Bioterrorism: the statistical issues

Bioterrorism research has had an upsurge since the autumn of 2001. Elizabeth Halloran and Ira Longini describe particular contributions that statisticians and mathematical modellers can make to bioterrorism research related to infectious diseases. They argue that much can be learned from emerging infectious diseases that is applicable to potential bioterrorist threats.     

秦汉律的罚金刑

秦律的赀罚与二年律令的罚金虽然名称完全不同,但两者具有继承关系。秦律的赀二甲是对盗窃额未满110钱-22钱的处罚,赀一盾是对未满22钱-1钱的处罚。秦律的这些内容由二年律令继承。赀罚原来分为赀一盾、赀二盾、赀一甲、赀二甲等四个等级,后来赀二盾逐渐消失,形成赀一盾、赀一甲、赀二甲三个等级,这三个等级的比例为1:2:4,与二年律令的罚金一两、二两、四两的比例关系相一致。赀一盾的罚额为672钱,与罚金一两的价额625钱相差不大。赀一盾的价额672钱与秦律规定的日均劳动价额8钱有关,以一日劳役为八钱计算,672钱相当于服役84天的价额。汉代的罚金制度与赎刑重复,尚未形成完整的体系,直至晋律,才将汉代的罚金精简为五个等级。     

ESTIMATING WITHIN-HOUSEHOLD CONTACT NETWORKS FROM EGOCENTRIC DATA

Acute respiratory diseases are transmitted over networks of social contacts. Large-scale simulation models are used to predict epidemic dynamics and evaluate the impact of various interventions, but the contact behavior in these models is based on simplistic and strong assumptions which are not informed by survey data. These assumptions are also used for estimating transmission measures such as the basic reproductive number and secondary attack rates. Development of methodology to infer contact networks from survey data could improve these models and estimation methods. We contribute to this area by developing a model of within-household social contacts and using it to analyze the Belgian POLYMOD data set, which contains detailed diaries of social contacts in a 24-hour period. We model dependency in contact behavior through a latent variable indicating which household members are at home. We estimate age-specific probabilities of being at home and age-specific probabilities of contact conditional on two members being at home. Our results differ from the standard random mixing assumption. In addition, we find that the probability that all members contact each other on a given day is fairly low: 0.49 for households with two 0-5 year olds and two 19-35 year olds, and 0.36 for households with two 12-18 year olds and two 36+ year olds. We find higher contact rates in households with 2-3 members, helping explain the higher influenza secondary attack rates found in households of this size.     

Modeling Competing Infectious Pathogens from a Bayesian Perspective: Application to Influenza Studies with Incomplete Laboratory Results

In seasonal influenza epidemics, pathogens such as respiratory syncytial virus (RSV) often co-circulate with influenza and cause influenza-like illness (ILI) in human hosts. However, it is often impractical to test for each potential pathogen or to collect specimens for each observed ILI episode, making inference about influenza transmission difficult. In the setting of infectious diseases, missing outcomes impose a particular challenge because of the dependence among individuals. We propose a Bayesian competing-risk model for multiple co-circulating pathogens for inference on transmissibility and intervention efficacies under the assumption that missingness in the biological confirmation of the pathogen is ignorable. Simulation studies indicate a reasonable performance of the proposed model even if the number of potential pathogens is misspecified. They also show that a moderate amount of missing laboratory test results has only a small impact on inference about key parameters in the setting of close contact groups. Using the proposed model, we found that a non-pharmaceutical intervention is marginally protective against transmission of influenza A in a study conducted in elementary schools.     

Design and Evaluation of Prophylactic Interventions Using Infectious Disease Incidence Data from Close Contact Groups

Summary.  Prophylaxis of contacts of infectious cases such as household members and treatment of infectious cases are methods to prevent the spread of infectious diseases. We develop a method based on maximum likelihood to estimate the efficacy of such interventions and the transmission probabilities. We consider both the design with prospective follow-up of close contact groups and the design with ascertainment of close contact groups by an index case as well as randomization by groups and by individuals. We compare the designs by using simulations. We estimate the efficacy of the influenza antiviral agent oseltamivir in reducing susceptibility and infectiousness in two case-ascertained household trials.     

ESTIMATING WITHIN-SCHOOL CONTACT NETWORKS TO UNDERSTAND INFLUENZA TRANSMISSION

Many epidemic models approximate social contact behavior by assuming random mixing within mixing groups (e.g., homes, schools, and workplaces). The effect of more realistic social network structure on estimates of epidemic parameters is an open area of exploration. We develop a detailed statistical model to estimate the social contact network within a high school using friendship network data and a survey of contact behavior. Our contact network model includes classroom structure, longer durations of contacts to friends than non-friends and more frequent contacts with friends, based on reports in the contact survey. We performed simulation studies to explore which network structures are relevant to influenza transmission. These studies yield two key findings. First, we found that the friendship network structure important to the transmission process can be adequately represented by a dyad-independent exponential random graph model (ERGM). This means that individual-level sampled data is sufficient to characterize the entire friendship network. Second, we found that contact behavior was adequately represented by a static rather than dynamic contact network. We then compare a targeted antiviral prophylaxis intervention strategy and a grade closure intervention strategy under random mixing and network-based mixing. We find that random mixing overestimates the effect of targeted antiviral prophylaxis on the probability of an epidemic when the probability of transmission in 10 minutes of contact is less than 0.004 and underestimates it when this transmission probability is greater than 0.004. We found the same pattern for the final size of an epidemic, with a threshold transmission probability of 0.005. We also find random mixing overestimates the effect of a grade closure intervention on the probability of an epidemic and final size for all transmission probabilities. Our findings have implications for policy recommendations based on models assuming random mixing, and can inform further development of network-based models.     

Comparison of Two Smoothing Methods for Exploring Waning Vaccine Effects

We consider the statistical evaluation and estimation of vaccine efficacy when the protective effect wanes with time. We reanalyse data from a 5-year trial of two oral cholera vaccines in Matlab, Bangladesh. In this field trial, one vaccine appears to confer better initial protection than the other, but neither appears to offer protection for a period longer than about 3 years. Time-dependent vaccine effects are estimated by obtaining smooth estimates of a time-varying relative risk RR( t ) using survival analysis. We compare two approaches based on the Cox model in terms of their strategies for detecting time-varying vaccine effects, and their estimation techniques for obtaining a time-dependent RR( t ) estimate. These methods allow an exploration of time-varying vaccine effects while making minimal parametric assumptions about the functional form of RR( t ) for vaccinated compared wit unvaccinated subjects.     

Estimating the transmission probability of human immunodeficiency virus in injecting drug users in Thailand

We estimate the transmission probability for the human immunodeficiency virus from seroconversion data of a cohort of injecting drug users (IDUs) in Thailand. The transmission probability model developed accounts for interval censoring and incorporates each IDU's reported frequency of needle sharing and injecting acts. Using maximum likelihood methods, the per needle sharing act transmission probability estimate between infectious and susceptible IDUs is 0.008. The effects of covariates, disease dynamics, mismeasured exposure information and the uncertainty of the disease prevalence on the transmission probability estimate are considered.     

AN ADAPTIVE MULTIVARIATE APPROACH TO TIME SERIES FORECASTING

In recent years, time series analysts have shifted their interest from univariate to multivariate forecasting approaches. Among them, the Box-Jenkins transfer function process and the state space method have received the most attention. This paper presents a simplified approach that embodies some desirable features of existing methods. It stresses empirical analysis, has a unified modeling structure, is easily applicable, and is adaptive to changes without necessitating prior information on the evolution of a system under study. The core of the method relies on the Carbone-Longini adaptive estimation procedure (AEP). Results of a comparative study based on the well-known Lydia E. Pinkham data and the Box-Jenkins sales/leading indicator data illustrate the merits of multivariate AEP in improving forecasting accuracy while simplifying the analysis process. Subject Area: Forecasting.     

AN ADAPTIVE APPROACH TO TIME-SERIES FORECASTING

This paper extends the applicability of the Carbone-Longini adaptive estimation procedure (AEP) to time-series forecasting. Comparisons with adaptive filtering, the Box-Jenkins methodology, and multiple regression analysis as it applies to time-series analysis are provided. Specific time-series data examined by Box and Jenkins and Box and Tiao constitute the basis for these comparisons. The analysis of the results indicate the robustness and performance superiority of the simple distributive-lag forecast model coupled with the concept of adaptively “tracking” rather than “fitting” historical data.