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.

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.

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.

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.

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.

Understanding the Impact of Rainfall on Diarrhea: Testing the Concentration-Dilution Hypothesis Using a Systematic Review and Meta-Analysis.

BACKGROUND: Projected increases in extreme weather may change relationships between rain-related climate exposures and diarrheal disease. Whether rainfall increases or decreases diarrhea rates is unclear based on prior literature. The concentration-dilution hypothesis suggests that these conflicting results are explained by the background level of rain: Rainfall following dry periods can flush pathogens into surface water, increasing diarrhea incidence, whereas rainfall following wet periods can dilute pathogen concentrations in surface water, thereby decreasing diarrhea incidence. OBJECTIVES: In this analysis, we explored the extent to which the concentration-dilution hypothesis is supported by published literature. METHODS: To this end, we conducted a systematic search for articles assessing the relationship between rain, extreme rain, flood, drought, and season (rainy vs. dry) and diarrheal illness. RESULTS: A total of 111 articles met our inclusion criteria. Overall, the literature largely supports the concentration-dilution hypothesis. In particular, extreme rain was associated with increased diarrhea when it followed a dry period [incidence rate ratio (IRR)=1.26; 95% confidence interval (CI): 1.05, 1.51], with a tendency toward an inverse association for extreme rain following wet periods, albeit nonsignificant, with one of four relevant studies showing a significant inverse association (IRR=0.911; 95% CI: 0.771, 1.08). Incidences of bacterial and parasitic diarrhea were more common during rainy seasons, providing pathogen-specific support for a concentration mechanism, but rotavirus diarrhea showed the opposite association. Information on timing of cases within the rainy season (e.g., early vs. late) was lacking, limiting further analysis. We did not find a linear association between nonextreme rain exposures and diarrheal disease, but several studies found a nonlinear association with low and high rain both being associated with diarrhea. DISCUSSION: Our meta-analysis suggests that the effect of rainfall depends on the antecedent conditions. Future studies should use standard, clearly defined exposure variables to strengthen understanding of the relationship between rainfall and diarrheal illness. https://doi.org/10.1289/EHP6181.

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.

Predicting re-emergence times of dengue epidemics at low reproductive numbers: DENV1 in Rio de Janeiro, 1986-1990.

Predicting arbovirus re-emergence remains challenging in regions with limited off-season transmission and intermittent epidemics. Current mathematical models treat the depletion and replenishment of susceptible (non-immune) hosts as the principal drivers of re-emergence, based on established understanding of highly transmissible childhood diseases with frequent epidemics. We extend an analytical approach to determine the number of 'skip' years preceding re-emergence for diseases with continuous seasonal transmission, population growth and under-reporting. Re-emergence times are shown to be highly sensitive to small changes in low R0 (secondary cases produced from a primary infection in a fully susceptible population). We then fit a stochastic Susceptible-Infected-Recovered (SIR) model to observed case data for the emergence of dengue serotype DENV1 in Rio de Janeiro. This aggregated city-level model substantially over-estimates observed re-emergence times either in terms of skips or outbreak probability under forward simulation. The inability of susceptible depletion and replenishment to explain re-emergence under 'well-mixed' conditions at a city-wide scale demonstrates a key limitation of SIR aggregated models, including those applied to other arboviruses. The predictive uncertainty and high skip sensitivity to epidemiological parameters suggest a need to investigate the relevant spatial scales of susceptible depletion and the scaling of microscale transmission dynamics to formulate simpler models that apply at coarse resolutions.

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.

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.

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.

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.

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.

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.

A sample size calculator for SMART pilot studies.

In clinical practice, as well as in other areas where interventions are provided, a sequential individualized approach to treatment is often necessary, whereby each treatment is adapted based on the object's response. An adaptive intervention is a sequence of decision rules which formalizes the provision of treatment at critical decision points in the care of an individual. In order to inform the development of an adaptive intervention, scientists are increasingly interested in the use of sequential multiple assignment randomized trials (SMART), which is a type of multi-stage randomized trial where individuals are randomized repeatedly at critical decision points to a set treatment options. While there is great interest in the use of SMART and in the development of adaptive interventions, both are relatively new to the medical and behavioral sciences. As a result, many clinical researchers will first implement a SMART pilot study (i.e., a small-scale version of a SMART) to examine feasibility and acceptability considerations prior to conducting a full-scale SMART study. A primary aim of this paper is to introduce a new methodology to calculate minimal sample size necessary for conducting a SMART pilot.

Trends of HIV-1 incidence with credible intervals in Sweden 2002-09 reconstructed using a dynamic model of within-patient IgG growth.

BACKGROUND: HIV-1 is a lifelong disease, often without serious symptoms for years after infection, and thus many infected persons go undetected for a long time. This makes it difficult to track incidence, and thus epidemics may go through dramatic changes largely unnoticed, only to be detected years later. Because direct measurement of incidence is expensive and difficult, several biomarker-based tests and algorithms have been developed to distinguish between recent and long-term infections. However, current methods have been criticized and demands for novel methods have been raised. METHODS: We developed and applied a biomarker-based incidence model, joining a time-continuous model of immunoglobulin G (IgG) growth (measured by the IgG-capture BED-enzyme immunoassay) with statistical corrections for both sample size and unobserved diagnoses. Our method uses measurements of IgG concentration in newly diagnosed people to calculate the posterior distribution of infection times. Time from infection to diagnosis is modelled for all individuals in a given period and is used to calculate a sample weight to correct for undiagnosed individuals. We then used a bootstrapping method to reconstruct point estimates and credible intervals of the incidence of HIV-1 in Sweden based on a sample of newly diagnosed people. RESULTS: We found evidence for: (i) a slowly but steadily increasing trend in both the incidence and incidence rate in Sweden; and (ii) an increasing but well-controlled epidemic in gay men in Stockholm. Sensitivity analyses showed that our method was robust to realistic levels (up to 15%) of BED misclassification of non-recently infected persons as early infections. CONCLUSIONS: We developed a novel incidence estimator based on previously published theoretical work that has the potential to provide rapid, up-to-date estimates of HIV-1 incidence in populations where BED test data are available.

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.

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.