if the probability of going from one state to another is independent of the time on which the transition occurs. Homogeneity in time holds true for the process of CKD. Hence, one can assume that the finite homogenous continuous-time Markov chain may be an appropriate model of CKD.
Table (1): Definition of the States of the CKD Model
Table (1): Definition of the States of the CKD Model
State No.
State Name
GFR, ml/min
1
Kidney damage with mild reduction in GFR
60 -90
2
Kidney damage with moderate reduction in GFR
30-59
3
Kidney damage with severe reduction in GFR
15-29
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4
ESRD implying RRT (regardless of GFR)
< 15
5
Death
GFR ; glomerular filtration rate: to measure level of kidney function and determine stage of kidney disease.
Depending on the general illustrative model of CKD progression presented in Fig.1, the transition rate matrix of the CKD Progression Model is as follows:
V is a 5×5 matrix,its elementsλ_ijare the instantaneous rates of transition from one state to another. It can be noticed that λ_ij is independent of time because the CKD process is homogenous with respect to time. Sometimes matrix V is called the generator matrix or the infinitesimal matrix. The elements of V are the model parameters which are population-specific and should be estimated when data is available using the appropriate method of estimation. The initial state probability is given by). This can be written as a vector:
This probability defines the probability of being in one of the states of the process at the beginning of the study. Using the analogy of CKD progression process, the initial vector indicates the initial condition of the CKD patients defined as the proportions of patients in each state of the process at the beginning of the study. Entries of initial vector should be nonnegative and their sum should equal to one. Let us also define the transition probability, p_ij (τ,t), which indicates the probability of being in state i at time τ and would be in state j at timet. The transition probabilities p_ij (τ,t) can also be represented in matrix form.
The rows of P(τ,t) should satisfy the same conditions of the initial state probability vector. The transition probability matrix contains all information necessary to model the movement of a patient among the course of CKD until death. ACTMC is fully characterized oncethe transition rate between different states of the system, V, is specified, or conversely when its transition probability matrix is specified along with the expected sojourn time of each state[7]. For simpler CTMC’s whose transition rate matrix contains a lot of zero elements, it is appropriate to define transition probability functions in terms of transition intensities through solving system of Kolmogorov differential equations. Kolmogorov’s differential equations play central role in the treatment of Markov processes in continuous time. The forward Kolmogorov differential equations (1) describethe probability distribution of a state in time tkeeping the initial point fixed by a so-called “last step analysis”. On the other hand, the backward Kolmogorov differential equations (2) describes the transition probabilities in their dependence on the initial point iby the ”first step analysis”.
(1) with the initial condition P(τ,τ)=I where I is the identity matrix. And
(2) with the initial condition P(t,t)=I [8]
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Solving system of forward Kolmogorov differential equations yields into the transition probabilitiesas functions of λ_ij's which are the model parameters. Those parameters are very essential to the solution of the system. Theseparameters may be estimated by different ways. Possibility1: When we have a set of observed data where patients are observed in different time points. One can form a likelihood function that reflects all the contributions for all transitions between different observations using the solution of the system of Kolmogorov differential equations as the probability density of transitions between each pair of states of the system. Then one can obtain maximum likelihood estimates of the model parameters. Possibility 2: Monte Carlo Markov Chain simulation may be used to simulate life time patient-level trajectories between different states of the system. This requires knowledge of the probability distribution underlying the parameters of the system. This usually requires a lot of time as this application needs a lot of simulations if the data set required is large. The main objective of this article is to present a solution of the system of forward Kolmogorov equation of CKD process. Then presenting forms of some extractor functions that may be of great importance for the clinicians and health policy makers.
III. Model
3.1 Transition Probability Functions There are different ways for obtaining an analytical expression for each element of P(τ,t) in terms of the model parameter V, such as finding the matrix exponentials of the generator matrix V, method of successive approximations, and the spectral methods. For special models, it is possible to calculate an analytic expression for each element of P(τ,t) by solving the forward Kolmogorov differential equations in (1). This is generally quicker and avoids the possible numerical instability of finding the matrix exponentials [14]. By solving system of equations in (1), we get
(3)
where
(4)
where
(5)
where
(6)
(7) where
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P44 τ,t = e− λ45 (t−τ)
(21)
P45 τ,t = 1− e− λ45 (t−τ)
(22)
P51 τ,t = 0
(23)
P52 τ,t = 0
(24)
P53 τ,t = 0
(25)
P54 τ,t = 0
(26)
P55 τ,t = 1
(27)
It makes sense that we have P_ij (τ,t)= 0 for i>j as CKD is irreversible progressive disease, and P_55 (τ,t)= 1 since state “5” represents “Death” which is absorbing. 3.2 Mean sojourn time Since CKD is one of the progressive diseases, the patient is not supposed to have many visits to a single state. In other words, the mean sojourn time which describes the expected duration of a single stay in a state will be equivalent to the total length of stay or the mean time spent by the patient in a given state of the process. The mean sojourn time in a state of a CTMC is calculated in terms of transition rates. It is assumed that the sojourn times e_j's are independent and exponentially distributed random variables with mean 1/λ_j [9] where λ_j=-λ_jj for j=1,…,4. Hence, we conclude that
e1= 1λ12+λ15
( 28)
e2= 1λ23+λ25
( 29)
e3= 1λ34+λ35
( 30)
e4= 1λ45
( 31)
3.3 State Probability Distribution It is important to estimate the state probability distribution of CKD process in order to calculate the probability that the system will be in a particular state at a specific time point t. Let us assume that the state probability distribution, sometimes known by the marginal distribution, of the process at time t is Π(t). For homogenous CTMC, Π(t) can be evaluated by solving the following system of differential equations Π^' (t)=Π(t)×V (32) with the initial condition Π(0)= (■(π_01&π_02&π_03&π_04&0)). Generally, the solution of this system of equations depends on the form of V. Our hope for a solution in some special cases depends on V resulting in a simple system of equations. The solution of (32) are as follows:
π1(t)= π01e−c1t
(33)
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For CKD process with 5 states, where the first four are transient states and the last is absorbing. We can partition the system as follows:
Also, we can partition the Kolmogorov forward differential equations in (1) as follows:
[P′ t pκ′ (t)]=[P t pκ(t)] BA00
(38)
Where the matrix B is the transition matrix within transient states, the column vector A is the transition rates from the transient states to the absorbing state. Hence, A = -B 1^T, where 1^T is a (k-1)×1 column vector all its elements are ones. The system of equations in (38) may be written as follows,
P′ t =P t Bpn′ t =P t A
(39-a)
(39-b)
Solving (39-a), we get
P t =P 0 eBt
(40)
Substituting by (40) in (39-b), we have
pn′ t =P 0 eBtA
(41)
Note that e^Bt is the matrix exponentials of B, defined as follows:
eBt=I+Bt+ 12(Bt)2+ 13(Bt)3+⋯= 1i! Bt i∞ i=0
(42)
According to [8] as well as other authors, the solution of the first equation of (39-a) given in equation (40) is an explicit solution of the forward Kolmogorov equation and P(0)is the transition probability matrix at initial time point t = 0 which equals to I, the identity matrix. Given that τ_κ is the time to reach the absorbing state from the initial time point, we have
Fκ t =pr τκ ≤t =pr X t =κ = pκ t = 1−P t 1T= 1− P 0 eBt1T
(43)
Random variables which have cumulative distribution function of such form presented in (43), their mean and other moments can be evaluated using the moment theorem for Laplace transforms. First, CTMC with an absorbing state will be presented in Laplace transform such that
[sP∗ s −P(0) spκ∗ (s)]=[P∗ s p∗ κ(s)] BA00
(44)
Hence, equation (44) is presented as follows
sP∗ s −P(0) =P∗ s Bspκ∗ (s)=P∗ s A
(45)
And (40) and (41) will be:
P∗ s =P 0 (sI−B)−1pκ∗ s = 1sP∗ s A= 1s P 0 (sI−B)−1 A
(46)
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It turns out that:
F∗ κ t = 1s P 0 (sI−B)−1 A
(47)
and
f∗ κ t =s F∗ κ t = P 0 (sI−B)−1 A
(48)
Then we can evaluate the mean time to absorption (with A=-B 1^T), E[τ_κ ]=├ (-1) (d〖f^*〗_κ (t))/ds┤|_(s=0)
E τκ = −1 df∗ κ t ds s=0 = −1 P 0 sI−B −2 A s=0 =P 0 −B −11T
(49)
[7] Hence, life expectancy of a CKD patient can be evaluated using (49), where B= −λ12−λ15λ12000−λ23−λ25λ23000−λ34−λ35λ34000−λ45 , and P(0)=I. Thus,
E τ15 = 1λ12+λ15+ λ12 (λ23+λ25) λ12+λ15+ λ12λ23 (λ34+λ35) (λ12+λ15)(λ23+λ25) + λ12λ23λ34(λ23+λ25)(λ45) (λ12+λ15)(λ34+λ35)
(50)
E τ25 = 1λ23+λ25+ λ23 (λ34+λ35) λ23+λ25+ λ23λ34λ45(λ23+λ25)(λ34+λ35)
(51)
E τ35 = 1λ34+λ35+ λ34λ45λ34+λ35
(52)
E τ45 = 1λ45
(53)
The mean time to absorption is equivalent to the life expectancy of a CKD patient, therefore E(τ_i5 ),i=1,…,4 can be interpreted as follows: the life expectancy of a patient given that he observed his illness in state i. 3.5 Expected Number of Patients in Each State let m(0) be the size of patients an initial time point t=0. The initial size of patients m(0)= Σ_(j=1)^4▒〖m_j (0)〗, where m_j (0) is the initial size of patients at state j given that there is m_5 (0)=0 patients at state 5 which is “Death” at the initial time point. Assuming that patients move independently within the states of the system and at the end of the time interval (0,t), there is M_j (t)for j=1,…,4 patients in state j at time t and M_5 (t) deaths at time t. Using equations (3.43), (3.44), (3.45) and (3.46), then the expected number of patients in each state at time t can be computed directly as follows,
E Mj(t) mj(0) = mi 0 pij t n−1i=1 for j=1,…,n−1.
(54)
and
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E M5(t) mj(0) = mi 0 pi5 t n−1i=1 ∀j
(55)
Equation (54) can be presented in details as follows
E M1 t m1 0 = m1 0 p11 t
(56)
E M2 t m1 0 ,m2 0 = m1 0 p12 t +m2 0 p22 t
(57)
E M3 t m1 0 ,m2 0 ,m3 0 = m1 0 p13 t +m2 0 p23 t +m3 0 p33 t
(58)
E M4 t m1 0 ,m2 0 ,m3 0 ,m4 0 = m1 0 p14 t +m2 0 p24 t +m3 0 p34 t +m4 0 p44 t
(59)
and the expected number of deaths will be
E M5(t) m1 0 ,m2 0 ,m3 0 ,m4 0 =m1 0 p15 t +m2 0 p25 t +m3 0 p35 t +m4 0 p45 t
(60)
IV. Numerical Example
This example is adapted from the study of Begun et al. (2013). They used data from a dialysis center serving a region of 310,000 inhabitants. the sample consisted of 2097 CKD patient with at least 2 measurements during January 2005 to December 2010. Our system, showed in figure (1) consists of 5 states. The states of the system are defined in Table.1. Given V= −0.160.15000.010−0.370.2700.100−1.371.270.1000−1.81.800000 We find the one-year transition probability matrix as follows P(1)= 0.850.110.020.0030.0200.690.190.060.06000.250.270.480000.160.8400001 The mean time spent by a CKD patient in state 1 approximately equals 6 years and 3 months, while it decreases in state 2to be about 2 years and 9 months. The deterioration in health state of a CKD patient become rapid in more severe stages than mild stages since the mean time spent by a patient in states 3 and 4 of the system is about 8 and 6 months respectively. Assuming that the initial distribution of patients among the states of the system is Π 0 = 0.40.30.20.10 , then the distribution of this cohort of patients after one year will be approximately as follows: Π 1 = 0.340.250.110.080.22 . The life expectancy of a patient is about 8 years given that he entered the system in state 1, 5 years for state 2, 2years and 6 months for state 3 and about 7 months for state 4. Let m 0 =1000 paitients and divided among the five states of the system as follows, 3002004001000 . Then the expected distribution of this cohort of CKD patients after 1 year is 255171144136294 .
V. Discussion
Chronic diseases represent a major concern to health policy makers, especially in developing countries. When a disease is detected at an early stage, it may be more amenable to treatment [13]. Knowledge about the progression of chronic diseases is important because it may help health policy makers to evaluate expected burden of disease in future and to evaluate cost effectiveness of competing interventions. The Markov chain
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approach is often used for analyzing progression of diseases by describing the time evolution of an individual in the multistate model [5]. CTMC is more appropriate than discrete-time Markov chain for studying patient progression through successive stages of a chronic disease where transitions may be slow, therefore have small probabilities and cannot be described accurately in discrete time units. Kolmogorov’s differential equation plays a key role in defining uniquely CTMC. The solution of Kolmogorov’s differential equation depends on the form of the generator matrix of the model. For simpler forms of the generator matrix, the analytical solution of Kolmogorov’s forward system of differential equation is achievable. The resulting Mathematical relations between the probability of transition and rate of transition can be used to formulate a likelihood function of transitions, then estimating the elements of the generator function which is the model parameters. One should take into consideration some important precautions when estimating the model parameters. For example, kinds of data that may exhibit different types of censoring and pay attention to what form of probability density reflects accurately the observed transitions of a patient in order to formulate realistic likelihood of transitions that yields in a maximum likelihood estimate of the generator matrix the closest description to reality of the natural history of the disease. Begun and others, in 2012, considered three kinds of data structure that can be met in such studies and differentiated between the contributions of possible transitions to the full likelihood which is then used to obtain the maximum likelihood estimate to model parameters. Kalbfleicsh and Lawless in 1985, and recently Jackson in 2011, presented a general methods for evaluating the likelihood for general multistate model in continuous time depending on the form of the transition probability matrix. They differentiated between likelihood for intermittently-observed processes, in other words panel data, exactly-observed death times, exactly-observed transition times and censored states. Some advanced models may be applicable to model natural history of chronic diseases, such as hidden Markov models(see for example, [13]), continuous-time latent Markov model (see for example, [19]) and semi- Markov models (see for example, [10]). In conclusion, we have presented an explicit form of the transition probability matrix of CKD process with 5 states, the first four of them represent the 2nd, 3rd, 4th , and ESRD of CKD according to the KDOQI classification, and the last state is death. Besides, we presented also explicit forms for some important extractor functions which depends primarily on the transition instantaneous rates. References
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