Forrest W. Crawford

Unifying the spatial epidemiology and molecular evolution of emerging epidemics

We introduce a conceptual bridge between the previously unlinked fields of phylogenetics and mathematical spatial ecology, which enables the spatial parameters of an emerging epidemic to be directly estimated from sampled pathogen genome sequences. By using phylogenetic history to correct for spatial autocorrelation, we illustrate how a fundamental spatial variable, the diffusion coefficient, can be estimated using robust nonparametric statistics, and how heterogeneity in dispersal can be readily quantified. We apply this framework to the spread of the West Nile virus across North America, an important recent instance of spatial invasion by an emerging infectious disease. We demonstrate that the dispersal of West Nile virus is greater and far more variable than previously measured, such that its dissemination was critically determined by rare, long-range movements that are unlikely to be discerned during field observations. Our results indicate that, by ignoring this heterogeneity, previous models of the epidemic have substantially overestimated its basic reproductive number. More generally, our approach demonstrates that easily obtainable genetic data can be used to measure the spatial dynamics of natural populations that are otherwise difficult or costly to quantify.

The burden of typhoid fever in low- and middle-income countries: A meta-regression approach

Background Upcoming vaccination efforts against typhoid fever require an assessment of the baseline burden of disease in countries at risk. There are no typhoid incidence data from most low- and middle-income countries (LMICs), so model-based estimates offer insights for decision-makers in the absence of readily available data. Methods We developed a mixed-effects model fit to data from 32 population-based studies of typhoid incidence in 22 locations in 14 countries. We tested the contribution of economic and environmental indices for predicting typhoid incidence using a stochastic search variable selection algorithm. We performed out-of-sample validation to assess the predictive performance of the model. Results We estimated that 17.8 million cases of typhoid fever occur each year in LMICs (95% credible interval: 6.9–48.4 million). Central Africa was predicted to experience the highest incidence of typhoid, followed by select countries in Central, South, and Southeast Asia. Incidence typically peaked in the 2–4 year old age group. Models incorporating widely available economic and environmental indicators were found to describe incidence better than null models. Conclusions Recent estimates of typhoid burden may under-estimate the number of cases and magnitude of uncertainty in typhoid incidence. Our analysis permits prediction of overall as well as age-specific incidence of typhoid fever in LMICs, and incorporates uncertainty around the model structure and estimates of the predictors. Future studies are needed to further validate and refine model predictions and better understand year-to-year variation in cases.

Estimation for general birth-death processes

Birth-death processes (BDPs) are continuous-time Markov chains that track the number of “particles” in a system over time. While widely used in population biology, genetics, and ecology, statistical inference of the instantaneous particle birth and death rates remains largely limited to restrictive linear BDPs in which per-particle birth and death rates are constant. Researchers often observe the number of particles at discrete times, necessitating data augmentation procedures such as expectation-maximization (EM) to find maximum likelihood estimates (MLEs). For BDPs on finite state-spaces, there are powerful matrix methods for computing the conditional expectations needed for the E-step of the EM algorithm. For BDPs on infinite state-spaces, closed-form solutions for the E-step are available for some linear models, but most previous work has resorted to time-consuming simulation. Remarkably, we show that the E-step conditional expectations can be expressed as convolutions of computable transition probabilities for any general BDP with arbitrary rates. This important observation, along with a convenient continued fraction representation of the Laplace transforms of the transition probabilities, allows for novel and efficient computation of the conditional expectations for all BDPs, eliminating the need for truncation of the state-space or costly simulation. We use this insight to derive EM algorithms that yield maximum likelihood estimation for general BDPs characterized by various rate models, including generalized linear models (GLM). We show that our Laplace convolution technique outperforms competing methods when they are available and demonstrate a technique to accelerate EM algorithm convergence. We validate our approach using synthetic data and then apply our methods to cancer cell growth and estimation of mutation parameters in microsatellite evolution.

Did Large-Scale Vaccination Drive Changes in the Circulating Rotavirus Population in Belgium?

Vaccination can place selective pressures on viral populations, leading to changes in the distribution of strains as viruses evolve to escape immunity from the vaccine. Vaccine-driven strain replacement is a major concern after nationwide rotavirus vaccine introductions. However, the distribution of the predominant rotavirus genotypes varies from year to year in the absence of vaccination, making it difficult to determine what changes can be attributed to the vaccines. To gain insight in the underlying dynamics driving changes in the rotavirus population, we fitted a hierarchy of mathematical models to national and local genotype-specific hospitalization data from Belgium, where large-scale vaccination was introduced in 2006. We estimated that natural- and vaccine-derived immunity was strongest against completely homotypic strains and weakest against fully heterotypic strains, with an intermediate immunity amongst partially heterotypic strains. The predominance of G2P[4] infections in Belgium after vaccine introduction can be explained by a combination of natural genotype fluctuations and weaker natural and vaccine-induced immunity against infection with strains heterotypic to the vaccine, in the absence of significant variation in strain-specific vaccine effectiveness against disease. However, the incidence of rotavirus gastroenteritis is predicted to remain low despite vaccine-driven changes in the distribution of genotypes.

Relationship between choline and apparent diffusion coefficient in patients with gliomas

To examine the relationship between apparent diffusion coefficients (ADC) from diffusion weighted imaging (DWI) and choline levels from proton magnetic resonance spectroscopic imaging (MRSI) in newly diagnosed Grade II and IV gliomas within distinct anatomic regions.

The Graphical Structure of Respondent-driven Sampling

Respondent-driven sampling (RDS) is a chain-referral method for sampling members of hidden or hard-to-reach populations, such as sex workers, homeless people, or drug users, via their social networks. Most methodological work on RDS has focused on inference of population means under the assumption that subjects’ network degree determines their probability of being sampled. Criticism of existing estimators is usually focused on missing data: the underlying network is only partially observed, so it is difficult to determine correct sampling probabilities. In this article, the author shows that data collected in ordinary RDS studies contain information about the structure of the respondents’ social network. The author constructs a continuous-time model of RDS recruitment that incorporates the time series of recruitment events, the pattern of coupon use, and the network degrees of sampled subjects. Together, the observed data and the recruitment model place a well-defined probability distribution on the recruitment-induced subgraph of respondents. The author shows that this distribution can be interpreted as an exponential random graph model and develops a computationally efficient method for estimating the hidden graph. The author validates the method using simulated data and applies the technique to an RDS study of injection drug users in St. Petersburg, Russia.

Combining List Experiment and Direct Question Estimates of Sensitive Behavior Prevalence

Survey respondents may give untruthful answers to sensitive questions when asked directly. In recent years, researchers have turned to the list experiment (also known as the item count technique) to overcome this difficulty. While list experiments are arguably less prone to bias than direct questioning, list experiments are also more susceptible to sampling variability. We show that researchers need not abandon direct questioning altogether in order to gain the advantages of list experimentation. We develop a nonparametric estimator of the prevalence of sensitive behaviors that combines list experimentation and direct questioning. We prove that this estimator is asymptotically more efficient than the standard difference-in-means estimator, and we provide a basis for inference using Wald-type confidence intervals. Additionally, leveraging information from the direct questioning, we derive two nonparametric placebo tests for assessing identifying assumptions underlying list experiments. We demonstrate the effectiveness of our combined estimator and placebo tests with an original survey experiment.

Diversity, Disparity, and Evolutionary Rate Estimation for Unresolved Yule Trees

The branching structure of biological evolution confers statistical dependencies on phenotypic trait values in related organisms. For this reason, comparative macroevolutionary studies usually begin with an inferred phylogeny that describes the evolutionary relationships of the organisms of interest. The probability of the observed trait data can be computed by assuming a model for trait evolution, such as Brownian motion, over the branches of this fixed tree. However, the phylogenetic tree itself contributes statistical uncertainty to estimates of rates of phenotypic evolution, and many comparative evolutionary biologists regard the tree as a nuisance parameter. In this article, we present a framework for analytically integrating over unknown phylogenetic trees in comparative evolutionary studies by assuming that the tree arises from a continuous-time Markov branching model called the Yule process. To do this, we derive a closed-form expression for the distribution of phylogenetic diversity (PD), which is the sum of branch lengths connecting the species in a clade. We then present a generalization of PD which is equivalent to the expected trait disparity in a set of taxa whose evolutionary relationships are generated by a Yule process and whose traits evolve by Brownian motion. We find expressions for the distribution of expected trait disparity under a Yule tree. Given one or more observations of trait disparity in a clade, we perform fast likelihood-based estimation of the Brownian variance for unresolved clades. Our method does not require simulation or a fixed phylogenetic tree. We conclude with a brief example illustrating Brownian rate estimation for 12 families in the mammalian order Carnivora, in which the phylogenetic tree for each family is unresolved.

The Burden of Stigma on Health and Well-Being: A Taxonomy of Concealment, Course, Disruptiveness, Aesthetics, Origin, and Peril Across 93 Stigmas:

Most individuals are stigmatized at some point. However, research often examines stigmas separately, thus underestimating the overall impact of stigma and precluding comparisons across stigmatized identities and conditions. In their classic text, Social Stigma: The Psychology of Marked Relationships, Edward Jones and colleagues laid the groundwork for unifying the study of different stigmas by considering the shared dimensional features of stigmas: aesthetics, concealability, course, disruptiveness, origin, peril. Despite the prominence of this framework, no study has documented the extent to which stigmas differ along these dimensions, and the implications of this variation for health and well-being. We reinvigorated this framework to spur a comprehensive account of stigma’s impact by classifying 93 stigmas along these dimensions. With the input of expert and general public raters, we then located these stigmas in a six-dimensional space and created discrete clusters organized around these dimensions. Next, we linked this taxonomy to health and stigma-related mechanisms. This quantitative taxonomy offers parsimonious insights into the relationship among the numerous qualities of numerous stigmas and health.

Historical Biogeography Using Species Geographical Ranges

Spatial variation in biodiversity is the result of complex interactions between evolutionary history and ecological factors. Methods in historical biogeography combine phylogenetic information with current species locations to infer the evolutionary history of a clade through space and time. A major limitation of most methods for historical biogeographic inference is the requirement of single locations for terminal lineages, reducing contemporary species geographical ranges to a point in two-dimensional space. In reality, geographic ranges usually show complex geographic patterns, irregular shapes, or discontinuities. In this article, we describe a method for phylogeographic analysis using polygonal species geographic ranges of arbitrary complexity. By integrating the geographic diversification process across species ranges, we provide a method to infer the geographic location of ancestors in a Bayesian framework. By modeling migration conditioned on a phylogenetic tree, this approach permits reconstructing the geographic location of ancestors through time. We apply this new method to the diversification of two neotropical bird genera, Trumpeters (Psophia) and Cinclodes ovenbirds. We demonstrate the usefulness of our method (called rase) in phylogeographic reconstruction of species ancestral locations and contrast our results with previous methods that compel researchers to reduce the distribution of species to one point in space. We discuss model extensions to enable a more general, spatially explicit framework for historical biogeographic analysis.