Christopher S. McMahan

Regression models for group testing data with pool dilution effects

Group testing is widely used to reduce the cost of screening individuals for infectious diseases. There is an extensive literature on group testing, most of which traditionally has focused on estimating the probability of infection in a homogeneous population. More recently, this research area has shifted towards estimating individual-specific probabilities in a regression context. However, existing regression approaches have assumed that the sensitivity and specificity of pooled biospecimens are constant and do not depend on the pool sizes. For those applications, where this assumption may not be realistic, these existing approaches can lead to inaccurate inference, especially when pool sizes are large. Our new approach, which exploits the information readily available from underlying continuous biomarker distributions, provides reliable inference in settings where pooling would be most beneficial and does so even for larger pool sizes. We illustrate our methodology using hepatitis B data from a study involving Irish prisoners.

Regression analysis for current status data using the EM algorithm

We propose new expectation-maximization algorithms to analyze current status data under two popular semiparametric regression models: the proportional hazards (PH) model and the proportional odds (PO) model. Monotone splines are used to model the baseline cumulative hazard function in the PH model and the baseline odds function in the PO model. The proposed algorithms are derived by exploiting a data augmentation based on Poisson latent variables. Unlike previous regression work with current status data, our PH and PO model fitting methods are fast, flexible, easy to implement, and provide variance estimates in closed form. These techniques are evaluated using simulation and are illustrated using uterine fibroid data from a prospective cohort study on early pregnancy.

Two-stage hierarchical group testing for multiple infections with application to the infertility prevention project

Screening for sexually transmitted diseases (STDs) has benefited greatly from the use of group testing (pooled testing) to lower costs. With the development of assays that detect multiple infections, screening practices now involve testing pools of individuals for multiple infections simultaneously. Building on the research for single infection group testing procedures, we examine the performance of group testing for multiple infections. Our work is motivated by chlamydia and gonorrhea testing for the infertility prevention project (IPP), a national program in the United States. We consider a two-stage pooling algorithm currently used to perform testing for the IPP. We first derive the operating characteristics of this algorithm for classification purposes (e.g., expected number of tests, misclassification probabilities, etc.) and identify pool sizes that minimize the expected number of tests. We then develop an expectation-maximization (EM) algorithm to estimate probabilities of infection using both group and individual retest responses. Our research shows that group testing can offer large cost savings when classifying individuals for multiple infections and can provide prevalence estimates that are actually more efficient than those from individual testing.

A flexible, computationally efficient method for fitting the proportional hazards model to interval-censored data

The proportional hazards model (PH) is currently the most popular regression model for analyzing time-to-event data. Despite its popularity, the analysis of interval-censored data under the PH model can be challenging using many available techniques. This article presents a new method for analyzing interval-censored data under the PH model. The proposed approach uses a monotone spline representation to approximate the unknown nondecreasing cumulative baseline hazard function. Formulating the PH model in this fashion results in a finite number of parameters to estimate while maintaining substantial modeling flexibility. A novel expectation-maximization (EM) algorithm is developed for finding the maximum likelihood estimates of the parameters. The derivation of the EM algorithm relies on a two-stage data augmentation involving latent Poisson random variables. The resulting algorithm is easy to implement, robust to initialization, enjoys quick convergence, and provides closed-form variance estimates. The performance of the proposed regression methodology is evaluated through a simulation study, and is further illustrated using data from a large population-based randomized trial designed and sponsored by the United States National Cancer Institute.

Regression analysis of bivariate current status data under the Gamma-frailty proportional hazards model using the EM algorithm

The Gamma-frailty proportional hazards (PH) model is commonly used to analyze correlated survival data. Despite this models popularity, the analysis of correlated current status data under the Gamma-frailty PH model can prove to be challenging using traditional techniques. Consequently, in this paper we develop a novel expectation-maximization (EM) algorithm under the Gamma-frailty PH model to study bivariate current status data. Our method uses a monotone spline representation to approximate the unknown conditional cumulative baseline hazard functions. Proceeding in this fashion leads to the estimation of a finite number of parameters while simultaneously allowing for modeling flexibility. The derivation of the proposed EM algorithm relies on a three-stage data augmentation involving Poisson latent variables. The resulting algorithm is easy to implement, robust to initialization, and enjoys quick convergence. Simulation results suggest that the proposed method works well and is robust to the misspecification of the frailty distribution. Our methodology is used to analyze chlamydia and gonorrhea data collected by the Nebraska Public Health Laboratory as a part of the Infertility Prevention Project.

Forecasting United States heartworm Dirofilaria immitis prevalence in dogs

BackgroundThis paper forecasts next year’s canine heartworm prevalence in the United States from 16 climate, geographic and societal factors. The forecast’s construction and an assessment of its performance are described.MethodsThe forecast is based on a spatial-temporal conditional autoregressive model fitted to over 31 million antigen heartworm tests conducted in the 48 contiguous United States during 2011–2015. The forecast uses county-level data on 16 predictive factors, including temperature, precipitation, median household income, local forest and surface water coverage, and presence/absence of eight mosquito species. Non-static factors are extrapolated into the forthcoming year with various statistical methods. The fitted model and factor extrapolations are used to estimate next year’s regional prevalence.ResultsThe correlation between the observed and model-estimated county-by-county heartworm prevalence for the 5-year period 2011–2015 is 0.727, demonstrating reasonable model accuracy. The correlation between 2015 observed and forecasted county-by-county heartworm prevalence is 0.940, demonstrating significant skill and showing that heartworm prevalence can be forecasted reasonably accurately.ConclusionsThe forecast presented herein can a priori alert veterinarians to areas expected to see higher than normal heartworm activity. The proposed methods may prove useful for forecasting other diseases.

Factors associated with Anaplasma spp. seroprevalence among dogs in the United States

BackgroundDogs in the United States are hosts to a diverse range of ticks and tick-borne pathogens, including A. phagocytophilum, an important emerging canine and human pathogen. Previously, a Companion Animal Parasite Council (CAPC)-sponsored workshop proposed factors purported to be associated with the infection risk for tick-transmitted pathogens in dogs in the United States, including climate conditions, socioeconomic characteristics, local topography, and vector distribution.MethodsApproximately four million test results from routine veterinary diagnostic tests from 2011–2013, which were collected on a county level across the contiguous United States, are statistically analyzed with the proposed factors via logistic regression and generalized estimating equations. Spatial prevalence maps of baseline Anaplasma spp. prevalence are constructed from Kriging and head-banging smoothing methods.ResultsAll of the examined factors, with the exception of surface water coverage, were significantly associated with Anaplasma spp. prevalence. Overall, Anaplasma spp. prevalence increases with increasing precipitation and forestation coverage and decreases with increasing temperature, population density, relative humidity, and elevation. Interestingly, socioeconomic status and deer/vehicle collisions were positively and negatively correlated with canine Anaplasma seroprevalence, respectively. A spatial map of the canine Anaplasma hazard is an auxiliary product of the analysis. Anaplasma spp. prevalence is highest in New England and the Upper Midwest.ConclusionsThe results from the two posited statistical models (one that contains an endemic areas assumption and one that does not) are in general agreement, with the major difference being that the endemic areas model estimates a larger prevalence in Western Texas, New Mexico, and Colorado. As A. phagocytophilum is zoonotic, the results of this analysis could also help predict areas of high risk for human exposure to this pathogen.

Variable Infection Dynamics in Four Peromyscus Species Following Experimental Inoculation with Baylisascaris procyonis

Abstract Wild rodents such as Peromyscus spp. are intermediate hosts for the zoonotic ascarid Baylisascaris procyonis (raccoon roundworm), and previous studies indicate Peromyscus leucopus (white-footed mouse) likely serves an important role in parasite ecology. Natural infections have been sporadically identified in a few Peromyscus spp., but no data are available on differences in susceptibility among the many other species. We compared survival and infection dynamics of B. procyonis in 4 species (P. leucopus, Peromyscus maniculatus [deer mouse], Peromyscus californicus [California mouse], Peromyscus polionotus [Oldfield mouse]) from regions of varying habitat types as well as B. procyonis prevalence in raccoons. Six captive-bred mice of each species were inoculated per os with 1 of 3 biologically-relevant doses of embryonated B. procyonis eggs (∼10, ∼50, or ∼500). Animals were monitored twice daily for clinical signs and behavioral abnormalities and were euthanized at the onset of neurological signs or extensive (≥20%) weight loss, or at 45 days post-infection if no disease developed. Larvae were counted in the brain via microscopic examination and in skeletal muscle and visceral organs via artificial digestion. In the high-dose group, all but 1 mouse developed severe neurologic disease and were euthanized. In the medium-dose group, survival was variable and ranged from 33–85% across species. Little to no disease was observed in the low-dose group, although 1 P. maniculatus developed disease and was euthanized. Survival analysis reveals P. leucopus had a longer time until clinical disease onset versus the other species, which did not differ significantly from each other. Interestingly, larval recovery relative to dose was nearly identical across species and doses; however, larvae were differentially distributed in skeletal muscle, visceral organs, and brain among species. These data indicate that P. leucopus may be more resilient toward severe baylisascariasis compared to the other species and that even closely-related rodents may experience differential mortality. This variation in tolerance may have ecological implications for the different species as B. procyonis intermediate hosts, although more work is needed to put these experimental findings into context.

A general regression framework for group testing data, which incorporates pool dilution effects

Group testing, through the use of pooling, has been widely implemented as a more efficient means to screen individuals for infectious diseases. Typically, in these settings, practitioners are tasked with the complimentary goals of both case identification and estimation. For these purposes, many group testing strategies have been proposed, which address issues such as preserving anonymity in estimation studies, quality control, and classification. In general, these strategies require that a significant number of the individuals be retested, either in pools or individually. In order to provide practitioners with a general methodology that can be used to accurately and precisely analyze data of this form, herein, we propose a binary regression framework that can incorporate data arising from any group testing strategy. Further, we relax previously made assumptions regarding testing error rates by relating the diagnostic testing results to the latent biological marker levels of the individuals being tested. We investigate the finite sample performance of our proposed methodology through simulation and by applying our techniques to hepatitis B data collected as part of a study involving Irish prisoners.

A Bayesian spatio-temporal model for forecasting the prevalence of antibodies to Ehrlichia species in domestic dogs within the contiguous United States

BackgroundDogs in the United States are hosts to a diverse range of vector-borne pathogens, several of which are important zoonoses. This paper describes factors deemed to be significantly related to the prevalence of antibodies to Ehrlichia spp. in domestic dogs, including climatic conditions, geographical factors, and societal factors. These factors are used in concert with a spatio-temporal model to construct an annual seroprevalence forecast. The proposed method of forecasting and an assessment of its fidelity are described.MethodsApproximately twelve million serological test results for canine exposure to Ehrlichia spp. were used in the development of a Bayesian approach to forecast canine infection. Data used were collected on the county level across the contiguous United States from routine veterinary diagnostic tests between 2011–2015. Maps depicting the spatial baseline Ehrlichia spp. prevalence were constructed using Kriging and head-banging smoothing methods. Data were statistically analyzed to identify factors related to antibody prevalence via a Bayesian spatio-temporal conditional autoregressive (CAR) model. Finally, a forecast of future Ehrlichia seroprevalence was constructed based on the proposed model using county-level data on five predictive factors identified at a workshop hosted by the Companion Animal Parasite Council and published in 2014: annual temperature, percentage forest coverage, percentage surface water coverage, population density and median household income. Data were statistically analyzed to identify factors related to disease prevalence via a Bayesian spatio-temporal model. The fitted model and factor extrapolations were then used to forecast the regional seroprevalence for 2016.ResultsThe correlation between the observed and model-estimated county-by-county Ehrlichia seroprevalence for the five-year period 2011–2015 is 0.842, demonstrating reasonable model accuracy. The weighted correlation (acknowledging unequal sample sizes) between 2015 observed and forecasted county-by-county Ehrlichia seroprevalence is 0.970, demonstrating that Ehrlichia seroprevalence can be forecasted accurately.ConclusionsThe forecast presented herein can be an a priori alert to veterinarians regarding areas expected to see expansion of Ehrlichia beyond the accepted endemic range, or in some regions a dynamic change from historical average prevalence. Moreover, this forecast could potentially serve as a surveillance tool for human health and prove useful for forecasting other vector-borne diseases.