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1.  Comparing Bounds for Vaccine Effects on Infectiousness 
Epidemiology (Cambridge, Mass.)  2012;23(6):931-932.
PMCID: PMC3482261  PMID: 23038122
Causal inference; infectious disease; infectiousness; interference; principal stratification; vaccine efficacy
Biometrics  2013;69(1):235-244.
Evaluating vaccine efficacy for protection against colonisation with bacterial pathogens is an area of growing interest. Colonisation of the nasopharynx is an asymptomatic carrier state responsible for person-to-person transmission. It differs from most clinical outcomes in that it is common, recurrent and observed only in its prevalent state. To estimate rates of acquisition and clearance of colonisation requires repeated active sampling of the same individuals over time, an expensive and invasive undertaking. Motivated by feasibility constraints in efficacy trials with colonisation endpoints, investigators have been estimating vaccine efficacy from cross-sectional studies without principled methods. We present two examples of vaccine studies estimating vaccine efficacy from cross-sectional data on nasopharyngeal colonisation by Streptococcus pneumoniae (pneumococcus). This study presents a framework for defining and estimating strain-specific and overall vaccine efficacy for susceptibility to acquisition of colonisation (VEacq) when there is a large number of strains with mutual interactions and recurrent dynamics of colonisation. We develop estimators based on one observation of the current status per study subject, evaluate their robustness, and re-analyse the two vaccine trials. Methodologically, the proposed estimators are closely related to case-control studies with prevalent cases, with appropriate consideration of the at-risk time in choosing the controls.
PMCID: PMC3622115  PMID: 23379663
Case-control studies; Multiple colonisation; Pneumococcus; Polyvalent vaccine; Recurrent infection; Risk-set sampling; Strain interaction; Vaccine efficacy
3.  Case Definition and Design Sensitivity 
In a case-referent study, cases of disease are compared to non-cases with respect to their antecedent exposure to a treatment in an effort to determine whether exposure causes some cases of the disease. Because exposure is not randomly assigned in the population, as it would be if the population were a vast randomized trial, exposed and unexposed subjects may differ prior to exposure with respect to covariates that may or may not have been measured. After controlling for measured pre-exposure differences, for instance by matching, a sensitivity analysis asks about the magnitude of bias from unmeasured covariates that would need to be present to alter the conclusions of a study that presumed matching for observed covariates removes all bias. The definition of a case of disease affects sensitivity to unmeasured bias. We explore this issue using: (i) an asymptotic tool, the design sensitivity, (ii) a simulation for finite samples, and (iii) an example. Under favorable circumstances, a narrower case definition can yield an increase in the design sensitivity, and hence an increase in the power of a sensitivity analysis. Also, we discuss an adaptive method that seeks to discover the best case definition from the data at hand while controlling for multiple testing. An implementation in R is available as SensitivityCaseControl.
PMCID: PMC3904399  PMID: 24482549
Case-control study; matching; observational study; sensitivity analysis
4.  Causal Inference for Vaccine Effects on Infectiousness 
The International Journal of Biostatistics  2012;8(2):10.2202/1557-4679.1354 /j/ijb.2012.8.issue-2/1557-4679.1354/1557-4679.1354.xml.
If a vaccine does not protect individuals completely against infection, it could still reduce infectiousness of infected vaccinated individuals to others. Typically, vaccine efficacy for infectiousness is estimated based on contrasts between the transmission risk to susceptible individuals from infected vaccinated individuals compared with that from infected unvaccinated individuals. Such estimates are problematic, however, because they are subject to selection bias and do not have a causal interpretation. Here, we develop causal estimands for vaccine efficacy for infectiousness for four different scenarios of populations of transmission units of size two. These causal estimands incorporate both principal stratification, based on the joint potential infection outcomes under vaccine and control, and interference between individuals within transmission units. In the most general scenario, both individuals can be exposed to infection outside the transmission unit and both can be assigned either vaccine or control. The three other scenarios are special cases of the general scenario where only one individual is exposed outside the transmission unit or can be assigned vaccine. The causal estimands for vaccine efficacy for infectiousness are well defined only within certain principal strata and, in general, are identifiable only with strong unverifiable assumptions. Nonetheless, the observed data do provide some information, and we derive large sample bounds on the causal vaccine efficacy for infectiousness estimands. An example of the type of data observed in a study to estimate vaccine efficacy for infectiousness is analyzed in the causal inference framework we developed.
PMCID: PMC3348179  PMID: 22499732
causal inference; principal stratification; interference; infectious disease; vaccine
5.  The Effects of Vector Movement and Distribution in a Mathematical Model of Dengue Transmission 
PLoS ONE  2013;8(10):e76044.
Mathematical models have been used to study the dynamics of infectious disease outbreaks and predict the effectiveness of potential mass vaccination campaigns. However, models depend on simplifying assumptions to be tractable, and the consequences of making such assumptions need to be studied. Two assumptions usually incorporated by mathematical models of vector-borne disease transmission is homogeneous mixing among the hosts and vectors and homogeneous distribution of the vectors.
Methodology/Principal Findings
We explored the effects of mosquito movement and distribution in an individual-based model of dengue transmission in which humans and mosquitoes are explicitly represented in a spatial environment. We found that the limited flight range of the vector in the model greatly reduced its ability to transmit dengue among humans. A model that does not assume a limited flight range could yield similar attack rates when transmissibility of dengue was reduced by 39%. A model in which mosquitoes are distributed uniformly across locations behaves similarly to one in which the number of mosquitoes per location is drawn from an exponential distribution with a slightly higher mean number of mosquitoes per location. When the models with different assumptions were calibrated to have similar human infection attack rates, mass vaccination had nearly identical effects.
Small changes in assumptions in a mathematical model of dengue transmission can greatly change its behavior, but estimates of the effectiveness of mass dengue vaccination are robust to some simplifying assumptions typically made in mathematical models of vector-borne disease.
PMCID: PMC3804532  PMID: 24204590
6.  Components of the indirect effect in vaccine trials: identification of contagion and infectiousness effects 
Epidemiology (Cambridge, Mass.)  2012;23(5):751-761.
Vaccination of one person may prevent the infection of another either because the vaccine prevents the first from being infected and from infecting the second, or because, even if the first person is infected, the vaccine may render the infection less infectious. We might refer to the first of these mechanisms as a contagion effect and the second as an infectiousness effect. In the simple setting of a randomized vaccine trial with households of size two, we use counterfactual theory under interference to provide formal definitions of a contagion effect and an unconditional infectiousness effect. Using ideas analogous to mediation analysis, we show that the indirect effect (the effect of one person’s vaccine on another’s outcome) can be decomposed into a contagion effect and an unconditional infectiousness effect on the risk-difference, risk-ratio, odds-ratio and vaccine-efficacy scales. We provide identification assumptions for such contagion and unconditional infectiousness effects, and describe a simple statistical technique to estimate these effects when they are identified. We also give a sensitivity-analysis technique to assess how inferences would change under violations of the identification assumptions. The concepts and results of this paper are illustrated with hypothetical vaccine-trial data.
PMCID: PMC3415570  PMID: 22828661
7.  The Effect of Age on Transmission of 2009 Pandemic Influenza A (H1N1) in a Camp and Associated Households 
Epidemiology (Cambridge, Mass.)  2011;22(2):10.1097/EDE.0b013e3182060ca5.
A major portion of influenza disease burden during the 2009 pandemic was observed among young people.
We examined the effect of age on the transmission of influenza-like illness associated with the 2009 pandemic influenza A (H1N1) virus (pH1N1) for an April–May 2009 outbreak among youth-camp participants and household contacts in Washington State.
An influenza-like illness attack rate of 51% was found among 96 camp participants. We observed a cabin secondary attack rate of 42% (95% confidence interval = 21%–66%) and a camp local reproductive number of 2.7 (1.7–4.1) for influenza-like illness among children (less than 18 years old). Among the 136 contacts in the 41 households with an influenza-like illness index case who attended the camp, the influenza-like illness secondary attack rate was 11% for children (5%–21%) and 4% for adults (2%–8%). The odds ratio for influenza-like illness among children versus adults was 3.1 (1.3–7.3).
The strong age effect, combined with the low number of susceptible children per household (1.2), plausibly explains the lower-than-expected household secondary attack rate for influenza-like illness, illustrating the importance of other venues where children congregate for sustaining community transmission. Quantifying the effects of age on pH1N1 transmission is important for informing effective intervention strategies.
PMCID: PMC3755879  PMID: 21233714
8.  Economic evaluation of influenza pandemic mitigation strategies in the us using a stochastic microsimulation transmission model 
To project the potential economic impact of pandemic influenza mitigation strategies from a societal perspective in the United States.
We use a stochastic agent-based model to simulate pandemic influenza in the community. We compare 17 strategies: targeted antiviral prophylaxis (TAP) alone and in combination with school closure as well as prevaccination.
In the absence of intervention, we predict a 50% attack rate with an economic impact of $187 per capita as loss to society. Full TAP is the most effective single strategy, reducing number of cases by 54% at the lowest cost to society ($127 per capita). Prevaccination reduces number of cases by 48% and is the second least costly alternative ($140 per capita). Adding school closure to full TAP or prevaccination further improves health outcomes, but increases total cost to society by approximately $2700 per capita.
Full targeted antiviral prophylaxis is an effective and cost-saving measure for mitigating pandemic influenza.
PMCID: PMC3710126  PMID: 18671770
Influenza; Human Disease Outbreaks; Cost-Benefit Analysis; Economics; Pharmaceutical Models; Theoretical; Computer Simulation
9.  The Minicommunity Design to Assess Indirect Effects of Vaccination 
Epidemiologic methods  2012;1(1):83-105.
We propose the minicommunity design to estimate indirect effects of vaccination. Establishing indirect effects of vaccination in unvaccinated subpopulations could have important implications for global vaccine policies. In the minicommunity design, the household or other small transmission unit serves as the cluster in which to estimate indirect effects of vaccination, similar to studies in larger communities to estimate indirect, total, and overall effects. Examples from the literature include studies in small transmission units to estimate indirect effects of pertussis, pneumococcal, influenza, and cholera vaccines. We characterize the minicommunity design by several methodologic considerations, including the assignment mechanism, ascertainment, the role of transmission outside the transmission unit, and the relation of the size of the transmission unit to number of people vaccinated. The minicommunity study for indirect effects is contrasted with studies to estimate vaccine effects on infectiousness and protective effects under conditions of household exposure within small transmission units. The minicommunity design can be easily implemented in individually randomized studies by enrolling and following-up members of households of the randomized individuals. The methodology for the minicommunity design for estimating indirect effects of vaccination deserves much future research.
PMCID: PMC3627501  PMID: 23599908
10.  Invited Commentary: Evaluating Vaccination Programs Using Genetic Sequence Data 
American Journal of Epidemiology  2009;170(12):1464-1466.
Genomic data will become an increasingly important component of epidemiologic studies in coming years. The authors of the accompanying Journal article, van Ballegooijen et al. (Am J Epidemiol. 2009;170(12):1455–1463), are to be commended for attempting to use the coalescent analysis of viral sequence data to evaluate a hepatitis B vaccination program. Coalescent theory attempts to link the phylogenetic history of populations with rates of population growth and decline. In particular, under certain assumptions, a reduction in genetic diversity can be interpreted as a reduction in disease incidence. However, the authors of this commentary contend that van Ballegooijen et al.’s interpretation of changes in viral genetic diversity as a measure of hepatitis B vaccine effectiveness has major limitations. Because of the potential use of these methods in future vaccination studies, the authors discuss the utility of these methods and the data requirements needed for them to be convincing. First, data sets should be large enough to provide sufficient epidemiologic-scale resolution. Second, data need to reflect sufficiently fine-grained temporal sampling. Third, other processes that can potentially influence genetic diversity and confuse demographic inferences should be considered.
PMCID: PMC2800275  PMID: 19910381
communicable diseases; disease notification; disease transmission, infectious; genetic variation; hepatitis B virus; molecular sequence data; vaccination
11.  Optimal Vaccine Allocation for the Early Mitigation of Pandemic Influenza 
PLoS Computational Biology  2013;9(3):e1002964.
With new cases of avian influenza H5N1 (H5N1AV) arising frequently, the threat of a new influenza pandemic remains a challenge for public health. Several vaccines have been developed specifically targeting H5N1AV, but their production is limited and only a few million doses are readily available. Because there is an important time lag between the emergence of new pandemic strain and the development and distribution of a vaccine, shortage of vaccine is very likely at the beginning of a pandemic. We coupled a mathematical model with a genetic algorithm to optimally and dynamically distribute vaccine in a network of cities, connected by the airline transportation network. By minimizing the illness attack rate (i.e., the percentage of people in the population who become infected and ill), we focus on optimizing vaccine allocation in a network of 16 cities in Southeast Asia when only a few million doses are available. In our base case, we assume the vaccine is well-matched and vaccination occurs 5 to 10 days after the beginning of the epidemic. The effectiveness of all the vaccination strategies drops off as the timing is delayed or the vaccine is less well-matched. Under the best assumptions, optimal vaccination strategies substantially reduced the illness attack rate, with a maximal reduction in the attack rate of 85%. Furthermore, our results suggest that cooperative strategies where the resources are optimally distributed among the cities perform much better than the strategies where the vaccine is equally distributed among the network, yielding an illness attack rate 17% lower. We show that it is possible to significantly mitigate a more global epidemic with limited quantities of vaccine, provided that the vaccination campaign is extremely fast and it occurs within the first weeks of transmission.
Author Summary
In the past, the emergence of new strains of influenza has been sometimes responsible for large and deadly pandemics. With a very high mortality rate, (i.e., about 60% of the reported cases), H5N1AV influenza, commonly known as bird flu, is thought to be an important potential threat for a new pandemic. Because of this, several vaccines have been developed, but only a few million doses are readily available. Other zoonotic influenza strains, particularly in pigs, also threaten, and vaccines are being produced for them as well. In the event of an influenza pandemic, utilizing these resources optimally could make the difference between dealing with a serious infectious disease at a global scale and reducing it to a highly localized and controlled outbreak. In this paper, we address this issue by developing a mathematical model of influenza transmission on a network of cities. We couple the model with an optimization algorithm to allocate vaccine in time and space through the network. We find that our optimal allocation strategies can mitigate a pandemic, provided that vaccination occurs quickly, within the first weeks of a potential pandemic. In addition, our analysis highlights the importance of cooperative and coordinated vaccine distribution, if we want to mitigate a pandemic.
PMCID: PMC3605056  PMID: 23555207
12.  Performance of rapid influenza H1N1 diagnostic tests: a meta-analysis 
Following the outbreaks of 2009 pandemic H1N1 infection, rapid influenza diagnostic tests have been used to detect H1N1 infection. However, no meta-analysis has been undertaken to assess the diagnostic accuracy when this manuscript was drafted.
The literature was systematically searched to identify studies that reported the performance of rapid tests. Random effects meta-analyses were conducted to summarize the overall performance.
Seventeen studies were selected with 1879 cases and 3477 non-cases. The overall sensitivity and specificity estimates of the rapid tests were 0.51 (95%CI: 0.41, 0.60) and 0.98 (95%CI: 0.94, 0.99). Studies reported heterogeneous sensitivity estimates, ranging from 0.11 to 0.88. If the prevalence was 30%, the overall positive and negative predictive values were 0.94 (95%CI: 0.85, 0.98) and 0.82 (95%CI: 0.79, 0.85). The overall specificities from different manufacturers were comparable, while there were some differences for the overall sensitivity estimates. BinaxNOW had a lower overall sensitivity of 0.39 (95%CI: 0.24, 0.57) compared to all the others (p-value < 0.001), whereas QuickVue had a higher overall sensitivity of 0.57 (95%CI: 0.50, 0.63) compared to all the others (p-value = 0.005).
Rapid tests have high specificity but low sensitivity and thus limited usefulness.
PMCID: PMC3288365  PMID: 21883964
meta analysis; H1N1; diagnostic tests; rapid tests; sensitivity and specificity
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.
PMCID: PMC3359895  PMID: 22639701
contact network; epidemic model; influenza; simulation model; social network
14.  A Hybrid EM and Monte Carlo EM Algorithm and Its Application to Analysis of Transmission of Infectious Diseases 
Biometrics  2012;68(4):1238-1249.
In epidemics of infectious diseases such as influenza, an individual may have one of four possible final states: prior immune, escaped from infection, infected with symptoms, and infected asymptomatically. The exact state is often not observed. In addition, the unobserved transmission times of asymptomatic infections further complicate analysis. Under the assumption of missing at random, data-augmentation techniques can be used to integrate out such uncertainties. We adapt an importance-sampling-based Monte Carlo EM (MCEM) algorithm to the setting of an infectious disease transmitted in close contact groups. Assuming the independence between close contact groups, we propose a hybrid EM-MCEM algorithm that applies the MCEM or the traditional EM algorithms to each close contact group depending on the dimension of missing data in that group, and discuss the variance estimation for this practice. In addition, we propose a bootstrap approach to assess the total Monte Carlo error and factor that error into the variance estimation. The proposed methods are evaluated using simulation studies. We use the hybrid EM-MCEM algorithm to analyze two influenza epidemics in the late 1970s to assess the effects of age and pre-season antibody levels on the transmissibility and pathogenicity of the viruses.
PMCID: PMC3402623  PMID: 22506893
Data augmentation; EM algorithm; Infectious disease; Missing data; Monte Carlo
15.  Toward Causal Inference With Interference 
A fundamental assumption usually made in causal inference is that of no interference between individuals (or units); that is, the potential outcomes of one individual are assumed to be unaffected by the treatment assignment of other individuals. However, in many settings, this assumption obviously does not hold. For example, in the dependent happenings of infectious diseases, whether one person becomes infected depends on who else in the population is vaccinated. In this article, we consider a population of groups of individuals where interference is possible between individuals within the same group. We propose estimands for direct, indirect, total, and overall causal effects of treatment strategies in this setting. Relations among the estimands are established; for example, the total causal effect is shown to equal the sum of direct and indirect causal effects. Using an experimental design with a two-stage randomization procedure (first at the group level, then at the individual level within groups), unbiased estimators of the proposed estimands are presented. Variances of the estimators are also developed. The methodology is illustrated in two different settings where interference is likely: assessing causal effects of housing vouchers and of vaccines.
PMCID: PMC2600548  PMID: 19081744
Group-randomized trials; Potential outcomes; Stable unit treatment value assumption; SUTVA; Vaccine
16.  Controlling Dengue with Vaccines in Thailand 
Dengue is a mosquito-borne infectious disease that constitutes a growing global threat with the habitat expansion of its vectors Aedes aegyti and A. albopictus and increasing urbanization. With no effective treatment and limited success of vector control, dengue vaccines constitute the best control measure for the foreseeable future. With four interacting dengue serotypes, the development of an effective vaccine has been a challenge. Several dengue vaccine candidates are currently being tested in clinical trials. Before the widespread introduction of a new dengue vaccine, one needs to consider how best to use limited supplies of vaccine given the complex dengue transmission dynamics and the immunological interaction among the four dengue serotypes.
Methodology/Principal Findings
We developed an individual-level (including both humans and mosquitoes), stochastic simulation model for dengue transmission and control in a semi-rural area in Thailand. We calibrated the model to dengue serotype-specific infection, illness and hospitalization data from Thailand. Our simulations show that a realistic roll-out plan, starting with young children then covering progressively older individuals in following seasons, could reduce local transmission of dengue to low levels. Simulations indicate that this strategy could avert about 7,700 uncomplicated dengue fever cases and 220 dengue hospitalizations per 100,000 people at risk over a ten-year period.
Vaccination will have an important role in controlling dengue. According to our modeling results, children should be prioritized to receive vaccine, but adults will also need to be vaccinated if one wants to reduce community-wide dengue transmission to low levels.
Author Summary
An estimated 40% of the world's population is at risk of infection with dengue, a mosquito-borne disease that can lead to hospitalization or death. Dengue vaccines are currently being tested in clinical trials and at least one product will likely be available within a couple of years. Before widespread deployment, one should plan how best to use limited supplies of vaccine. We developed a mathematical model of dengue transmission in semi-rural Thailand to help evaluate different vaccination strategies. Our modeling results indicate that children should be prioritized to receive vaccine to reduce dengue-related morbidity, but adults will also need to be vaccinated if one wants to eliminate local dengue transmission. Dengue is a challenging disease to study because of its four interacting serotypes, seasonality of its transmission, and pre-existing immunity in a population. Models such as this one are useful coherent framework for synthesizing these complex issues and evaluating potential public health interventions such as mass vaccination.
PMCID: PMC3493390  PMID: 23145197
17.  Planning for the Control of Pandemic Influenza A (H1N1) in Los Angeles County and the United States 
American Journal of Epidemiology  2011;173(10):1121-1130.
Mathematical and computer models can provide guidance to public health officials by projecting the course of an epidemic and evaluating control measures. The authors built upon an existing collaboration between an academic research group and the Los Angeles County, California, Department of Public Health to plan for and respond to the first and subsequent years of pandemic influenza A (H1N1) circulation. The use of models allowed the authors to 1) project the timing and magnitude of the epidemic in Los Angeles County and the continental United States; 2) predict the effect of the influenza mass vaccination campaign that began in October 2009 on the spread of pandemic H1N1 in Los Angeles County and the continental United States; and 3) predict that a third wave of pandemic influenza in the winter or spring of 2010 was unlikely to occur. The close collaboration between modelers and public health officials during pandemic H1N1 spread in the fall of 2009 helped Los Angeles County officials develop a measured and appropriate response to the unfolding pandemic and establish reasonable goals for mitigation of pandemic H1N1.
PMCID: PMC3121321  PMID: 21427173
communicable disease control; influenza, human; influenza vaccines; mass vaccination
18.  Design and Evaluation of Prophylactic Interventions Using Infectious Disease Incidence Data from Close Contact Groups 
Prophylaxis of contacts of infectious cases such as household members and treatment of infectious cases are methods to prevent 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 using simulations. We estimate the efficacy of the influenza antiviral agent oseltamivir in reducing susceptibility and infectiousness in two case-ascertained household trials.
PMCID: PMC3312606  PMID: 22457545
Antiviral agent; Community trial; Infectious disease; Intervention efficacy; Left truncation
The annals of applied statistics  2011;5(3):1816-1838.
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.
PMCID: PMC3306235  PMID: 22427793
20.  School opening dates predict pandemic influenza A (H1N1) epidemics in the USA 
The Journal of infectious diseases  2010;202(6):877-880.
The opening of schools in late summer of 2009 may have triggered the fall wave of pandemic influenza A(H1N1) in the United States. We found that elevated percent of outpatient visits for influenza-like illness (ILI%) occurred an average of 14 days after schools opened in a state in the fall of 2009. The timing of these events was highly correlated (Spearman’s correlation coefficient=0.62, p < 1.0 × 10−5). This result provides evidence that transmission in schools catalyzes community-wide transmission. School opening dates can be useful for future pandemic planning, and influenza mitigation strategies should be targeted at school populations before the influenza season.
PMCID: PMC2939723  PMID: 20704486
Children; Epidemics; Human Influenza; Pandemics
21.  The Global Transmission and Control of Influenza 
PLoS ONE  2011;6(5):e19515.
New strains of influenza spread around the globe via the movement of infected individuals. The global dynamics of influenza are complicated by different patterns of influenza seasonality in different regions of the world. We have released an open-source stochastic mathematical model of the spread of influenza across 321 major, strategically located cities of the world. Influenza is transmitted between cities via infected airline passengers. Seasonality is simulated by increasing the transmissibility in each city at the times of the year when influenza has been observed to be most prevalent. The spatiotemporal spread of pandemic influenza can be understood through clusters of global transmission and links between them, which we identify using the epidemic percolation network (EPN) of the model. We use the model to explain the observed global pattern of spread for pandemic influenza A(H1N1) 2009–2010 (pandemic H1N1 2009) and to examine possible global patterns of spread for future pandemics depending on the origin of pandemic spread, time of year of emergence, and basic reproductive number (). We also use the model to investigate the effectiveness of a plausible global distribution of vaccine for various pandemic scenarios. For pandemic H1N1 2009, we show that the biggest impact of vaccination was in the temperate northern hemisphere. For pandemics starting in the temperate northern hemisphere in May or April, vaccination would have little effect in the temperate southern hemisphere and a small effect in the tropics. With the increasing interconnectedness of the world's population, we must take a global view of infectious disease transmission. Our open-source, computationally simple model can help public health officials plan for the next pandemic as well as deal with interpandemic influenza.
PMCID: PMC3089626  PMID: 21573121
22.  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.
PMCID: PMC3070363  PMID: 21472041
Missing data; MCMC; Infectious disease; Competing risks; Intervention efficacy
23.  On Influenza and School Closings: Time for Prospective Studies 
Epidemiology (Cambridge, Mass.)  2009;20(6):793-795.
PMCID: PMC2903453  PMID: 19770772
24.  Efficacy of Trivalent, Cold-Adapted, Influenza Virus Vaccine Against Influenza A (Fujian), a Drift Variant, during 2003–2004 
Vaccine  2007;25(20):4038-4045.
In the 2003–2004 influenza season, the predominant circulating influenza A (H3N2) virus in the United States was similar antigenically to A/Fujian/411/2002 (H3N2), a drift variant of A/Panama/2007/99 (H3N2), the vaccine strain. That year, a field study of trivalent live-attenuated influenza vaccine (LAIV-T) was conducted in Temple-Belton, Texas, as part of a larger community-based, non-randomized, open-label study in three communities that began in August 1998 [1, 2, 3]. Participants were healthy children aged 5 – 18 years. The analysis here concerns 6,403 children in the Scott & White Health Plan (SWHP) database living within zip codes of the Temple-Belton area, of whom 1,706 received LAIV-T and 548 received trivalent inactivated vaccine (TIV) in 2003, 983 had been previously vaccinated in 1998–2001, but not in 2002–2003 or 2003, and 3,166 had never been vaccinated. The main outcome measure was medically-attended acute respiratory illness (MAARI). Surveillance culture results were incorporated into the analysis to estimate efficacy against culture-confirmed influenza illness. Vaccine effectiveness of LAIV-T against MAARI was 26% (95% confidence interval (CI) 11,39). Vaccine efficacy of LAIV-T against culture-confirmed influenza illness including surveillance cultures of children in the SWHP database in the validation calculation was 56% (95% CI 24,84). LAIV-T was cross-protective with a drift variant strain in 2003–2004, evidence that such vaccines could be important for preparing for a pandemic and for annual influenza.
PMCID: PMC2883284  PMID: 17395338
efficacy; influenza; surveillance; vaccine
25.  The Transmissibility and Control of Pandemic Influenza A (H1N1) Virus 
Science (New York, N.Y.)  2009;326(5953):729-733.
Pandemic influenza A (H1N1) 2009 (pandemic H1N1) is spreading throughout the planet. It has become the dominant strain in the southern hemisphere, where the influenza season is underway. Here, based on reported case clusters in the USA, we estimate the household secondary attack rate for pandemic H1N1 to be 27.3% (95% CI: 12.2%–50.5%). From a school outbreak, we estimate a school child infects 2.4 (95% CI: 1.8–3.2) other children within the school. We estimate the basic reproductive number, R0, to range from 1.3–1.7 and the generation interval to range from 2.6–3.2 days. We use a simulation model to evaluate the effectiveness of vaccination strategies in the USA for the Fall, 2009. If vaccine were available soon enough, vaccination of children, followed by adults, reaching 70% overall coverage, in addition to high risk and essential workforce groups, could mitigate a severe epidemic.
PMCID: PMC2880578  PMID: 19745114

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