Qualitative analysis of generalized multistage epidemic model with immigration.

A model with multiple disease stages is discussed; its main feature is that it considers a general incidence rate, functions for death and immigration rates in all populations. We show via a suitable Lyapunov function that the unique endemic equilibrium is globally asymptotically stable. We conclude that, in order to obtain the existence and global stability of the equilibrium point of general models, conditions must be imposed on the functions present in the model. In addition, the model has no basic reproduction number due to the constant flow of infected people, which makes its eradication impossible; therefore, there is no equilibrium point free of infection.

Event-level positive and negative reinforcement risk factors for alcohol use: Moderation by individual-level alcohol consequences and post-traumatic stress disorder symptom severity.

BACKGROUND: The multistage model of drug addiction posits that risk processes contributing to alcohol use change as individuals develop alcohol use disorders. However, few studies have tested this theory outside of the lab or at the event level. We assessed whether event-level associations between positive reinforcement (e.g., positive affect, sociability expectancies) and negative reinforcement risk factors (e.g., negative affect, tension reduction expectancies) and same-/next-day alcohol consumption varied as a function of an individual's level of alcohol consequences. Given elevated alcohol use consequences among individuals with post-traumatic stress disorder (PTSD) and disruptions in reward processing that affect this population, we also tested whether these processes differed based on the presence and severity of PTSD. METHODS: We used data from a 30-day ecological momentary assessment study with 174 undergraduate women who regularly engaged in heavy episodic drinking. A majority (78%) of the sample had experienced sexual assault and 44% had current PTSD. Analyses used Bayesian multilevel structural equation modeling with diffuse (non-informative) priors. We used markov chain monte carlo (MCMC) algorithms to generate a series of 10,000 random draws from the multivariate posterior distribution of our sample for each model. RESULTS: Results partially supported the multistage model. Event-level negative reinforcement risk factors only predicted more alcohol consumption among individuals who experienced more alcohol consequences. Findings for positive reinforcement risk factors were partially consistent with hypotheses. Overall, findings appear to operate similarly across PTSD symptom severity. CONCLUSIONS: Results suggest that interventions for heavy episodic drinking could benefit from attending to an individual's level of alcohol consequences. For example, preventive interventions for individuals who tend to experience few consequences may benefit more from addressing positive reinforcement risk factors, while treatment interventions for those who experience more consequences may benefit from attending to both positive and negative reinforcement.

A multistage deep neural network model for blood pressure estimation using photoplethysmogram signals.

OBJECTIVE: Easy access bio-signals are useful to alleviate the shortcomings and difficulties of cuff-based and invasive blood pressure (BP) measuring techniques. This study proposes a multistage model based on deep neural networks to estimate systolic and diastolic blood pressures using the photoplethysmogram (PPG) signal. METHODS: The proposed model consists of two key ingredients, using two successive stages. The first stage includes two convolutional neural networks (CNN) to extract morphological features from each PPG segment and then to estimate systolic and diastolic BPs separately. The second stage relies on long short-term memory (LSTM) to capture temporal dependencies. Further, the method incorporates the dynamic relationship between systolic and diastolic BPs to improve accuracy. RESULTS: The proposed multistage model was evaluated on 200 subjects using the standards of the British Hypertension Society (BHS) and the Association for the Advancement of Medical Instrumentation (AAMI). The results revealed that our model performance met the requirements of the AAMI standard. Also, according to the BHS standard, it achieved grade A in estimating both systolic and diastolic BPs. The mean and standard deviation of error for systolic and diastolic blood pressure estimations were +1.91±5.55mmHg and +0.67±2.84mmHg, respectively. CONCLUSION: Our results highlight the benefits of the proposed model in terms of appropriate feature extraction as well as estimation consistency.

Stochastic modelling of multistage carcinogenesis and progression of human lung cancer.

In this paper, we propose a stochastic multistage model that incorporates clonal expansion of premalignant cells and mutational events. Using the age-specific lung cancer as the test system, the proposed model is used to fit the incidence data in the Surveillance, Epidemiology, and End Results (SEER) registry. We first use the model with different numbers of mutations to fit the data of all lung cancer patients. Our results demonstrate that, although from two to six driver mutations in the genome of lung stem cells are reasonable for normal lung stem cells to become a malignant cell, three driver mutations are most likely to occur in the development of lung cancer. In addition, the models are employed to fit the data of female and male patients separately. The interesting result is that, for female patient data the best fit model contains four mutations while that for male patient data is the three-stage model. Finally, robustness analysis suggests that the decrease of cell net proliferation rates is more effective than the decrease of mutation rates in reducing the lung cancer risk.

Inflammation as a Cancer Co-Initiator: New Mechanistic Model Predicts Low/Negligible Risk at Noninflammatory Carcinogen Doses.

Linear-no-threshold (LNT) risk extrapolation has long been applied to estimate risks posed by low-level environmental carcinogen exposures, based on the 60-year-old multistage somatic mutation/clonal expansion (MSM) cancer theory. Recent evidence supports an alternative theory: Malignant tumors arise most efficiently from a stem cell that incurs requisite mutations and also is activated by inflammation to an epigenetically mediated and maintained state of adaptive hyperplasia (AH). This new inflammation-MSM (ISM) theory posits that inflammation-activated stem cells normally restricted to sites of injury-induced inflammation and tissue repair become uniquely susceptible to efficient carcinogenesis if normal post-inflammation AH termination is blocked by mutation. This theory posits that inflammation generally thus co-initiates cancer and transiently amplifies activated stem cells, implying that MSM theory (eg, the 2-stage stochastic "Moolgavkar, Venzon, Knudson [MVK]" model) is incomplete. Because inflammation dose-response typically is not LNT, the ISM theory predicts this is also true for most (perhaps all) carcinogens. The ISM (but not the MVK) model is shown to be consistent with recent data showing ∼100% carcinoma incidence (but not DNA adducts) in livers of rats exposed to aflatoxin B1 and was eliminated when that dose was co-administered with a highly potent anti-inflammatory agent. Experimental approaches to test ISM theory more robustly are discussed.

Asymptotic Relative Risk Results from a Simplified Armitage and Doll Model of Carcinogenesis.

We examine basic asymptotic properties of relative risk for two families of generalized Erlang processes (where each one is based off of a simplified Armitage and Doll multistage model) in order to predict relative risk data from cancer. The main theorems that we are able to prove are all corroborated by large clinical studies involving relative risk for former smokers and transplant recipients. We then show that at least some of these theorems do not extend to other Armitage and Doll multistage models. We conclude with suggestions for lifelong increased cancer screening for both former smoker and transplant recipient subpopulations of individuals and possible future directions of research.

Mutation Mechanisms of Human Breast Cancer.

Cancer is a class of diseases caused by the accumulation of gene mutations. All mutated genes constitute a genetic network for cancer progression. It is very helpful for tumor diagnosis and therapy if we know how many mutated genes are needed for human breast cancer. In this article, we investigate the mutation mechanisms of human breast cancer by modeling the data of surveillance, epidemiology, and end results registry. The data are age-specific incidence rates of breast cancer of females in the United States. We set up stochastic multistage models to estimate the age-specific incidence rates by using several coupled ordinary differential equations derived from the Kolmogorov backward equations. Our results suggest that 2-14 mutations in the genome of breast stem cells are required for normal breast stem cells to become a malignant cell, and 3 gene mutations are most likely to occur in the development of female breast cancer.

A two-phase Poisson process model and its application to analysis of cancer mortality among A-bomb survivors.

We consider a two-phase Poisson process model where only early successive transitions are assumed to be sensitive to exposure. In the case where intensity transitions are low, we derive analytically an approximate formula for the distribution of time to event for the excess hazard ratio (EHR) due to a single point exposure. The formula for EHR is a polynomial in exposure dose. Since the formula for EHR contains no unknown parameters except for the number of total stages, number of exposure-sensitive stages, and a coefficient of exposure effect, it is applicable easily under a variety of situations where there exists a possible latency time from a single point exposure to occurrence of event. Based on the multistage hypothesis of cancer, we formulate a radiation carcinogenesis model in which only some early consecutive stages of the process are sensitive to exposure, whereas later stages are not affected. An illustrative analysis using the proposed model is given for cancer mortality among A-bomb survivors.

Fractional reactive extraction for symmetrical separation of 4-nitro-D,L-phenylalanine in centrifugal contactor separators: experiments and modeling.

The enantioselective liquid-liquid extraction of 4-nitro-D,L-phenylalanine (D,L-Nphy) using PdCl2 {(s)-BINAP} as extractant in dichloroethane was studied experimentally in a countercurrent cascade of 10 centrifugal contactor separators (CCSs) at 5°C, involving flow ratio, extractant concentration, and Cl(-) concentration. The steady-state enantiomeric excess (ee) in both stream exits was 90.86% at a 93.29% yield. The predicted value was modeled using an equilibrium stage approach. The correlation between model and experiment was satisfactory. The model was applied to optimize the production of both enantiomers in >97% ee and >99% ee. 14 stages and 16 stages are required for 97% ee and 99% ee for both enantiomers, respectively.

Simultaneous confidence bands for low-dose risk estimation with quantal data.

Risk assessment studies where human, animal or ecological data are used to set safe low dose levels of a toxic agent are challenging as study information is limited to high dose levels of the agent. Simultaneous hyperbolic confidence bands for low-dose risk estimation with quantal data have been proposed in the literature. In this paper, a new method using three-segment confidence bands to construct simultaneous upper confidence limits on extra risks and simultaneous lower bounds on the benchmark dose for quantal data is proposed. The proposed method is illustrated with a real data application and simulation studies.

Estimation of a benchmark dose in the presence or absence of hormesis using posterior averaging.

U.S. Environment Protection Agency benchmark doses for dichotomous cancer responses are often estimated using a multistage model based on a monotonic dose-response assumption. To account for model uncertainty in the estimation process, several model averaging methods have been proposed for risk assessment. In this article, we extend the usual parameter space in the multistage model for monotonicity to allow for the possibility of a hormetic dose-response relationship. Bayesian model averaging is used to estimate the benchmark dose and to provide posterior probabilities for monotonicity versus hormesis. Simulation studies show that the newly proposed method provides robust point and interval estimation of a benchmark dose in the presence or absence of hormesis. We also apply the method to two data sets on carcinogenic response of rats to 2,3,7,8-tetrachlorodibenzo-p-dioxin.

An Application of Endpoint Detection to Bivariate Data in Tau-Path Order.

The Fligner and Verducci (1988) multistage model for rankings is modified to create the moving average maximum likelihood estimator (MAMLE), a locally smooth estimator that measures stage-wise agreement between two long ranked lists, and provides a stopping rule for the detection of the endpoint of agreement. An application of this MAMLE stopping rule to bivariate data set in tau-path order (Yu, Verducci and Blower (2011)) is discussed. Data from the National Cancer Institute measuring associations between gene expression and compound potency are studied using this application, providing insights into the length of the relationship between the variables.

How Stable Are Top Choices Over Time? An Investigation Into Preferences Among Popular Baby Names In The United States.

For the problem of assessing initial agreement between two rankings of long lists, inference in the Fligner and Verducci (1988) multistage model for rankings is modified to provide a locally smooth estimator of stage-wise agreement. An extension to the case of overlapping but different sets of items in the two lists, and a stopping rule to identify the endpoint of agreement, are also provided. Simulations show that this approach performs very well under several conditions. The methodology is applied to a database of popular names for newborns in the United States and provides insights into trends as well as differences in naming conventions between the two sexes.

Transcriptional output in a prospective design conditionally on follow-up and exposure: the multistage model of cancer.

Transcriptomics as the analysis of mRNA and microRNA could be implemented in prospective studies both in peripheral blood and tissues. Its application in cancer epidemiology could provide a new understanding of the functional changes underlying the multistage model of carcinogenesis, as well as the relationship between these changes and exposure to carcinogens. Transcriptomics is not merely another -omics technology for risk assessment in traditional prospective studies. Instead, this novel approach has the potential to estimate the distribution of gene expression conditionally on different exposures, and to study the length of the different stages of carcinogenesis. If it proves to be a valid approach, transcriptomics could be an opportunity to make meaningful advances in our understanding of the carcinogenic process.

Is There a Partial Consensus Ordering Between Rankings?

We propose an innovative approach to the problem recently posed by Hall and Schimek (2012): determining at what point the agreement between two rankings of a long list of items degenerates into noise. We modify the method of estimation in Fligner and Verducci's (1988) multistage model for rankings, from maximum likelihood of conditional agreement over a sample of rankings to a locally smooth estimator of agreement. Through simulations we show that this innovation performs very well under several conditions. Some ramifications are discussed as planned extensions.