Hierarchical Bayesian inference for HIV dynamic differential equation models incorporating multiple treatment factors

Drug Treatment Effect Model Based on MODWT and Hawkes Self-Exciting Point Process

In precision medicine, especially in the pharmacodynamic area, the lack of an adequate long-term drug effect monitoring model leads to a quite low robustness to the instant drug treatment. Modelling the effect of drug based on the monitoring variables is essential to measure the drug benefit and its side effect preciously. In order to model the complex drug behavior in the context of time series, a sin function is selected to describe the basic trend of heart rate variable that is medically monitored. A Hawkes self-exciting point process model is chosen to describe the effect caused by multiple and sequential drug usage at different time points. The model considers the time lag between the drug given time and the drug effect during the whole drug emission period. A cumulative Gamma distribution is employed to describe the time lag effect. Simulation results demonstrate the established model effectively when describing the baseline trend and the drug effect with low noise levels, where the maximal overlap discrete wavelet transformation is utilized for the information decomposition in the frequency zone. The real data of the variables heart rate and drug liquemin from a medical database is analyzed. Instead of the original time series, scale variable s4 is selected according to the Granger cointegration test. The results show that the model accurately characterizes the cumulative drug effect with the Pearson correlation test value as 0.22, which is more significant for the value under 0.1. In the future, the model can be extended to more complicated scenarios through taking into account multiple monitoring variables and different kinds of drugs.

Handling of uncertainty in medical data using machine learning and probability theory techniques: a review of 30 years (1991-2020)

Understanding the data and reaching accurate conclusions are of paramount importance in the present era of big data. Machine learning and probability theory methods have been widely used for this purpose in various fields. One critically important yet less explored aspect is capturing and analyzing uncertainties in the data and model. Proper quantification of uncertainty helps to provide valuable information to obtain accurate diagnosis. This paper reviewed related studies conducted in the last 30 years (from 1991 to 2020) in handling uncertainties in medical data using probability theory and machine learning techniques. Medical data is more prone to uncertainty due to the presence of noise in the data. So, it is very important to have clean medical data without any noise to get accurate diagnosis. The sources of noise in the medical data need to be known to address this issue. Based on the medical data obtained by the physician, diagnosis of disease, and treatment plan are prescribed. Hence, the uncertainty is growing in healthcare and there is limited knowledge to address these problems. Our findings indicate that there are few challenges to be addressed in handling the uncertainty in medical raw data and new models. In this work, we have summarized various methods employed to overcome this problem. Nowadays, various novel deep learning techniques have been proposed to deal with such uncertainties and improve the performance in decision making.

Parameter Estimation and Variable Selection for Big Systems of Linear Ordinary Differential Equations: A Matrix-Based Approach

Ordinary differential equations (ODEs) are widely used to model the dynamic behavior of a complex system. Parameter estimation and variable selection for a "Big System" with linear ODEs are very challenging due to the need of nonlinear optimization in an ultra-high dimensional parameter space. In this article, we develop a parameter estimation and variable selection method based on the ideas of similarity transformation and separable least squares (SLS). Simulation studies demonstrate that the proposed matrix-based SLS method could be used to estimate the coefficient matrix more accurately and perform variable selection for a linear ODE system with thousands of dimensions and millions of parameters much better than the direct least squares (LS) method and the vector-based two-stage method that are currently available. We applied this new method to two real data sets: a yeast cell cycle gene expression data set with 30 dimensions and 930 unknown parameters and the Standard & Poor 1500 index stock price data with 1250 dimensions and 1,563,750 unknown parameters, to illustrate the utility and numerical performance of the proposed parameter estimation and variable selection method for big systems in practice.

Occurrence of HIV eradication for preexposure prophylaxis treatment with a deterministic HIV model

The authors examine the human immunodeficiency virus (HIV) eradication in this study using a mathematical model and analyse the occurrence of virus eradication during the early stage of infection. To this end they use a deterministic HIV-infection model, modify it to describe the pharmacological dynamics of antiretroviral HIV drugs, and consider the clinical experimental results of preexposure prophylaxis HIV treatment. They also use numerical simulation to model the experimental scenario, thereby supporting the clinical results with a model-based explanation. The study results indicate that the protocol employed in the experiment can eradicate HIV in infected patients at the early stage of the infection.

Episomal HIV-1 DNA and its relationship to other markers of HIV-1 persistence

Reverse transcription of HIV-1 results in the generation of a linear cDNA that serves as the precursor to the integrated provirus. Other classes of extrachromosomal viral cDNA molecules can be found in acutely infected cells including the 1-LTR and 2-LTR circles of viral DNA, also referred as episomal HIV-1 DNA. Circulating CD4⁺ T-cells of treatment-naïve individuals contain significant levels of unintegrated forms of HIV-1 DNA. However, the importance of episomal HIV-1 DNA in the study of viral persistence during antiviral therapy (ART) is debatable. 2-LTR circles are preferentially observed in the effector memory CD4⁺ T cell subset of long-term treated subjects. Treatment intensification of standard regimens has been used to determine if more potent ART can impact viral reservoir activity. Adding a potent antiretroviral drug to a stable triple-drug regimen has no measurable impact on plasma HIV-1 RNA levels, suggesting that ongoing cycles of HIV-1 replication are not a major mechanism driving persistent plasma viremia during triple-drug ART. However, in randomized clinical trials of HIV-1-infected adults on apparently effective ART, the addition of an integrase inhibitor (raltegravir) to stable regimens resulted in a transient increase in 2-LTR circles in some patients, suggesting a pre-intensification steady-state in which the processes of virion generation and de novo infection were occurring. Mathematical modeling of 2-LTR production during integrase inhibitor intensification suggests the coexistence, at different levels, of ongoing de novo infection and de novo replication mechanisms, specifically in inflamed lymphoid drug sanctuaries. Most reports looking into potential changes in 2-LTR circles in interventional clinical studies have simultaneously assessed other potential surrogate markers of viral persistence. Transient increases in 2-LTR circles have been correlated to decreases in CD8⁺ T-cell activation, transient CD45RA⁻CD4⁺ T-cell redistribution, and decreases in the hypercoagulation biomarker D-dimer in ART-intensified individuals. It is difficult, however, to establish a systematic association because the level of correlation with different types of markers differs significantly among studies. In conclusion, despite suppressive ART, a steady-state of de novo infection may persist in some infected individuals and that this may drive immune activation and inflammation changes reflecting residual viral reservoir activity during otherwise apparently suppressive ART.

Experiment Design for Early Molecular Events in HIV Infection

The recent introduction of integrase inhibitors to the HIV antiviral repertoire permits us to create in vitro experiments that reliably terminate HIV infection at the point of chromosomal integration. This allows us to isolate the dynamics of a single round of infection, without needing to account for the influence of multiple overlapping rounds of infection. By measuring the various nucleic acid concentrations in a population of infected target cells at multiple time points, we can infer the rates of these molecular events with great accuracy, which allows us to compare the rates between target cells with different functional phenotypes. This information will help in understanding the behavior of the various populations of reservoir cells such as active and quiescent T-cells which maintain HIV infection in treated patients. In this paper, we introduce a family of models of the early molecular events in HIV infection, with either linear dynamics or age-structured delays at each step. We introduce an experimental design metric based on the delta AIC (Akaike Information Criteria) between a model fit for simulated data from a matching model vs a mismatched model, which allows us to determine a candidate experiment design's ability to discriminate between models. Using parameters values drawn from experimentally-derived priors corrupted with appropriate measurement noise, we confirm that a proposed sampling schedule at different time points allows us to consistently discriminate between candidate models.

Modelling the effects of phylogeny and body size on within-host pathogen replication and immune response

Understanding how quickly pathogens replicate and how quickly the immune system responds is important for predicting the epidemic spread of emerging pathogens. Host body size, through its correlation with metabolic rates, is theoretically predicted to impact pathogen replication rates and immune system response rates. Here, we use mathematical models of viral time courses from multiple species of birds infected by a generalist pathogen (West Nile Virus; WNV) to test more thoroughly how disease progression and immune response depend on mass and host phylogeny. We use hierarchical Bayesian models coupled with nonlinear dynamical models of disease dynamics to incorporate the hierarchical nature of host phylogeny. Our analysis suggests an important role for both host phylogeny and species mass in determining factors important for viral spread such as the basic reproductive number, WNV production rate, peak viraemia in blood and competency of a host to infect mosquitoes. Our model is based on a principled analysis and gives a quantitative prediction for key epidemiological determinants and how they vary with species mass and phylogeny. This leads to new hypotheses about the mechanisms that cause certain taxonomic groups to have higher viraemia. For example, our models suggest that higher viral burst sizes cause corvids to have higher levels of viraemia and that the cellular rate of virus production is lower in larger species. We derive a metric of competency of a host to infect disease vectors and thereby sustain the disease between hosts. This suggests that smaller passerine species are highly competent at spreading the disease compared with larger non-passerine species. Our models lend mechanistic insight into why some species (smaller passerine species) are pathogen reservoirs and some (larger non-passerine species) are potentially dead-end hosts for WNV. Our techniques give insights into the role of body mass and host phylogeny in the spread of WNV and potentially other zoonotic diseases. The major contribution of this work is a computational framework for infectious disease modelling at the within-host level that leverages data from multiple species. This is likely to be of interest to modellers of infectious diseases that jump species barriers and infect multiple species. Our method can be used to computationally determine the competency of a host to infect mosquitoes that will sustain WNV and other zoonotic diseases. We find that smaller passerine species are more competent in spreading the disease than larger non-passerine species. This suggests the role of host phylogeny as an important determinant of within-host pathogen replication. Ultimately, we view our work as an important step in linking within-host viral dynamics models to between-host models that determine spread of infectious disease between different hosts.

Mathematical Modeling of HIV Dynamics After Antiretroviral Therapy Initiation: A Review

This review shows the potential ground-breaking impact that mathematical tools may have in the analysis and the understanding of the HIV dynamics. In the first part, early diagnosis of immunological failure is inferred from the estimation of certain parameters of a mathematical model of the HIV infection dynamics. This method is supported by clinical research results from an original clinical trial: data just after 1 month following therapy initiation are used to carry out the model identification. The diagnosis is shown to be consistent with results from monitoring of the patients after 6 months. In the second part of this review, prospective research results are given for the design of individual anti-HIV treatments optimizing the recovery of the immune system and minimizing side effects. In this respect, two methods are discussed. The first one combines HIV population dynamics with pharmacokinetics and pharmacodynamics models to generate drug treatments using impulsive control systems. The second one is based on optimal control theory and uses a recently published differential equation to model the side effects produced by highly active antiretroviral therapy therapies. The main advantage of these revisited methods is that the drug treatment is computed directly in amounts of drugs, which is easier to interpret by physicians and patients.

Long-term antiretroviral treatment initiated at primary HIV-1 infection affects the size, composition, and decay kinetics of the reservoir of HIV-1-infected CD4 T cells

Initiation of antiretroviral therapy during the earliest stages of HIV-1 infection may limit the seeding of a long-lasting viral reservoir, but long-term effects of early antiretroviral treatment initiation remain unknown. Here, we analyzed immunological and virological characteristics of nine patients who started antiretroviral therapy at primary HIV-1 infection and remained on suppressive treatment for >10 years; patients with similar treatment duration but initiation of suppressive therapy during chronic HIV-1 infection served as controls. We observed that independently of the timing of treatment initiation, HIV-1 DNA in CD4 T cells decayed primarily during the initial 3 to 4 years of treatment. However, in patients who started antiretroviral therapy in early infection, this decay occurred faster and was more pronounced, leading to substantially lower levels of cell-associated HIV-1 DNA after long-term treatment. Despite this smaller size, the viral CD4 T cell reservoir in persons with early treatment initiation consisted more dominantly of the long-lasting central-memory and T memory stem cells. HIV-1-specific T cell responses remained continuously detectable during antiretroviral therapy, independently of the timing of treatment initiation. Together, these data suggest that early HIV-1 treatment initiation, even when continued for >10 years, is unlikely to lead to viral eradication, but the presence of low viral reservoirs and durable HIV-1 T cell responses may make such patients good candidates for future interventional studies aiming at HIV-1 eradication and cure.

IMPORTANCE

Antiretroviral therapy can effectively suppress HIV-1 replication to undetectable levels; however, HIV-1 can persist despite treatment, and viral replication rapidly rebounds when treatment is discontinued. This is mainly due to the presence of latently infected CD4 T cells, which are not susceptible to antiretroviral drugs. Starting treatment in the earliest stages of HIV-1 infection can limit the number of these latently infected cells, raising the possibility that these viral reservoirs are naturally eliminated if suppressive antiretroviral treatment is continued for extremely long periods of time. Here, we analyzed nine patients who started on antiretroviral therapy within the earliest weeks of the disease and continued treatment for more than 10 years. Our data show that early treatment accelerated the decay of infected CD4 T cells and led to very low residual levels of detectable HIV-1 after long-term therapy, levels that were otherwise detectable in patients who are able to maintain a spontaneous, drug-free control of HIV-1 replication. Thus, long-term antiretroviral treatment started during early infection cannot eliminate HIV-1, but the reduced reservoirs of HIV-1 infected cells in such patients may increase their chances to respond to clinical interventions aiming at inducing a drug-free remission of HIV-1 infection.

Identification and experimental validation of an HIV model for HAART treated patients

The objective of this paper is to identify the parameters of a human immunodeficiency virus (HIV) evolution model from a clinical data set of patients treated with two different highly active antiretroviral therapy (HAART) protocols. After introducing a model with six state variables, a preliminary step considers the reduction of the number of parameters to be identified by means of sensitivity analysis, and then identifiability items are discussed. A nonlinear optimization-based procedure for identification is developed, which divides the unknown parameters into two families: the group dependent and the patient dependent parameters. Numerical results show that the identified model can be individually adapted to each patient and this result is promising for predicting the effects (e.g., failures or successes) of therapeutic actions.

Resistance to protease inhibitors in a model of HIV-1 infection with impulsive drug effects

BACKGROUND

The emergence of drug resistance is one of the most prevalent reasons for treatment failure in HIV therapy. This has severe implications for the cost of treatment, survival and quality of life.

METHODS

We use mathematical modelling to describe the interaction between T cells, HIV-1 and protease inhibitors. We use impulsive differential equations to examine the effects of different levels of protease inhibitors in a T cell. We classify three different regimes according to whether the drug efficacy is low, intermediate or high. The model includes two strains: the wild-type strain, which initially dominates in the absence of drugs, and the mutant strain, which is the less efficient competitor, but has more resistance to the drugs.

RESULTS

Drug regimes may take trajectories through one, two or all three regimes, depending on the dosage and the dosing schedule. Stability analysis shows that resistance does not emerge at low drug levels. At intermediate drug levels, drug resistance is guaranteed to emerge. At high drug levels, either the drug-resistant strain will dominate or, in the absence of longer-lived reservoirs of infected cells, a region exists where viral elimination could theoretically occur. We provide estimates of a range of dosages and dosing schedules where the trajectories lie either solely within a region or cross multiple regions.

CONCLUSION

Under specific circumstances, if the drug level is physiologically tolerable, elimination of free virus is theoretically possible. This forms the basis for theoretical control using combination therapy and for understanding the effects of partial adherence.

Modelling HIV-1 2-LTR dynamics following raltegravir intensification

A model of reservoir activation and viral replication is introduced accounting for the production of 2-LTR HIV-1 DNA circles following antiviral intensification with the HIV integrase inhibitor raltegravir, considering contributions of de novo infection events and exogenous sources of infected cells, including quiescent infected cell activation. The model shows that a monotonic increase in measured 2-LTR concentration post intensification is consistent with limited de novo infection primarily maintained by sources of infected cells unaffected by raltegravir, such as quiescent cell activation, while a transient increase in measured 2-LTR concentration is consistent with significant levels of efficient (R0 > 1) de novo infection. The model is validated against patient data from the INTEGRAL study and is shown to have a statistically significant fit relative to the null hypothesis of random measurement variation about a mean. We obtain estimates and confidence intervals for the model parameters, including 2-LTR half-life. Seven of the 13 patients with detectable 2-LTR concentrations from the INTEGRAL study have measured 2-LTR dynamics consistent with significant levels of efficient replication of the virus prior to treatment intensification.

Adherence to and effectiveness of highly active antiretroviral treatment for HIV infection: assessing the bidirectional relationship

BACKGROUND

It is well established that high adherence to HIV-infected patients on highly active antiretroviral treatment (HAART) is a major determinant of virological and immunologic success. Furthermore, psychosocial research has identified a wide range of adherence factors including patients' subjective beliefs about the effectiveness of HAART. Current statistical approaches, mainly based on the separate identification either of factors associated with treatment effectiveness or of those associated with adherence, fail to properly explore the true relationship between adherence and treatment effectiveness. Adherence behavior may be influenced not only by perceived benefits-which are usually the focus of related studies-but also by objective treatment benefits reflected in biological outcomes.

METHODS

Our objective was to assess the bidirectional relationship between adherence and response to treatment among patients enrolled in the ANRS CO8 APROCO-COPILOTE study. We compared a conventional statistical approach based on the separate estimations of an adherence and an effectiveness equation to an econometric approach using a 2-equation simultaneous system based on the same 2 equations.

RESULTS

Our results highlight a reciprocal relationship between adherence and treatment effectiveness. After controlling for endogeneity, adherence was positively associated with treatment effectiveness. Furthermore, CD4 count gain after baseline was found to have a positive significant effect on adherence at each observation period. This immunologic parameter was not significant when the adherence equation was estimated separately. In the 2-equation model, the covariances between disturbances of both equations were found to be significant, thus confirming the statistical appropriacy of studying adherence and treatment effectiveness jointly.

CONCLUSIONS

Our results, which suggest that positive biological results arising as a result of high adherence levels, in turn reinforce continued adherence and strengthen the argument that patients who do not experience rapid improvement in their immunologic and clinical statuses after HAART initiation should be prioritized when developing adherence support interventions. Furthermore, they invalidate the hypothesis that HAART leads to "false reassurance" among HIV-infected patients.

HIV model parameter estimates from interruption trial data including drug efficacy and reservoir dynamics

Mathematical models based on ordinary differential equations (ODE) have had significant impact on understanding HIV disease dynamics and optimizing patient treatment. A model that characterizes the essential disease dynamics can be used for prediction only if the model parameters are identifiable from clinical data. Most previous parameter identification studies for HIV have used sparsely sampled data from the decay phase following the introduction of therapy. In this paper, model parameters are identified from frequently sampled viral-load data taken from ten patients enrolled in the previously published AutoVac HAART interruption study, providing between 69 and 114 viral load measurements from 3-5 phases of viral decay and rebound for each patient. This dataset is considerably larger than those used in previously published parameter estimation studies. Furthermore, the measurements come from two separate experimental conditions, which allows for the direct estimation of drug efficacy and reservoir contribution rates, two parameters that cannot be identified from decay-phase data alone. A Markov-Chain Monte-Carlo method is used to estimate the model parameter values, with initial estimates obtained using nonlinear least-squares methods. The posterior distributions of the parameter estimates are reported and compared for all patients.

Clinical management of HIV drug resistance

Combination antiretroviral therapy for HIV-1 infection has resulted in profound reductions in viremia and is associated with marked improvements in morbidity and mortality. Therapy is not curative, however, and prolonged therapy is complicated by drug toxicity and the emergence of drug resistance. Management of clinical drug resistance requires in depth evaluation, and includes extensive history, physical examination and laboratory studies. Appropriate use of resistance testing provides valuable information useful in constructing regimens for treatment-experienced individuals with viremia during therapy. This review outlines the emergence of drug resistance in vivo, and describes clinical evaluation and therapeutic options of the individual with rebound viremia during therapy.