Informing policy via dynamic models: Cholera in Haiti.

Public health decisions must be made about when and how to implement interventions to control an infectious disease epidemic. These decisions should be informed by data on the epidemic as well as current understanding about the transmission dynamics. Such decisions can be posed as statistical questions about scientifically motivated dynamic models. Thus, we encounter the methodological task of building credible, data-informed decisions based on stochastic, partially observed, nonlinear dynamic models. This necessitates addressing the tradeoff between biological fidelity and model simplicity, and the reality of misspecification for models at all levels of complexity. We assess current methodological approaches to these issues via a case study of the 2010-2019 cholera epidemic in Haiti. We consider three dynamic models developed by expert teams to advise on vaccination policies. We evaluate previous methods used for fitting these models, and we demonstrate modified data analysis strategies leading to improved statistical fit. Specifically, we present approaches for diagnosing model misspecification and the consequent development of improved models. Additionally, we demonstrate the utility of recent advances in likelihood maximization for high-dimensional nonlinear dynamic models, enabling likelihood-based inference for spatiotemporal incidence data using this class of models. Our workflow is reproducible and extendable, facilitating future investigations of this disease system.

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.

Assessing Real-Time Moderation for Developing Adaptive Mobile Health Interventions for Medical Interns: Micro-Randomized Trial.

BACKGROUND: Individuals in stressful work environments often experience mental health issues, such as depression. Reducing depression rates is difficult because of persistently stressful work environments and inadequate time or resources to access traditional mental health care services. Mobile health (mHealth) interventions provide an opportunity to deliver real-time interventions in the real world. In addition, the delivery times of interventions can be based on real-time data collected with a mobile device. To date, data and analyses informing the timing of delivery of mHealth interventions are generally lacking. OBJECTIVE: This study aimed to investigate when to provide mHealth interventions to individuals in stressful work environments to improve their behavior and mental health. The mHealth interventions targeted 3 categories of behavior: mood, activity, and sleep. The interventions aimed to improve 3 different outcomes: weekly mood (assessed through a daily survey), weekly step count, and weekly sleep time. We explored when these interventions were most effective, based on previous mood, step, and sleep scores. METHODS: We conducted a 6-month micro-randomized trial on 1565 medical interns. Medical internship, during the first year of physician residency training, is highly stressful, resulting in depression rates several folds higher than those of the general population. Every week, interns were randomly assigned to receive push notifications related to a particular category (mood, activity, sleep, or no notifications). Every day, we collected interns' daily mood valence, sleep, and step data. We assessed the causal effect moderation by the previous week's mood, steps, and sleep. Specifically, we examined changes in the effect of notifications containing mood, activity, and sleep messages based on the previous week's mood, step, and sleep scores. Moderation was assessed with a weighted and centered least-squares estimator. RESULTS: We found that the previous week's mood negatively moderated the effect of notifications on the current week's mood with an estimated moderation of -0.052 (P=.001). That is, notifications had a better impact on mood when the studied interns had a low mood in the previous week. Similarly, we found that the previous week's step count negatively moderated the effect of activity notifications on the current week's step count, with an estimated moderation of -0.039 (P=.01) and that the previous week's sleep negatively moderated the effect of sleep notifications on the current week's sleep with an estimated moderation of -0.075 (P<.001). For all three of these moderators, we estimated that the treatment effect was positive (beneficial) when the moderator was low, and negative (harmful) when the moderator was high. CONCLUSIONS: These findings suggest that an individual's current state meaningfully influences their receptivity to mHealth interventions for mental health. Timing interventions to match an individual's state may be critical to maximizing the efficacy of interventions. TRIAL REGISTRATION: ClinicalTrials.gov NCT03972293; http://clinicaltrials.gov/ct2/show/NCT03972293.

Cardiovascular Risk Factors, Depression, and Alcohol Consumption During Joblessness and During Recessions Among Young Adults in CARDIA.

Research has shown that recessions are associated with lower cardiovascular mortality, but unemployed individuals have a higher risk of cardiovascular disease (CVD) or death. We used data from 8 consecutive examinations (1985-2011) of the Coronary Artery Risk Development in Young Adults (CARDIA) cohort, modeled in fixed-effect panel regressions, to investigate simultaneously the associations of CVD risk factors with the employment status of individuals and the macroeconomic conditions prevalent in the state where the individual lives. We found that unemployed individuals had lower levels of blood pressure, high-density lipoprotein cholesterol, and physical activity, and they had significantly higher depression scores, but they were similar to their counterparts in smoking status, alcohol consumption, low-density lipoprotein cholesterol levels, body mass index, and waist circumference. A 1-percentage-point higher unemployment rate at the state level was associated with lower systolic (-0.41 mm Hg, 95% CI: -0.65, -0.17) and diastolic (-0.19, 95% CI: -0.39, 0.01) blood pressure, higher physical activity levels, higher depressive symptom scores, lower waist circumference, and less smoking. We conclude that levels of CVD risk factors tend to improve during recessions, but mental health tends to deteriorate. Unemployed individuals are significantly more depressed, and they likely have lower levels of physical activity and high-density lipoprotein cholesterol.

Inference for dynamic and latent variable models via iterated, perturbed Bayes maps.

Iterated filtering algorithms are stochastic optimization procedures for latent variable models that recursively combine parameter perturbations with latent variable reconstruction. Previously, theoretical support for these algorithms has been based on the use of conditional moments of perturbed parameters to approximate derivatives of the log likelihood function. Here, a theoretical approach is introduced based on the convergence of an iterated Bayes map. An algorithm supported by this theory displays substantial numerical improvement on the computational challenge of inferring parameters of a partially observed Markov process.

Population health and the economy: Mortality and the Great Recession in Europe.

We analyze the evolution of mortality-based health indicators in 27 European countries before and after the start of the Great Recession. We find that in the countries where the crisis has been particularly severe, mortality reductions in 2007-2010 were considerably bigger than in 2004-2007. Panel models adjusted for space-invariant and time-invariant factors show that an increase of 1 percentage point in the national unemployment rate is associated with a reduction of 0.5% (p < .001) in the rate of age-adjusted mortality. The pattern of mortality oscillating procyclically is found for total and sex-specific mortality, cause-specific mortality due to major causes of death, and mortality for ages 30-44 and 75 and over, but not for ages 0-14. Suicides appear increasing when the economy decelerates-countercyclically-but the evidence is weak. Results are robust to using different weights in the regression, applying nonlinear methods for detrending, expanding the sample, and using as business cycle indicator gross domestic product per capita or employment-to-population ratios rather than the unemployment rate. We conclude that in the European experience of the past 20 years, recessions, on average, have beneficial short-term effects on mortality of the adult population.

Individual joblessness, contextual unemployment, and mortality risk.

Longitudinal studies at the level of individuals find that employees who lose their jobs are at increased risk of death. However, analyses of aggregate data find that as unemployment rates increase during recessions, population mortality actually declines. We addressed this paradox by using data from the US Department of Labor and annual survey data (1979-1997) from a nationally representative longitudinal study of individuals-the Panel Study of Income Dynamics. Using proportional hazards (Cox) regression, we analyzed how the hazard of death depended on 1) individual joblessness and 2) state unemployment rates, as indicators of contextual economic conditions. We found that 1) compared with the employed, for the unemployed the hazard of death was increased by an amount equivalent to 10 extra years of age, and 2) each percentage-point increase in the state unemployment rate reduced the mortality hazard in all individuals by an amount equivalent to a reduction of 1 year of age. Our results provide evidence that 1) joblessness strongly and significantly raises the risk of death among those suffering it, and 2) periods of higher unemployment rates, that is, recessions, are associated with a moderate but significant reduction in the risk of death among the entire population.

Insecticide-treated net use before and after mass distribution in a fishing community along Lake Victoria, Kenya: successes and unavoidable pitfalls.

BACKGROUND: Insecticide-treated nets (ITNs) have proven instrumental in the successful reduction of malaria incidence in holoendemic regions during the past decade. As distribution of ITNs throughout sub-Saharan Africa (SSA) is being scaled up, maintaining maximal levels of coverage will be necessary to sustain current gains. The effectiveness of mass distribution of ITNs, requires careful analysis of successes and failures if impacts are to be sustained over the long term. METHODS: Mass distribution of ITNs to a rural Kenyan community along Lake Victoria was performed in early 2011. Surveyors collected data on ITN use both before and one year following this distribution. At both times, household representatives were asked to provide a complete accounting of ITNs within the dwelling, the location of each net, and the ages and genders of each person who slept under that net the previous night. Other data on household material possessions, education levels and occupations were recorded. Information on malaria preventative factors such as ceiling nets and indoor residual spraying was noted. Basic information on malaria knowledge and health-seeking behaviours was also collected. Patterns of ITN use before and one year following net distribution were compared using spatial and multi-variable statistical methods. Associations of ITN use with various individual, household, demographic and malaria related factors were tested using logistic regression. RESULTS: After infancy (<1 year), ITN use sharply declined until the late teenage years then began to rise again, plateauing at 30 years of age. Males were less likely to use ITNs than females. Prior to distribution, socio-economic factors such as parental education and occupation were associated with ITN use. Following distribution, ITN use was similar across social groups. Household factors such as availability of nets and sleeping arrangements still reduced consistent net use, however. CONCLUSIONS: Comprehensive, direct-to-household, mass distribution of ITNs was effective in rapidly scaling up coverage, with use being maintained at a high level at least one year following the intervention. Free distribution of ITNs through direct-to-household distribution method can eliminate important constraints in determining consistent ITN use, thus enhancing the sustainability of effective intervention campaigns.

Inapparent infections and cholera dynamics.

In many infectious diseases, an unknown fraction of infections produce symptoms mild enough to go unrecorded, a fact that can seriously compromise the interpretation of epidemiological records. This is true for cholera, a pandemic bacterial disease, where estimates of the ratio of asymptomatic to symptomatic infections have ranged from 3 to 100 (refs 1-5). In the absence of direct evidence, understanding of fundamental aspects of cholera transmission, immunology and control has been based on assumptions about this ratio and about the immunological consequences of inapparent infections. Here we show that a model incorporating high asymptomatic ratio and rapidly waning immunity, with infection both from human and environmental sources, explains 50 yr of mortality data from 26 districts of Bengal, the pathogen's endemic home. We find that the asymptomatic ratio in cholera is far higher than had been previously supposed and that the immunity derived from mild infections wanes much more rapidly than earlier analyses have indicated. We find, too, that the environmental reservoir (free-living pathogen) is directly responsible for relatively few infections but that it may be critical to the disease's endemicity. Our results demonstrate that inapparent infections can hold the key to interpreting the patterns of disease outbreaks. New statistical methods, which allow rigorous maximum likelihood inference based on dynamical models incorporating multiple sources and outcomes of infection, seasonality, process noise, hidden variables and measurement error, make it possible to test more precise hypotheses and obtain unexpected results. Our experience suggests that the confrontation of time-series data with mechanistic models is likely to revise our understanding of the ecology of many infectious diseases.

EXACT PHYLODYNAMIC LIKELIHOOD VIA STRUCTURED MARKOV GENEALOGY PROCESSES.

We consider genealogies arising from a Markov population process in which individuals are categorized into a discrete collection of compartments, with the requirement that individuals within the same compartment are statistically exchangeable. When equipped with a sampling process, each such population process induces a time-evolving tree-valued process defined as the genealogy of all sampled individuals. We provide a construction of this genealogy process and derive exact expressions for the likelihood of an observed genealogy in terms of filter equations. These filter equations can be numerically solved using standard Monte Carlo integration methods. Thus, we obtain statistically efficient likelihood-based inference for essentially arbitrary compartment models based on an observed genealogy of individuals sampled from the population.

Inference on spatiotemporal dynamics for coupled biological populations.

Mathematical models in ecology and epidemiology must be consistent with observed data in order to generate reliable knowledge and evidence-based policy. Metapopulation systems, which consist of a network of connected sub-populations, pose technical challenges in statistical inference owing to nonlinear, stochastic interactions. Numerical difficulties encountered in conducting inference can obstruct the core scientific questions concerning the link between the mathematical models and the data. Recently, an algorithm has been proposed that enables computationally tractable likelihood-based inference for high-dimensional partially observed stochastic dynamic models of metapopulation systems. We use this algorithm to build a statistically principled data analysis workflow for metapopulation systems. Via a case study of COVID-19, we show how this workflow addresses the limitations of previous approaches. The COVID-19 pandemic provides a situation where mathematical models and their policy implications are widely visible, and we revisit an influential metapopulation model used to inform basic epidemiological understanding early in the pandemic. Our methods support self-critical data analysis, enabling us to identify and address model weaknesses, leading to a new model with substantially improved statistical fit and parameter identifiability. Our results suggest that the lockdown initiated on 23 January 2020 in China was more effective than previously thought.

Successes and shortcomings of polio eradication: a transmission modeling analysis.

Polio eradication is on the cusp of success, with only a few regions still maintaining transmission. Improving our understanding of why some regions have been successful and others have not will help with both global eradication of polio and development of more effective vaccination strategies for other pathogens. To examine the past 25 years of eradication efforts, we constructed a transmission model for wild poliovirus that incorporates waning immunity (which affects both infection risk and transmissibility of any resulting infection), age-mediated vaccination rates, and transmission of oral polio vaccine. The model produces results consistent with the 4 country categories defined by the Global Polio Eradication Program: elimination with no subsequent outbreaks; elimination with subsequent transient outbreaks; elimination with subsequent outbreaks and transmission detected for more than 12 months; and endemic polio transmission. Analysis of waning immunity rates and oral polio vaccine transmissibility reveals that higher waning immunity rates make eradication more difficult because of increasing numbers of infectious adults, and that higher oral polio vaccine transmission rates make eradication easier as adults become reimmunized. Given these dynamic properties, attention should be given to intervention strategies that complement childhood vaccination. For example, improvement in sanitation can reduce the reproduction number in problematic regions, and adult vaccination can lower adult transmission.

Bagged filters for partially observed interacting systems.

Bagging (i.e., bootstrap aggregating) involves combining an ensemble of bootstrap estimators. We consider bagging for inference from noisy or incomplete measurements on a collection of interacting stochastic dynamic systems. Each system is called a unit, and each unit is associated with a spatial location. A motivating example arises in epidemiology, where each unit is a city: the majority of transmission occurs within a city, with smaller yet epidemiologically important interactions arising from disease transmission between cities. Monte Carlo filtering methods used for inference on nonlinear non-Gaussian systems can suffer from a curse of dimensionality as the number of units increases. We introduce bagged filter (BF) methodology which combines an ensemble of Monte Carlo filters, using spatiotemporally localized weights to select successful filters at each unit and time. We obtain conditions under which likelihood evaluation using a BF algorithm can beat a curse of dimensionality, and we demonstrate applicability even when these conditions do not hold. BF can out-perform an ensemble Kalman filter on a coupled population dynamics model describing infectious disease transmission. A block particle filter also performs well on this task, though the bagged filter respects smoothness and conservation laws that a block particle filter can violate.

Cross-correlation map analyses show weather variation influences on mosquito abundance patterns in Saginaw County, Michigan, 1989-2005.

Weather is important determinant of mosquito abundance that, in turn, influences vectorborne disease dynamics. In temperate regions, transmission generally is seasonal as mosquito abundance and behavior varies with temperature, precipitation, and other meteorological factors. We investigated how such factors affected species-specific mosquito abundance patterns in Saginaw County, MI, during a 17-yr period. Systematic sampling was undertaken at 22 trapping sites from May to September, during 1989-2005, for 19,228 trap-nights and 300,770 mosquitoes in total. Aedes vexans (Meigen), Culex pipiens L. and Culex restuans Theobald, the most abundant species, were analyzed. Weather data included local daily maximum temperature, minimum temperature, total precipitation, and average relative humidity. In addition to standard statistical methods, cross-correlation mapping was used to evaluate temporal associations with various lag periods between weather variables and species-specific mosquito abundances. Overall, the average number of mosquitoes was 4.90 per trap-night for Ae. vexans, 2.12 for Cx. pipiens, and 1.23 for Cx. restuans. Statistical analysis of the considerable temporal variability in species-specific abundances indicated that precipitation and relative humidity 1 wk prior were significantly positively associated with Ae. vexans, whereas elevated maximum temperature had a negative effect during summer. Cx. pipiens abundance was positively influenced by the preceding minimum temperature in the early season but negatively associated with precipitation during summer and with maximum temperature in July and August. Cx. restuans showed the least weather association, with only relative humidity 2-24 d prior being linked positively during late spring-early summer. The recently developed analytical method applied in this study could enhance our understanding of the influences of weather variability on mosquito population dynamics.

Forcing versus feedback: epidemic malaria and monsoon rains in northwest India.

Malaria epidemics in regions with seasonal windows of transmission can vary greatly in size from year to year. A central question has been whether these interannual cycles are driven by climate, are instead generated by the intrinsic dynamics of the disease, or result from the resonance of these two mechanisms. This corresponds to the more general inverse problem of identifying the respective roles of external forcings vs. internal feedbacks from time series for nonlinear and noisy systems. We propose here a quantitative approach to formally compare rival hypotheses on climate vs. disease dynamics, or external forcings vs. internal feedbacks, that combines dynamical models with recently developed, computational inference methods. The interannual patterns of epidemic malaria are investigated here for desert regions of northwest India, with extensive epidemiological records for Plasmodium falciparum malaria for the past two decades. We formulate a dynamical model of malaria transmission that explicitly incorporates rainfall, and we rely on recent advances on parameter estimation for nonlinear and stochastic dynamical systems based on sequential Monte Carlo methods. Results show a significant effect of rainfall in the inter-annual variability of epidemic malaria that involves a threshold in the disease response. The model exhibits high prediction skill for yearly cases in the malaria transmission season following the monsoonal rains. Consideration of a more complex model with clinical immunity demonstrates the robustness of the findings and suggests a role of infected individuals that lack clinical symptoms as a reservoir for transmission. Our results indicate that the nonlinear dynamics of the disease itself play a role at the seasonal, but not the interannual, time scales. They illustrate the feasibility of forecasting malaria epidemics in desert and semi-arid regions of India based on climate variability. This approach should be applicable to malaria in other locations, to other infectious diseases, and to other nonlinear systems under forcing.

Inference on high-dimensional implicit dynamic models using a guided intermediate resampling filter.

We propose a method for inference on moderately high-dimensional, nonlinear, non-Gaussian, partially observed Markov process models for which the transition density is not analytically tractable. Markov processes with intractable transition densities arise in models defined implicitly by simulation algorithms. Widely used particle filter methods are applicable to nonlinear, non-Gaussian models but suffer from the curse of dimensionality. Improved scalability is provided by ensemble Kalman filter methods, but these are inappropriate for highly nonlinear and non-Gaussian models. We propose a particle filter method having improved practical and theoretical scalability with respect to the model dimension. This method is applicable to implicitly defined models having analytically intractable transition densities. Our method is developed based on the assumption that the latent process is defined in continuous time and that a simulator of this latent process is available. In this method, particles are propagated at intermediate time intervals between observations and are resampled based on a forecast likelihood of future observations. We combine this particle filter with parameter estimation methodology to enable likelihood-based inference for highly nonlinear spatiotemporal systems. We demonstrate our methodology on a stochastic Lorenz 96 model and a model for the population dynamics of infectious diseases in a network of linked regions.

Effect of childhood rotavirus vaccination on community rotavirus prevalence in rural Ecuador, 2008-13.

BACKGROUND: Although live attenuated monovalent human rotavirus vaccine (Rotarix) efficacy has been characterized through randomized studies, its effectiveness, especially in non-clinical settings, is less clear. In this study, we estimate the impact of childhood Rotarix® vaccination on community rotavirus prevalence. METHODS: We analyse 10 years of serial population-based diarrhoea case-control study, which also included testing for rotavirus infection (n = 3430), and 29 months of all-cause diarrhoea active surveillance from a child cohort (n = 376) from rural Ecuador during a period in which Rotarix vaccination was introduced. We use weighted logistic regression from the case-control data to assess changes in community rotavirus prevalence (both symptomatic and asymptomatic) and all-cause diarrhoea after the vaccine was introduced. We also assess changes in all-cause diarrhoea rates in the child cohort (born 2008-13) using Cox regression, comparing time to first all-cause diarrhoea case by vaccine status. RESULTS: Overall, vaccine introduction among age-eligible children was associated with a 82.9% reduction [95% confidence interval (CI): 49.4%, 94.2%] in prevalence of rotavirus in participants without diarrhoea symptoms and a 46.0% reduction (95% CI: 6.2%, 68.9%) in prevalence of rotavirus infection among participants experiencing diarrhoea. Whereas all age groups benefited, this reduction was strongest among the youngest age groups. For young children, prevalence of symptomatic diarrhoea also decreased in the post-vaccine period in both the case-control study (reduction in prevalence for children <1 year of age = 69.3%, 95% CI: 8.7%, 89.7%) and the cohort study (reduction in hazard for receipt of two Rotarix doses among children aged 0.5-2 years = 57.1%, 95% CI: 16.6, 77.9%). CONCLUSIONS: Rotarix vaccination may suppress transmission, including asymptomatic transmission, in low- and middle-income settings. It was highly effective among children in a rural community setting and provides population-level benefits through indirect protection among adults.

Panel Data Analysis via Mechanistic Models.

Panel data, also known as longitudinal data, consist of a collection of time series. Each time series, which could itself be multivariate, comprises a sequence of measurements taken on a distinct unit. Mechanistic modeling involves writing down scientifically motivated equations describing the collection of dynamic systems giving rise to the observations on each unit. A defining characteristic of panel systems is that the dynamic interaction between units should be negligible. Panel models therefore consist of a collection of independent stochastic processes, generally linked through shared parameters while also having unit-specific parameters. To give the scientist flexibility in model specification, we are motivated to develop a framework for inference on panel data permitting the consideration of arbitrary nonlinear, partially observed panel models. We build on iterated filtering techniques that provide likelihood-based inference on nonlinear partially observed Markov process models for time series data. Our methodology depends on the latent Markov process only through simulation; this plug-and-play property ensures applicability to a large class of models. We demonstrate our methodology on a toy example and two epidemiological case studies. We address inferential and computational issues arising due to the combination of model complexity and dataset size. Supplementary materials for this article are available online.

The reversal of the relation between economic growth and health progress: Sweden in the 19th and 20th centuries.

Health progress, as measured by the decline in mortality rates and the increase in life expectancy, is usually conceived as related to economic growth, especially in the long run. In this investigation it is shown that economic growth is positively associated with health progress in Sweden throughout the 19th century. However, the relation becomes weaker as time passes and is completely reversed in the second half of the 20th century, when economic growth negatively affects health progress. The effect of the economy on health occurs mostly at lag 0 in the 19th century and is lagged up to 2 years in the 20th century. No evidence is found for economic effects on mortality at greater lags. These findings are shown to be robustly consistent across a variety of statistical procedures, including linear regression, spectral analysis, cross-correlation, and lag regression models. Models using inflation and unemployment as economic indicators reveal similar results. Evidence for reverse effects of health progress on economic growth is weak, and unobservable in the second half of the 20th century.

A second-order iterated smoothing algorithm.

Simulation-based inference for partially observed stochastic dynamic models is currently receiving much attention due to the fact that direct computation of the likelihood is not possible in many practical situations. Iterated filtering methodologies enable maximization of the likelihood function using simulation-based sequential Monte Carlo filters. Doucet et al. (2013) developed an approximation for the first and second derivatives of the log likelihood via simulation-based sequential Monte Carlo smoothing and proved that the approximation has some attractive theoretical properties. We investigated an iterated smoothing algorithm carrying out likelihood maximization using these derivative approximations. Further, we developed a new iterated smoothing algorithm, using a modification of these derivative estimates, for which we establish both theoretical results and effective practical performance. On benchmark computational challenges, this method beat the first-order iterated filtering algorithm. The method's performance was comparable to a recently developed iterated filtering algorithm based on an iterated Bayes map. Our iterated smoothing algorithm and its theoretical justification provide new directions for future developments in simulation-based inference for latent variable models such as partially observed Markov process models.