Parametric and Non Homogeneous Semi-Markov Process for HIV Control

Fuzzy SMC for Quantized Nonlinear Stochastic Switching Systems With Semi-Markovian Process and Application

This article is concerned with the issue of quantized sliding-mode control (SMC) design methodology for nonlinear stochastic switching systems subject to semi-Markovian switching parameters, T-S fuzzy strategy, uncertainty, signal quantization, and nonlinearity. Compared with the previous literature, the quantized control input is first considered in studying T-S fuzzy stochastic switching systems with a semi-Markovian process. A mode-independent sliding surface is adopted to avoid the potential repetitive jumping effects. Then, by means of the Lyapunov function, stochastic stability criteria are proposed to be dependent of sojourn time for the corresponding sliding-mode dynamics. Furthermore, the fuzzy-model-based SMC law is proposed to ensure the finite-time reachability of the sliding-mode dynamics. Finally, an application example of a modified series dc motor model is provided to demonstrate the effectiveness of the theoretical findings.

A Markov Model to Estimate Mortality Due to HIV/AIDS Using Viral Load Levels-Based States and CD4 Cell Counts: A Principal Component Analysis Approach

Introduction

Improvement of health in human immunodeficiency virus/acquired immunodeficiency syndrome (HIV/AIDS) patients on antiretroviral therapy (ART) is characterised by an increase in CD4 cell counts and a decrease in viral load to undetectable levels. In modelling HIV/AIDS progression in patients, researchers mostly deal with either viral load levels only or CD4 cell counts only, as they expect these two variables to be collinear. In this study, both variables will be in one model.

Methods

Principal component variables are created by fitting a regression model of CD4 cell counts on viral load levels to improve the efficiency of the model. The new orthogonal covariate is included to represent the CD4 cell counts covariate for the continuous time-homogeneous Markov model defined. Viral load levels are categorised to define the states for the Markov model.

Results

The likelihood ratio test and the estimated AICs show that the model with the orthogonal CD4 cell counts covariate gives a better prediction of mortality than the model in which the covariate is excluded. The study further revealed high accelerated mortality rates from undetectable viral load levels as well as accelerated risks of viral rebound from undetectable viral level for patients with lower CD4 cell counts than expected.

Conclusion

Inclusion of both viral load levels and CD4 cell counts, monitoring and management in time homogeneous Markov models help in the prediction of mortality in HIV/AIDS patients on ART. Higher CD4 cell counts improve the health and consequently survival of HIV/AIDS patients.

Effects of antiretroviral treatment and nadir CD4 count in progression to cardiovascular events and related comorbidities in a HIV Brazilian cohort: a multi-stage approach

The use of highly active antiretroviral therapy has resulted in changes of comorbidity profile in people living with HIV (PLHIV), increasing non-AIDS-related events. The occurrence of cardiovascular events is greater in PLHIV, but the mechanism responsible for it is still controversial. This article aimed to investigate factors associated with the progression to cardiovascular events in PLHIV using HAART. A 15-years cohort study with 1135 PLHIV was conducted in Rio de Janeiro-Brazil. Clinical progression was stratified in five states: No comorbidities (s₁), arterial hypertension (s₂), lipid abnormalities (s₃), hypertension and lipid abnormalities (s₄) and major cardiovascular events (stroke, coronary artery disease, thrombosis or death) (s₅). Semi-Markov models evaluated the effects of cardiovascular traditional factors, treatment and clinical covariates on transitions between these states. Hazard Ratios (HR) and 95% confidence intervals (CI) were provided. In addition to traditional factors (age, sex, educational level and skin color), the development of one comorbidity (lipid abnormalities or hypertension) increased in patients with low nadir CD4 (<50 cells/mm³), (HR = 1.59, CI 1.11-2.28 and 1.36, CI 1.11-1.66, respectively). The risk to experience a second comorbidity (s₃→s₄) increased 75% with low nadir CD4. Age was the only factor that increased the risk of major cardiovascular events once having lipid abnormalities with or without hypertension (s₃,s₄→s₅). The prolonged use of certain antiretroviral drugs (abacavir, didanosine, ritonavir, lopinavir, amprenavir and fosamprenavir) increased the risk of direct transition (s₁→s₅) to major cardiovascular events (HR = 5.29, CI 1.16-24.05). This analysis suggests that prolonged use of certain antiretroviral drugs led directly to major cardiovascular events, while low nadir CD4 only affected the occurrence of lipid abnormalities and hypertension. Management strategies, including rational use of complex exams (such as, computed-tomography angiography), statins and antihypertensives, should be developed based on the distinct roles of antiretroviral use and of HIV infection itself on the progression to cardiovascular events.

A comparison of time-homogeneous Markov chain and Markov process multi-state models

Time-homogeneous Markov models are widely used tools for analyzing longitudinal data about the progression of a chronic disease over time. There are advantages to modeling the true disease progression as a discrete time stationary Markov chain. However, one limitation of this method is its inability to handle uneven follow-up assessments or skipped visits. A continuous time version of a homogeneous Markov process multi-state model could be an alternative approach. In this article, we conduct comparisons of these two methods for unevenly spaced observations. Simulations compare the performance of the two methods and two applications illustrate the results.

Modeling of HIV/AIDS dynamic evolution using non-homogeneous semi-markov process

The purpose of this study is to model the progression of HIV/AIDS disease of an individual patient under ART follow-up using non-homogeneous semi-Markov processes. The model focuses on the patient's age as a relevant factor to forecast the transitions among the different levels of seriousness of the disease. A sample of 1456 patients was taken from a hospital record at Amhara Referral Hospitals, Amhara Region, Ethiopia, who were under ART follow up from June 2006 to August 2013. The states of disease progression adopted in the model were defined based on of the following CD4 cell counts: >500 cells/mm(3) (SI); 349 to 500 cells/mm(3) (SII); 199 to 350 cells/mm(3)(SIII); ≤200 cells/mm(3) (SIV); and death (D). The first four states are referred as living states. The probability that an HIV/AIDS patient with any one of the living states will transition to the death state is greater with increasing age, irrespective of the current state and age of the patient. More generally, the probability of dying decreases with increasing CD4 counts over time. For an HIV/AIDS patient in a specific state of the disease, the probability of remaining in the same state decreases with increasing age. Within the living states, the results show that the probability of being in a better state is non-zero, but less than the probability of being in a worse state for all ages. A reliability analysis also revealed that the survival probabilities are all declining over time. Computed conditional probabilities show differential subject response that depends on the age of the patient. The dynamic nature of AIDS progression is confirmed with particular findings that patients are more likely to be in a worse state than a better one unless interventions are made. Our findings suggest that ongoing ART treatment services could be provided more effectively with careful consideration of the recent disease status of patients.

Semi-Markov models for interval censored transient cognitive states with back transitions and a competing risk

Continuous-time multi-state stochastic processes are useful for modeling the flow of subjects from intact cognition to dementia with mild cognitive impairment and global impairment as intervening transient cognitive states and death as a competing risk. Each subject's cognition is assessed periodically resulting in interval censoring for the cognitive states while death without dementia is not interval censored. Since back transitions among the transient states are possible, Markov chains are often applied to this type of panel data. In this manuscript, we apply a semi-Markov process in which we assume that the waiting times are Weibull distributed except for transitions from the baseline state, which are exponentially distributed and in which we assume no additional changes in cognition occur between two assessments. We implement a quasi-Monte Carlo (QMC) method to calculate the higher order integration needed for likelihood estimation. We apply our model to a real dataset, the Nun Study, a cohort of 461 participants.