Direct Estimation of Parameters in ODE Models Using WENDy: Weak-Form Estimation of Nonlinear Dynamics.

We introduce the Weak-form Estimation of Nonlinear Dynamics (WENDy) method for estimating model parameters for non-linear systems of ODEs. Without relying on any numerical differential equation solvers, WENDy computes accurate estimates and is robust to large (biologically relevant) levels of measurement noise. For low dimensional systems with modest amounts of data, WENDy is competitive with conventional forward solver-based nonlinear least squares methods in terms of speed and accuracy. For both higher dimensional systems and stiff systems, WENDy is typically both faster (often by orders of magnitude) and more accurate than forward solver-based approaches. The core mathematical idea involves an efficient conversion of the strong form representation of a model to its weak form, and then solving a regression problem to perform parameter inference. The core statistical idea rests on the Errors-In-Variables framework, which necessitates the use of the iteratively reweighted least squares algorithm. Further improvements are obtained by using orthonormal test functions, created from a set of [Formula: see text] bump functions of varying support sizes.We demonstrate the high robustness and computational efficiency by applying WENDy to estimate parameters in some common models from population biology, neuroscience, and biochemistry, including logistic growth, Lotka-Volterra, FitzHugh-Nagumo, Hindmarsh-Rose, and a Protein Transduction Benchmark model. Software and code for reproducing the examples is available at https://github.com/MathBioCU/WENDy .

Direct Estimation of Parameters in ODE Models Using WENDy: Weak-form Estimation of Nonlinear Dynamics.

We introduce the Weak-form Estimation of Nonlinear Dynamics (WENDy) method for estimating model parameters for non-linear systems of ODEs. Without relying on any numerical differential equation solvers, WENDy computes accurate estimates and is robust to large (biologically relevant) levels of measurement noise. For low dimensional systems with modest amounts of data, WENDy is competitive with conventional forward solver-based nonlinear least squares methods in terms of speed and accuracy. For both higher dimensional systems and stiff systems, WENDy is typically both faster (often by orders of magnitude) and more accurate than forward solver-based approaches. The core mathematical idea involves an efficient conversion of the strong form representation of a model to its weak form, and then solving a regression problem to perform parameter inference. The core statistical idea rests on the Errors-In-Variables framework, which necessitates the use of the iteratively reweighted least squares algorithm. Further improvements are obtained by using orthonormal test functions, created from a set of C-infinity bump functions of varying support sizes. We demonstrate the high robustness and computational efficiency by applying WENDy to estimate parameters in some common models from population biology, neuroscience, and biochemistry, including logistic growth, Lotka-Volterra, FitzHugh-Nagumo, Hindmarsh-Rose, and a Protein Transduction Benchmark model. Software and code for reproducing the examples is available at (https://github.com/MathBioCU/WENDy).

Viral transmission and infection prevalence in a cannibalistic host-pathogen system.

Cannibalism, while prevalent in the natural world, is often viewed as detrimental to a cannibal's health, especially when they consume pathogen-infected conspecifics. The argument stems from the idea that cannibalizing infected individuals increases the chance of coming into contact with a pathogen and subsequently becoming infected. Using an insect pest, the fall armyworm (Spodoptera frugiperda), that readily cannibalizes at the larval stage and its lethal pathogen, we experimentally examined how cannibalism affects viral transmission at both an individual and population level. Prior to death, the pathogen in the system stops the larval host from growing, resulting in infected individuals being smaller than healthy individuals. This leads to size-structured cannibalism of infected individuals with the larger healthy larvae consuming the smaller infected larvae, which is commonly observed. At the individual level, we show that the probability of cannibalism is relatively high for both infected and uninfected individuals especially when the cannibal is larger than the victim. However, the probability of the cannibal becoming infected given that a pathogen-infected individual has been cannibalized is relatively low. On a population level, when cannibalism is allowed to occur transmission rates decline. Additionally, by cannibalizing infected larvae, cannibals lower the infection risk for non-cannibals. Thus, cannibalism can decrease infection prevalence and, therefore, may not be as deleterious as once thought. Under certain circumstances, cannibalizing infected individuals, from the uninfected host's perspective, may even be advantageous, as one obtains a meal and decreases competition for resources with little chance of becoming infected.

Can Eco-Evo Theory Explain Population Cycles in the Field?

AbstractEfforts to explain animal population cycles often invoke consumer-resource theory, which has shown that consumer-resource interactions alone can drive population cycles. Eco-evo theory instead argues that population cycles are partly driven by fluctuating selection for resistance in the resource, but support for eco-evo theory has come almost entirely from laboratory microcosms. Here we ask, Can eco-evo theory explain population cycles in the field? We compared the ability of eco-evo models and classical "eco-only" models to explain data on cycles in the insect Lymantria dispar, in which outbreaks of the insect are terminated by a fatal baculovirus. We carried out a statistical comparison of the ability of eco-only and eco-evo models to explain combined data from L. dispar outbreak cycles and baculovirus epizootics (epidemics in animals). Both models require high host variation in resistance to explain the epizootic data, but high host variation in the eco-evo model leads to consistently accurate predictions of outbreak cycles, whereas in the presence of high host variation the eco-only model can explain outbreak cycles only by invoking high levels of stochasticity, which leads to highly variable and often inaccurate predictions of outbreak cycles. Our work provides statistically robust evidence that eco-evo models can explain population cycles in the field.

A note on species richness and the variance of epidemic severity.

The commonly observed negative correlation between the number of species in an ecological community and disease risk, typically referred to as "the dilution effect", has received a substantial amount of attention over the past decade. Attempts to test this relationship experimentally have revealed that, in addition to the mean disease risk decreasing with species number, so too does the variance of disease risk. This is referred to as the "variance reduction effect", and has received relatively little attention in the disease-diversity literature. Here, we set out to clarify and quantify some of these relationships in an idealized model of a randomly assembled multi-species community undergoing an epidemic. We specifically investigate the variance of the community disease reproductive ratio, a multi-species extension of the basic reproductive ratio [Formula: see text], for a family of random-parameter community SIR models, and show how the variance of community [Formula: see text] varies depending on whether transmission is density or frequency-dependent. We finally outline areas of further research on how changes in variance affect transmission dynamics in other systems.

An Empirical Test of the Role of Small-Scale Transmission in Large-Scale Disease Dynamics.

A key assumption of epidemiological models is that population-scale disease spread is driven by close contact between hosts and pathogens. At larger scales, however, mechanisms such as spatial structure in host and pathogen populations and environmental heterogeneity could alter disease spread. The assumption that small-scale transmission mechanisms are sufficient to explain large-scale infection rates, however, is rarely tested. Here, we provide a rigorous test using an insect-baculovirus system. We fit a mathematical model to data from forest-wide epizootics while constraining the model parameters with data from branch-scale experiments, a difference in spatial scale of four orders of magnitude. This experimentally constrained model fits the epizootic data well, supporting the role of small-scale transmission, but variability is high. We then compare this model's performance to an unconstrained model that ignores the experimental data, which serves as a proxy for models with additional mechanisms. The unconstrained model has a superior fit, revealing a higher transmission rate across forests compared with branch-scale estimates. Our study suggests that small-scale transmission is insufficient to explain baculovirus epizootics. Further research is needed to identify the mechanisms that contribute to disease spread across large spatial scales, and synthesizing models and multiscale data are key to understanding these dynamics.

Stochasticity and Infectious Disease Dynamics: Density and Weather Effects on a Fungal Insect Pathogen.

In deterministic models of epidemics, there is a host abundance threshold above which the introduction of a few infected individuals leads to a severe epidemic. Studies of weather-driven animal pathogens often assume that abundance thresholds will be overwhelmed by weather-driven stochasticity, but tests of this assumption are lacking. We collected observational and experimental data for a fungal pathogen, Entomophaga maimaiga, that infects the gypsy moth, Lymantria dispar. We used an advanced statistical-computing algorithm to fit mechanistic models to our data, such that different models made different assumptions about the effects of host density and weather on E. maimaiga epizootics (epidemics in animals). We then used Akaike information criterion analysis to choose the best model. In the best model, epizootics are driven by a combination of weather and host density, and the model does an excellent job of explaining the data, whereas models that allow only for weather effects or only for density-dependent effects do a poor job of explaining the data. Density-dependent transmission in our best model produces a host density threshold, but this threshold is strongly blurred by the stochastic effects of weather. Our work shows that host-abundance thresholds may be important even if weather strongly affects transmission, suggesting that epidemiological models that allow for weather have an important role to play in understanding animal pathogens. The success of our model means that it could be useful for managing the gypsy moth, an important pest of hardwood forests in North America.

Tracking U.S. Pertussis Incidence: Correlation of Public Health Surveillance and Google Search Data Varies by State.

The Morbidity and Mortality Weekly Reports of the U.S. Centers for Disease Control and Prevention document a raw proxy for counts of pertussis cases in the U.S., and the Project Tycho (PT) database provides an improved source of these weekly data. These data are limited because of reporting delays, variation in state-level surveillance practices, and changes over time in diagnosis methods. We aim to assess whether Google Trends (GT) search data track pertussis incidence relative to PT data and if sociodemographic characteristics explain some variation in the accuracy of state-level models. GT and PT data were used to construct auto-correlation corrected linear models for pertussis incidence in 2004-2011 for the entire U.S. and each individual state. The national model resulted in a moderate correlation (adjusted R2 = 0.2369, p < 0.05), and state models tracked PT data for some but not all states. Sociodemographic variables explained approximately 30% of the variation in performance of individual state-level models. The significant correlation between GT models and public health data suggests that GT is a potentially useful pertussis surveillance tool. However, the variable accuracy of this tool by state suggests GT surveillance cannot be applied in a uniform manner across geographic sub-regions.

Recurring infection with ecologically distinct HPV types can explain high prevalence and diversity.

The high prevalence of human papillomavirus (HPV), the most common sexually transmitted infection, arises from the coexistence of over 200 genetically distinct types. Accurately predicting the impact of vaccines that target multiple types requires understanding the factors that determine HPV diversity. The diversity of many pathogens is driven by type-specific or "homologous" immunity, which promotes the spread of variants to which hosts have little immunity. To test for homologous immunity and to identify mechanisms determining HPV transmission, we fitted nonlinear mechanistic models to longitudinal data on genital infections in unvaccinated men. Our results provide no evidence for homologous immunity, instead showing that infection with one HPV type strongly increases the risk of infection with that type for years afterward. For HPV16, the type responsible for most HPV-related cancers, an initial infection increases the 1-year probability of reinfection by 20-fold, and the probability of reinfection remains 14-fold higher 2 years later. This increased risk occurs in both sexually active and celibate men, suggesting that it arises from autoinoculation, episodic reactivation of latent virus, or both. Overall, our results suggest that high HPV prevalence and diversity can be explained by a combination of a lack of homologous immunity, frequent reinfections, weak competition between types, and variation in type fitness between host subpopulations. Because of the high risk of reinfection, vaccinating boys who have not yet been exposed may be crucial to reduce prevalence, but our results suggest that there may also be large benefits to vaccinating previously infected individuals.

Eco-Evolutionary Theory and Insect Outbreaks.

Eco-evolutionary theory argues that population cycles in consumer-resource interactions are partly driven by natural selection, such that changes in densities and changes in trait values are mutually reinforcing. Evidence that the theory explains cycles in nature, however, is almost nonexistent. Experimental tests of model assumptions are logistically impractical for most organisms, while for others, evidence that population cycles occur in nature is lacking. For insect baculoviruses in contrast, tests of model assumptions are straightforward, and there is strong evidence that baculoviruses help drive population cycles in many insects, including the gypsy moth that we study here. We therefore used field experiments with the gypsy moth baculovirus to test two key assumptions of eco-evolutionary models of host-pathogen population cycles: that reduced host infection risk is heritable and that it is costly. Our experiments confirm both assumptions, and inserting parameters estimated from our data into eco-evolutionary insect-outbreak models gives cycles closely resembling gypsy moth outbreak cycles in North America, whereas standard models predict unrealistic stable equilibria. Our work shows that eco-evolutionary models are useful for explaining outbreaks of forest insect defoliators, while widespread observations of intense selection on defoliators in nature and of heritable and costly resistance in defoliators in the lab together suggest that eco-evolutionary dynamics may play a general role in defoliator outbreaks.

Flexible modeling of the hazard rate and treatment effects in long-term survival studies.

The effects of predictors on time to failure may be difficult to assess in cancer studies with longer follow-up, as the commonly used assumption of proportionality of hazards holding over an extended period is often questionable. Motivated by a long-term prostate cancer clinical trial, we contrast and compare four powerful methods for estimation of the hazard rate. These four methods allow for varying degrees of smoothness as well as covariates with effects that vary over time. We pay particular attention to an extended multiresolution hazard estimator, which is a flexible, semi-parametric, Bayesian method for joint estimation of predictor effects and the hazard rate. We compare the results of the extended multiresolution hazard model to three other commonly used, comparable models: Aalen's additive model, Kooperberg's hazard regression model, and an extended Cox model. Through simulations and the analysis of a large-scale randomized prostate cancer clinical trial, we use the different methods to examine patterns of biochemical failure and to estimate the time-varying effects of androgen deprivation therapy treatment and other covariates.

Effects of host heterogeneity on pathogen diversity and evolution.

Phenotypic variation is common in most pathogens, yet the mechanisms that maintain this diversity are still poorly understood. We asked whether continuous host variation in susceptibility helps maintain phenotypic variation, using experiments conducted with a baculovirus that infects gypsy moth (Lymantria dispar) larvae. We found that an empirically observed tradeoff between mean transmission rate and variation in transmission, which results from host heterogeneity, promotes long-term coexistence of two pathogen types in simulations of a population model. This tradeoff introduces an alternative strategy for the pathogen: a low-transmission, low-variability type can coexist with the high-transmission type favoured by classical non-heterogeneity models. In addition, this tradeoff can help explain the extensive phenotypic variation we observed in field-collected pathogen isolates, in traits affecting virus fitness including transmission and environmental persistence. Similar heterogeneity tradeoffs might be a general mechanism promoting phenotypic variation in any pathogen for which hosts vary continuously in susceptibility.

Research on Emissions, Air quality, Climate, and Cooking Technologies in Northern Ghana (REACCTING): study rationale and protocol.

BACKGROUND: Cooking over open fires using solid fuels is both common practice throughout much of the world and widely recognized to contribute to human health, environmental, and social problems. The public health burden of household air pollution includes an estimated four million premature deaths each year. To be effective and generate useful insight into potential solutions, cookstove intervention studies must select cooking technologies that are appropriate for local socioeconomic conditions and cooking culture, and include interdisciplinary measurement strategies along a continuum of outcomes. METHODS/DESIGN: REACCTING (Research on Emissions, Air quality, Climate, and Cooking Technologies in Northern Ghana) is an ongoing interdisciplinary randomized cookstove intervention study in the Kassena-Nankana District of Northern Ghana. The study tests two types of biomass burning stoves that have the potential to meet local cooking needs and represent different "rungs" in the cookstove technology ladder: a locally-made low-tech rocket stove and the imported, highly efficient Philips gasifier stove. Intervention households were randomized into four different groups, three of which received different combinations of two improved stoves, while the fourth group serves as a control for the duration of the study. Diverse measurements assess different points along the causal chain linking the intervention to final outcomes of interest. We assess stove use and cooking behavior, cooking emissions, household air pollution and personal exposure, health burden, and local to regional air quality. Integrated analysis and modeling will tackle a range of interdisciplinary science questions, including examining ambient exposures among the regional population, assessing how those exposures might change with different technologies and behaviors, and estimating the comparative impact of local behavior and technological changes versus regional climate variability and change on local air quality and health outcomes. DISCUSSION: REACCTING is well-poised to generate useful data on the impact of a cookstove intervention on a wide range of outcomes. By comparing different technologies side by side and employing an interdisciplinary approach to study this issue from multiple perspectives, this study may help to inform future efforts to improve health and quality of life for populations currently relying on open fires for their cooking needs.

Pathogen growth in insect hosts: inferring the importance of different mechanisms using stochastic models and response-time data.

Pathogen population dynamics within individual hosts can alter disease epidemics and pathogen evolution, but our understanding of the mechanisms driving within-host dynamics is weak. Mathematical models have provided useful insights, but existing models have only rarely been subjected to rigorous tests, and their reliability is therefore open to question. Most models assume that initial pathogen population sizes are so large that stochastic effects due to small population sizes, so-called demographic stochasticity, are negligible, but whether this assumption is reasonable is unknown. Most models also assume that the dynamic effects of a host's immune system strongly affect pathogen incubation times or "response times," but whether such effects are important in real host-pathogen interactions is likewise unknown. Here we use data for a baculovirus of the gypsy moth to test models of within-host pathogen growth. By using Bayesian statistical techniques and formal model-selection procedures, we are able to show that the response time of the gypsy moth virus is strongly affected by both demographic stochasticity and a dynamic response of the host immune system. Our results imply that not all response-time variability can be explained by host and pathogen variability, and that immune system responses to infection may have important effects on population-level disease dynamics.

Modeling the transmission of community-associated methicillin-resistant Staphylococcus aureus: a dynamic agent-based simulation.

BACKGROUND: Methicillin-resistant Staphylococcus aureus (MRSA) has been a deadly pathogen in healthcare settings since the 1960s, but MRSA epidemiology changed since 1990 with new genetically distinct strain types circulating among previously healthy people outside healthcare settings. Community-associated (CA) MRSA strains primarily cause skin and soft tissue infections, but may also cause life-threatening invasive infections. First seen in Australia and the U.S., it is a growing problem around the world. The U.S. has had the most widespread CA-MRSA epidemic, with strain type USA300 causing the great majority of infections. Individuals with either asymptomatic colonization or infection may transmit CA-MRSA to others, largely by skin-to-skin contact. Control measures have focused on hospital transmission. Limited public health education has focused on care for skin infections. METHODS: We developed a fine-grained agent-based model for Chicago to identify where to target interventions to reduce CA-MRSA transmission. An agent-based model allows us to represent heterogeneity in population behavior, locations and contact patterns that are highly relevant for CA-MRSA transmission and control. Drawing on nationally representative survey data, the model represents variation in sociodemographics, locations, behaviors, and physical contact patterns. Transmission probabilities are based on a comprehensive literature review. RESULTS: Over multiple 10-year runs with one-hour ticks, our model generates temporal and geographic trends in CA-MRSA incidence similar to Chicago from 2001 to 2010. On average, a majority of transmission events occurred in households, and colonized rather than infected agents were the source of the great majority (over 95%) of transmission events. The key findings are that infected people are not the primary source of spread. Rather, the far greater number of colonized individuals must be targeted to reduce transmission. CONCLUSIONS: Our findings suggest that current paradigms in MRSA control in the United States cannot be very effective in reducing the incidence of CA-MRSA infections. Furthermore, the control measures that have focused on hospitals are unlikely to have much population-wide impact on CA-MRSA rates. New strategies need to be developed, as the incidence of CA-MRSA is likely to continue to grow around the world.

Nonconvulsive seizures in subarachnoid hemorrhage link inflammation and outcome.

OBJECTIVE: Nonconvulsive seizures (NCSz) are frequent following acute brain injury and have been implicated as a cause of secondary brain injury, but mechanisms that cause NCSz are controversial. Proinflammatory states are common after many brain injuries, and inflammation-mediated changes in blood-brain barrier permeability have been experimentally linked to seizures. METHODS: In this prospective observational study of aneurysmal subarachnoid hemorrhage (SAH) patients, we explored the link between the inflammatory response following SAH and in-hospital NCSz studying clinical (systemic inflammatory response syndrome [SIRS]) and laboratory (tumor necrosis factor receptor 1 [TNF-R1], high-sensitivity C-reactive protein [hsCRP]) markers of inflammation. Logistic regression, Cox proportional hazards regression, and mediation analyses were performed to investigate temporal and causal relationships. RESULTS: Among 479 SAH patients, 53 (11%) had in-hospital NCSz. Patients with in-hospital NCSz had a more pronounced SIRS response (odds ratio [OR]=1.9 per point increase in SIRS, 95% confidence interval [CI]=1.3-2.9), inflammatory surges were more likely immediately preceding NCSz onset, and the negative impact of SIRS on functional outcome at 3 months was mediated in part through in-hospital NCSz. In a subset with inflammatory serum biomarkers, we confirmed these findings linking higher serum TNF-R1 and hsCRP to in-hospital NCSz (OR=1.2 per 20-point hsCRP increase, 95% CI=1.1-1.4; OR=2.5 per 100-point TNF-R1 increase, 95% CI=2.1-2.9). The association of inflammatory biomarkers with poor outcome was mediated in part through NCSz. INTERPRETATION: In-hospital NCSz were independently associated with a proinflammatory state following SAH as reflected in clinical symptoms and serum biomarkers of inflammation. Our findings suggest that inflammation following SAH is associated with poor outcome and that this effect is at least in part mediated through in-hospital NCSz.

Survival Analysis with Electronic Health Record Data: Experiments with Chronic Kidney Disease.

This paper presents a detailed survival analysis for chronic kidney disease (CKD). The analysis is based on the EHR data comprising almost two decades of clinical observations collected at New York-Presbyterian, a large hospital in New York City with one of the oldest electronic health records in the United States. Our survival analysis approach centers around Bayesian multiresolution hazard modeling, with an objective to capture the changing hazard of CKD over time, adjusted for patient clinical covariates and kidney-related laboratory tests. Special attention is paid to statistical issues common to all EHR data, such as cohort definition, missing data and censoring, variable selection, and potential for joint survival and longitudinal modeling, all of which are discussed alone and within the EHR CKD context.

Population-level differences in disease transmission: a Bayesian analysis of multiple smallpox epidemics.

Estimates of a disease's basic reproductive rate R0 play a central role in understanding outbreaks and planning intervention strategies. In many calculations of R0, a simplifying assumption is that different host populations have effectively identical transmission rates. This assumption can lead to an underestimate of the overall uncertainty associated with R0, which, due to the non-linearity of epidemic processes, may result in a mis-estimate of epidemic intensity and miscalculated expenditures associated with public-health interventions. In this paper, we utilize a Bayesian method for quantifying the overall uncertainty arising from differences in population-specific basic reproductive rates. Using this method, we fit spatial and non-spatial susceptible-exposed-infected-recovered (SEIR) models to a series of 13 smallpox outbreaks. Five outbreaks occurred in populations that had been previously exposed to smallpox, while the remaining eight occurred in Native-American populations that were naïve to the disease at the time. The Native-American outbreaks were close in a spatial and temporal sense. Using Bayesian Information Criterion (BIC), we show that the best model includes population-specific R0 values. These differences in R0 values may, in part, be due to differences in genetic background, social structure, or food and water availability. As a result of these inter-population differences, the overall uncertainty associated with the "population average" value of smallpox R0 is larger, a finding that can have important consequences for controlling epidemics. In general, Bayesian hierarchical models are able to properly account for the uncertainty associated with multiple epidemics, provide a clearer understanding of variability in epidemic dynamics, and yield a better assessment of the range of potential risks and consequences that decision makers face.

Epidemics of community-associated methicillin-resistant Staphylococcus aureus in the United States: a meta-analysis.

Staphylococcus aureus is the most frequent cause of skin and soft tissue infections in humans. Methicillin-resistant strains of S. aureus (MRSA) that emerged in the 1960s presented a relatively limited public health threat until the 1990s, when novel community-associated (CA-) MRSA strains began circulating. CA-MRSA infections are now common, resulting in serious and sometimes fatal infections in otherwise healthy people. Although some have suggested that there is an epidemic of CA-MRSA in the U.S., the origins, extent, and geographic variability of CA-MRSA infections are not known. We present a meta-analysis of published studies that included trend data from a single site or region, and derive summary epidemic curves of CA-MRSA spread over time. Our analysis reveals a dramatic increase in infections over the past two decades, with CA-MRSA strains now endemic at unprecedented levels in many US regions. This increase has not been geographically homogeneous, and appears to have occurred earlier in children than adults.

Who underreports smoking on birth records: a Monte Carlo predictive model with validation.

BACKGROUND: Research has shown that self-reports of smoking during pregnancy may underestimate true prevalence. However, little is known about which populations have higher rates of underreporting. Availability of more accurate measures of smoking during pregnancy could greatly enhance the usefulness of existing studies on the effects of maternal smoking offspring, especially in those populations where underreporting may lead to underestimation of the impact of smoking during pregnancy. METHODS AND FINDINGS: In this paper, we develop a statistical Monte Carlo model to estimate patterns of underreporting of smoking during pregnancy, and apply it to analyze the smoking self-report data from birth certificates in the state of Massachusetts. Our results illustrate non-uniform patterns of underreporting of smoking during pregnancy among different populations. Estimates of likely underreporting of smoking during pregnancy were highest among mothers who were college-educated, married, aged 30 years or older, employed full-time, and planning to breastfeed. The model's findings are validated and compared to an existing underreporting adjustment approach in the Maternal and Infant Smoking Study of East Boston (MISSEB). CONCLUSIONS: The validation results show that when biological assays are not available, the Monte Carlo method proposed can provide a more accurate estimate of the smoking status during pregnancy than self-reports alone. Such methods hold promise for providing a better assessment of the impact of smoking during pregnancy.