Longitudinal Fluctuations in Treatment Response After OnabotulinumToxinA and Sacral Neuromodulation for Refractory Urgency Incontinence.

PURPOSE: We compared fluctuations in treatment response after onabotulinumtoxinA and sacral neuromodulation for urgency incontinence using Markov models. MATERIALS AND METHODS: We fit data from a randomized trial to Markov models to compare transitions of success/failure over 6 months between 200 U onabotulinumtoxinA and sacral neuromodulation. Objective failure was <50% reduction in urgency incontinence episodes from baseline; subjective failure "strongly disagree" to "neutral" to the Patient Global Symptom Control questionnaire. RESULTS: Of the 357 participants (median baseline daily urgency incontinence episodes 4.7 [IQR 3.7-6.0]) 61% vs 51% and 3.2% vs 6.1% reported persistent states of objective success and failure over 6 months after onabotulinumtoxinA vs sacral neuromodulation. Participants receiving onabotulinumtoxinA vs sacral neuromodulation had lower 30-day transition probabilities from objective and subjective success to failure (10% vs 14%, ratio 0.75 [95% CI 0.55-0.95]; 14% vs 21%, ratio 0.70 [95% CI 0.51-0.89]). The 30-day transition probability from objective and subjective failure to success did not differ between onabotulinumtoxinA and sacral neuromodulation (40% vs 36%, ratio 1.11 [95% CI 0.73-1.50]; 18% vs 17%, ratio 1.14 [95% CI 0.65-1.64]). CONCLUSIONS: Over 6 months after treatment, 2 in 5 women's symptoms fluctuate. Within these initial 6 months, women receiving onabotulinumtoxinA transitioned from success to failure over 30 days less often than sacral neuromodulation. For both treatments, there was an almost 20%-40% probability over 30 days that women returned to subjective and objective success after failure. Markov models add important information to longitudinal models on how symptoms fluctuate after urgency incontinence treatment.

Cost Effectiveness of Definitive Treatment Strategies for Autonomously Functioning Thyroid Nodules.

OBJECTIVE: Autonomously functioning thyroid nodules (AFTN) can be treated with antithyroid drugs, radioactive iodine (RAI), thyroid lobectomy or radiofrequency ablation (RFA). Although surgery is most definitive, some patients require lifelong hormone supplementation. RFA avoids this sequela, but its efficacy depends on nodule size. This study aims to compare the relative cost-effectiveness of RAI, RFA and lobectomy for treatment of AFTNs. STUDY DESIGN: A Markov analysis model was created to simulate clinical outcomes, costs and utilities for three AFTN treatments: (1) thyroid lobectomy, (2) RAI, and (3) RFA. PATIENTS: This mathematical model was created using published literature and modeling. MEASUREMENTS: Transition probabilities, utilities and costs were extracted from published literature, Medicare, and RedBook. The willingness to pay threshold was set to $100,000 per quality-adjusted life year. The model simulated 2-year outcomes, reflecting RFA literature. Sensitivity analyses were conducted to account for uncertainty in model variables. RESULTS: In the base model, RAI dominated both lobectomy and RFA, with lower estimated cost ($2000 vs. $9452 and $10,087) and higher cumulative utility (1.89 vs. 1.82 and 1.78 quality-adjusted life years). One-way sensitivity analyses demonstrated that relative cost-effectiveness between surgery and RFA was driven by the probability of euthyroidism after RFA and hypothyroidism after lobectomy. RFA becomes more cost-effective than surgery if the rate of euthyroidism after ablation is higher than 69% (baseline 54%). CONCLUSION: Based on published data, RAI is most cost-effective in treating most AFTN. Surgery is more cost-effective than RFA in most scenarios, but RFA may be more resource-efficient for smaller nodules with a high likelihood of complete treatment.

Stacked probability plots of the extended illness-death model using constant transition hazards - an easy to use shiny app.

BACKGROUND: Extended illness-death models (a specific class of multistate models) are a useful tool to analyse situations like hospital-acquired infections, ventilation-associated pneumonia, and transfers between hospitals. The main components of these models are hazard rates and transition probabilities. Calculation of different measures and their interpretation can be challenging due to their complexity. METHODS: By assuming time-constant hazards, the complexity of these models becomes manageable and closed mathematical forms for transition probabilities can be derived. Using these forms, we created a tool in R to visualize transition probabilities via stacked probability plots. RESULTS: In this article, we present this tool and give some insights into its theoretical background. Using published examples, we give guidelines on how this tool can be used. Our goal is to provide an instrument that helps obtain a deeper understanding of a complex multistate setting. CONCLUSION: While multistate models (in particular extended illness-death models), can be highly complex, this tool can be used in studies to both understand assumptions, which have been made during planning and as a first step in analysing complex data structures. An online version of this tool can be found at https://eidm.imbi.uni-freiburg.de/ .

Lyme Disease Models of Tick-Mouse Dynamics with Seasonal Variation in Births, Deaths, and Tick Feeding.

Lyme disease is the most common vector-borne disease in the United States impacting the Northeast and Midwest at the highest rates. Recently, it has become established in southeastern and south-central regions of Canada. In these regions, Lyme disease is caused by Borrelia burgdorferi, which is transmitted to humans by an infected Ixodes scapularis tick. Understanding the parasite-host interaction is critical as the white-footed mouse is one of the most competent reservoir for B. burgdorferi. The cycle of infection is driven by tick larvae feeding on infected mice that molt into infected nymphs and then transmit the disease to another susceptible host such as mice or humans. Lyme disease in humans is generally caused by the bite of an infected nymph. The main aim of this investigation is to study how diapause delays and demographic and seasonal variability in tick births, deaths, and feedings impact the infection dynamics of the tick-mouse cycle. We model tick-mouse dynamics with fixed diapause delays and more realistic Erlang distributed delays through delay and ordinary differential equations (ODEs). To account for demographic and seasonal variability, the ODEs are generalized to a continuous-time Markov chain (CTMC). The basic reproduction number and parameter sensitivity analysis are computed for the ODEs. The CTMC is used to investigate the probability of Lyme disease emergence when ticks and mice are introduced, a few of which are infected. The probability of disease emergence is highly dependent on the time and the infected species introduced. Infected mice introduced during the summer season result in the highest probability of disease emergence.

Stability of a stochastic brucellosis model with semi-Markovian switching and diffusion.

To explore the influence of state changes on brucellosis, a stochastic brucellosis model with semi-Markovian switchings and diffusion is proposed in this paper. When there is no switching, we introduce a critical value R s and obtain the exponential stability in mean square when R s < 1 by using the stochastic Lyapunov function method. Sudden climate changes can drive changes in transmission rate of brucellosis, which can be modelled by a semi-Markov process. We study the influence of stationary distribution of semi-Markov process on extinction of brucellosis in switching environment including both stable states, during which brucellosis dies out, and unstable states, during which brucellosis persists. The results show that increasing the frequencies and average dwell times in stable states to certain extent can ensure the extinction of brucellosis. Finally, numerical simulations are given to illustrate the analytical results. We also suggest that herdsmen should reduce the densities of animal habitation to decrease the contact rate, increase slaughter rate of animals and apply disinfection measures to kill brucella.

Contrast Information Dynamics: A Novel Information Measure for Cognitive Modelling.

We present contrast information, a novel application of some specific cases of relative entropy, designed to be useful for the cognitive modelling of the sequential perception of continuous signals. We explain the relevance of entropy in the cognitive modelling of sequential phenomena such as music and language. Then, as a first step to demonstrating the utility of constrast information for this purpose, we empirically show that its discrete case correlates well with existing successful cognitive models in the literature. We explain some interesting properties of constrast information. Finally, we propose future work toward a cognitive architecture that uses it.

Untangling the role of temporal and spatial variations in persistence of populations.

We consider a population distributed between two habitats, in each of which it experiences a growth rate that switches periodically between two values, 1-ɛ>0 or -(1+ɛ)<0. We study the specific case where the growth rate is positive in one habitat and negative in the other one for the first half of the period, and conversely for the second half of the period, that we refer as the (±1) model. In the absence of migration, the population goes to 0 exponentially fast in each environment. In this paper, we show that, when the period is sufficiently large, a small dispersal between the two patches is able to produce a very high positive exponential growth rate for the whole population, a phenomena called inflation. We prove in particular that the threshold of the dispersal rate at which the inflation appears is exponentially small with the period. We show that inflation is robust to random perturbation, by considering a model where the values of the growth rate in each patch are switched at random times: we prove that inflation occurs for low switching rate and small dispersal. We also consider another stochastic model, where after each period of time T, the values of the growth rates in each patch is chosen randomly, independently from the other patch and from the past. Finally, we provide some extensions to more complicated models, especially epidemiological and density dependent models.

Batesian mimicry or general food deception? An evolutionary game between plants for pollinator services.

Floral food deception is a well-known phenomenon which is not thoroughly understood. Particularly, it is unclear what drives a plant towards Batesian mimicry or towards generalized food deception. We analysed the evolutionary game between a Model species with nectar-secreting flowers and a Deceiver species that provides no nectar who share pollinators for reproduction. We focused our analysis on the effect of similarity of floral signals between participating plants and on costs of nectar production. We defined payoffs in the game between Models and Deceivers as the stationary visitation frequencies to participating species with different signal similarities and nectar costs. Therefore, fitness payoff of each strategy was a product of complex interactions between plant species composing the community and the pollinators visiting them. Our model provides a unified framework in which consequences of Model species interaction with different deception modes can be compared. Our findings suggest that plant-pollinator systems, like other mutualistic systems, are prone to exploitation, and that exploitation may persist at a large range of conditions. We showed that floral similarity, and thus, pollinators' ability to discriminate between Model and deceptive species, governs the stability of Batesian mimicry, while pollinator switching and sampling behaviour enables the persistence of general food deception.

Probabilistic cellular automata modelling of intercellular interactions in airways: complex pattern formation in patients with chronic obstructive pulmonary disease.

Chronic obstructive pulmonary disease (COPD) is a highly prevalent lung disease characterized by chronic inflammation and tissue remodeling possibly induced by unusual interactions between fibrocytes and CD8+ T lymphocytes in the peribronchial area. To investigate this phenomenon, we developed a probabilistic cellular automata type model where the two types of cells follow simple local interaction rules taking into account cell death, proliferation, migration and infiltration. We conducted a rigorous mathematical analysis using multiscale experimental data obtained in control and disease conditions to estimate the model's parameters accurately. The simulation of the model is straightforward to implement, and two distinct patterns emerged that we can analyse quantitatively. In particular, we show that the change in fibrocyte density in the COPD condition is mainly the consequence of their infiltration into the lung during exacerbations, suggesting possible explanations for experimental observations in normal and COPD tissue. Our integrated approach that combines a probabilistic cellular automata model and experimental findings will provide further insights into COPD in future studies.

Study design for restricted mean time analysis of recurrent events and death.

The restricted mean time in favor (RMT-IF) of treatment has just been added to the analytic toolbox for composite endpoints of recurrent events and death. To help practitioners design new trials based on this method, we develop tools to calculate the sample size and power. Specifically, we formulate the outcomes as a multistate Markov process with a sequence of transient states for recurrent events and an absorbing state for death. The transition intensities, in this case the instantaneous risks of another nonfatal event or death, are assumed to be time-homogeneous but nonetheless allowed to depend on the number of past events. Using the properties of Coxian distributions, we derive the RMT-IF effect size under the alternative hypothesis as a function of the treatment-to-control intensity ratios along with the baseline intensities, the latter of which can be easily estimated from historical data. We also reduce the variance of the nonparametric RMT-IF estimator to calculable terms under a standard set-up for censoring. Simulation studies show that the resulting formulas provide accurate approximation to the sample size and power in realistic settings. For illustration, a past cardiovascular trial with recurrent-hospitalization and mortality outcomes is analyzed to generate the parameters needed to design a future trial. The procedures are incorporated into the rmt package along with the original methodology on the Comprehensive R Archive Network (CRAN).

Precision quality control: a dynamic model for risk-based analysis of analytical quality.

OBJECTIVES: There is continuing pressure to improve the cost effectiveness of quality control (QC) for clinical laboratory testing. Risk-based approaches are promising but recent research has uncovered problems in some common methods. There is a need for improvements in risk-based methods for quality control. METHODS: We provide an overview of a dynamic model for assay behavior. We demonstrate the practical application of the model using simulation and compare the performance of simple Shewhart QC monitoring against Westgard rules. We also demonstrate the utility of trade-off curves for analysis of QC performance. RESULTS: Westgard rules outperform simple Shewhart control over a narrow range of the trade-off curve of false-positive and false negative risk. The risk trade-off can be visualized in terms of risk, risk vs. cost, or in terms of cost. Risk trade-off curves can be "smoothed" by log transformation. CONCLUSIONS: Dynamic risk-models may provide advantages relative to static models for risk-based QC analysis.

A stochastic hierarchical model for low grade glioma evolution.

A stochastic hierarchical model for the evolution of low grade gliomas is proposed. Starting with the description of cell motion using a piecewise diffusion Markov process (PDifMP) at the cellular level, we derive an equation for the density of the transition probability of this Markov process based on the generalised Fokker-Planck equation. Then, a macroscopic model is derived via parabolic limit and Hilbert expansions in the moment equations. After setting up the model, we perform several numerical tests to study the role of the local characteristics and the extended generator of the PDifMP in the process of tumour progression. The main aim focuses on understanding how the variations of the jump rate function of this process at the microscopic scale and the diffusion coefficient at the macroscopic scale are related to the diffusive behaviour of the glioma cells and to the onset of malignancy, i.e., the transition from low-grade to high-grade gliomas.

An HIV stochastic model with cell-to-cell infection, B-cell immune response and distributed delay.

In this study, a delayed HIV stochastic model with virus-to-cell infection, cell-to-cell transmission and B-cell immune response is proposed. We first transform the stochastic differential equation with distributed delay into a high-dimensional degenerate stochastic differential equation, and then theoretically analyze the dynamic behaviour of the degenerate model. The unique global solution of the model is given by rigorous analysis. By formulating suitable Lyapunov functions, the existence of the stationary Markov process is obtained if the stochastic B-cell-activated reproduction number is greater than one. We also use the law of large numbers theorem and the spectral radius analysis method to deduce that the virus can be cleared if the stochastic B-cell-inactivated reproduction number is less than one. Through uncertainty and sensitivity analysis, we obtain key parameters that determine the value of the stochastic B-cell-activated reproduction number. Numerically, we examine that low level noise can maintain the number of the virus and B-cell populations at a certain range, while high level noise is helpful for the elimination of the virus. Furthermore, the effect of the cell-to-cell infection on model behaviour, and the influence of the key parameters on the size of the stochastic B-cell-activated reproduction number are also investigated.

Time varying Markov process with partially observed aggregate data: An application to coronavirus.

A major difficulty in the analysis of Covid-19 transmission is that many infected individuals are asymptomatic. For this reason, the total counts of infected individuals and of recovered immunized individuals are unknown, especially during the early phase of the epidemic. In this paper, we consider a parametric time varying Markov process of Coronavirus transmission and show how to estimate the model parameters and approximate the unobserved counts from daily data on infected and detected individuals and the total daily death counts. This model-based approach is illustrated in an application to French data, performed on April 6, 2020.

Controlling the Mean Time to Extinction in Populations of Bacteria.

Populations of ecological systems generally have demographic fluctuations due to birth and death processes. At the same time, they are exposed to changing environments. We studied populations composed of two phenotypes of bacteria and analyzed the impact that both types of fluctuations have on the mean time to extinction of the entire population if extinction is the final fate. Our results are based on Gillespie simulations and on the WKB approach applied to classical stochastic systems, here in certain limiting cases. As a function of the frequency of environmental changes, we observe a non-monotonic dependence of the mean time to extinction. Its dependencies on other system parameters are also explored. This allows the control of the mean time to extinction to be as large or as small as possible, depending on whether extinction should be avoided or is desired from the perspective of bacteria or the perspective of hosts to which the bacteria are deleterious.

Independence conditions and the analysis of life history studies with intermittent observation.

Multistate models provide a powerful framework for the analysis of life history processes when the goal is to characterize transition intensities, transition probabilities, state occupancy probabilities, and covariate effects thereon. Data on such processes are often only available at random visit times occurring over a finite period. We formulate a joint multistate model for the life history process, the recurrent visit process, and a random loss to follow-up time at which the visit process terminates. This joint model is helpful when discussing the independence conditions necessary to justify the use of standard likelihoods involving the life history model alone and provides a basis for analyses that accommodate dependence. We consider settings with disease-driven visits and routinely scheduled visits and develop likelihoods that accommodate partial information on the types of visits. Simulation studies suggest that suitably constructed joint models can yield consistent estimates of parameters of interest even under dependent visit processes, providing the models are correctly specified; identifiability and estimability issues are also discussed. An application is given to a cohort of individuals attending a rheumatology clinic where interest lies in progression of joint damage.

Markov genealogy processes.

We construct a family of genealogy-valued Markov processes that are induced by a continuous-time Markov population process. We derive exact expressions for the likelihood of a given genealogy conditional on the history of the underlying population process. These lead to a nonlinear filtering equation which can be used to design efficient Monte Carlo inference algorithms. We demonstrate these calculations with several examples. Existing full-information approaches for phylodynamic inference are special cases of the theory.

Allee Effects Plus Noise Induce Population Dynamics Resembling Binary Markov Highs and Lows.

We show that the combination of Allee effects and noise can produce a stochastic process with alternating sudden decline to a low population phase, followed, after a random time, by abrupt increase in population density. We introduce a new, flexible, deterministic model of attenuated Allee effects, which interpolates between the logistic and a usual Allee model. Into this model, we incorporate environmental and demographic noise. The solution of the resulting Kolmogorov forward equation shows a dichotomous distribution of residence times with heavy occupation of high, near saturation, and low population states. Investigation of simulated sample paths reveals that indeed attenuated Allee effects and noise, acting together, produce alternating, sustained, low and high population levels. We find that the transition times between the two types of states are approximately exponentially distributed, with different parameters, rendering the embedded hi-low process approximately Markov.

Persistence in a large network of sparsely interacting neurons.

This article presents a biological neural network model driven by inhomogeneous Poisson processes accounting for the intrinsic randomness of synapses. The main novelty is the introduction of sparse interactions: each firing neuron triggers an instantaneous increase in electric potential to a fixed number of randomly chosen neurons. We prove that, as the number of neurons approaches infinity, the finite network converges to a nonlinear mean-field process characterised by a jump-type stochastic differential equation. We show that this process displays a phase transition: the activity of a typical neuron in the infinite network either rapidly dies out, or persists forever, depending on the global parameters describing the intensity of interconnection. This provides a way to understand the emergence of persistent activity triggered by weak input signals in large neural networks.

Spiracular fluttering decouples oxygen uptake and water loss: a stochastic PDE model of respiratory water loss in insects.

In insect respiration, oxygen from the air diffuses through a branching system of air-filled tubes to the cells of the body and carbon dioxide produced in cellular respiration diffuses out. The tracheal system has a very large surface area, so water loss is a potential threat and the question of how insects regulate oxygen uptake and water loss has been an important issue in insect physiology for the past century. The tracheal system starts at spiracles on the surface of the body that insects can open and close, and three phases are observed experimentally, open or closed for relatively long periods of time and opening and closing rapidly, which is called fluttering. In previous work we have shown that during this flutter phase, no matter how small the percentage of time that the spiracles are open, the insect can absorb almost as much oxygen as if the spiracle were always open, if the insect flutters fast enough. This left open the question of water loss during the flutter phase, which is the question addressed in this paper. We formulate a stochastic diffusion-convection model for the concentration of water vapor in the tracheae. Mathematical analysis of the model yields an explicit formula for water loss as a function of six non-dimensional parameters and we use experimental data from various insects to show that, for parameters in the physiological ranges, water loss during the flutter phase is approximately proportional to the percentage of time open. This means that the insect can solve the oxygen uptake versus water loss problem by choosing to have their spiracles open a small percentage of time during the flutter phase and fluttering rapidly.