Subhash R. Lele

The Association Between Extreme Precipitation and Waterborne Disease Outbreaks in the United States, 1948–1994

OBJECTIVES Rainfall and runoff have been implicated in site-specific waterborne disease outbreaks. Because upward trends in heavy precipitation in the United States are projected to increase with climate change, this study sought to quantify the relationship between precipitation and disease outbreaks. METHODS The US Environmental Protection Agency waterborne disease database, totaling 548 reported outbreaks from 1948 through 1994, and precipitation data of the National Climatic Data Center were used to analyze the relationship between precipitation and waterborne diseases. Analyses were at the watershed level, stratified by groundwater and surface water contamination and controlled for effects due to season and hydrologic region. A Monte Carlo version of the Fisher exact test was used to test for statistical significance. RESULTS Fifty-one percent of waterborne disease outbreaks were preceded by precipitation events above the 90th percentile (P = .002), and 68% by events above the 80th percentile (P = .001). Outbreaks due to surface water contamination showed the strongest association with extreme precipitation during the month of the outbreak; a 2-month lag applied to groundwater contamination events. CONCLUSIONS The statistically significant association found between rainfall and disease in the United States is important for water managers, public health officials, and risk assessors of future climate change.

Declining Wild Salmon Populations in Relation to Parasites from Farm Salmon

Rather than benefiting wild fish, industrial aquaculture may contribute to declines in ocean fisheries and ecosystems. Farm salmon are commonly infected with salmon lice (Lepeophtheirus salmonis), which are native ectoparasitic copepods. We show that recurrent louse infestations of wild juvenile pink salmon (Oncorhynchus gorbuscha), all associated with salmon farms, have depressed wild pink salmon populations and placed them on a trajectory toward rapid local extinction. The louse-induced mortality of pink salmon is commonly over 80% and exceeds previous fishing mortality. If outbreaks continue, then local extinction is certain, and a 99% collapse in pink salmon population abundance is expected in four salmon generations. These results suggest that salmon farms can cause parasite outbreaks that erode the capacity of a coastal ecosystem to support wild salmon populations.

ESTIMATING DENSITY DEPENDENCE, PROCESS NOISE, AND OBSERVATION ERROR

We describe a discrete-time, stochastic population model with density depend ence, environmental-type process noise, and lognormal observation or sampling error. The model, a stochastic version of the Gompertz model, can be transformed into a linear Gaussian state-space model (Kaiman filter) for convenient fitting to time series data. The model has a multivariate normal likelihood function and is simple enough for a variety of uses ranging from theoretical study of parameter estimation issues to routine data analyses in population monitoring. A special case of the model is the discrete-time, stochastic exponential growth model (density independence) with environmental-type process error and lognormal observation error. We describe two methods for estimating parameters in the Gompertz state-space model, and we compare the statistical qualities of the methods with computer simulations. The methods are maximum likelihood based on observations and restricted maximum likelihood based on first differences. Both offer adequate statistical properties. Because the likelihood function is identical to a repeated-measures analysis of variance model with a random time effect, parameter estimates can be calculated using PROC MIXED of SAS. We use the model to analyze a data set from the Breeding Bird Survey. The fitted model suggests that over 70% of the noise in the populations growth rate is due to observation error. The model describes the autocovariance properties of the data especially well. While observation error and process noise variance parameters can both be estimated from one time series, multimodal likelihood functions can and do occur. For data arising from the model, the statistically consistent parameter estimates do not necessarily correspond to the global maximum in the likelihood function. Maximization, simulation, and bootstrapping programs must accommodate the phenomenon of multimodal likelihood functions to produce statistically valid results.

A Composite Likelihood Approach to Binary Spatial Data

Abstract Conventional geostatistics addresses the problem of estimation and prediction for continuous observations. But in many practical applications in public health, environmental remediation, or ecological research the most commonly available data are in the form of counts (e.g., number of cases) or indicator variables denoting above or below threshold values. Also, in many situations it is less expensive to obtain an imprecise categorical observation than to obtain precise measurements of the variable of interest (such as a contaminant). This article proposes a computationally simple method for estimation and prediction using binary or indicator data in space. The proposed method is based on pairwise likelihood contributions, and the large-sample properties of the estimators are obtained in a straightforward manner. We illustrate the methodology through application to indicator data related to gypsy moth defoliation in Massachusetts.

Euclidean Distance Matrix Analysis (EDMA): Estimation of mean form and mean form difference

Euclidean Distance Matrix Analysis (EDMA) of form is a coordinate free approach to the analysis of form using landmark data. In this paper, the problem of estimation of mean form, variance-covariance matrix, and mean form difference under the Gaussian perturbation model is considered using EDMA. The suggested estimators are based on the method of moments. They are shown to be consistent, that is as the sample size increases these estimators approach the true parameters. They are also shown to be computationally very simple. A method to improve their efficiency is suggested. Estimation in the presence of missing data is studied. In addition, it is shown that the superimposition method of estimation leads to incorrect mean form and variance-covariance structure.

Weighted distributions and estimation of resource selection probability functions.

Understanding how organisms selectively use resources is essential for designing wildlife management strategies. The probability that an individual uses a given resource, as characterized by environmental factors, can be quantified in terms of the resource selection probability function (RSPF). The present literature on the topic has claimed that, except when both used and unused sites are known, the RSPF is non-estimable and that only a function proportional to RSPF, namely, the resource selection function (RSF) can be estimated. This paper describes a close connection between the estimation of the RSPF and the estimation of the weight function in the theory of weighted distributions. This connection can be used to obtain fully efficient, maximum likelihood estimators of the resource selection probability function under commonly used survey designs in wildlife management. The method is illustrated using GPS collar data for mountain goats (Oreamnos americanus de Blainville 1816) in northwest British Columbia, Canada.

Predicting key malaria transmission factors, biting and entomological inoculation rates, using modelled soil moisture in Kenya

While malaria transmission varies seasonally, large inter‐annual heterogeneity of malaria incidence occurs. Variability in entomological parameters, biting rates and entomological inoculation rates (EIR) have been strongly associated with attack rates in children. The goal of this study was to assess the weathers impact on weekly biting and EIR in the endemic area of Kisian, Kenya. Entomological data collected by the U.S. Army from March 1986 through June 1988 at Kisian, Kenya was analysed with concurrent weather data from nearby Kisumu airport. A soil moisture model of surface‐water availability was used to combine multiple weather parameters with landcover and soil features to improve disease prediction. Modelling soil moisture substantially improved prediction of biting rates compared to rainfall; soil moisture lagged two weeks explained up to 45% of An. gambiae biting variability, compared to 8% for raw precipitation. For An. funestus, soil moisture explained 32% variability, peaking after a 4‐week lag. The interspecies difference in response to soil moisture was significant (P < 0.00001). A satellite normalized differential vegetation index (NDVI) of the study site yielded a similar correlation (r2= 0.42 An. gambiae). Modelled soil moisture accounted for up to 56% variability of An. gambiae EIR, peaking at a lag of six weeks. The relationship between temperature and An. gambiae biting rates was less robust; maximum temperature r2=−0.20, and minimum temperature r2= 0.12 after lagging one week. Benefits of hydrological modelling are compared to raw weather parameters and to satellite NDVI. These findings can improve both current malaria risk assessments and those based on El Niño forecasts or global climate change model projections.

Estimability and Likelihood Inference for Generalized Linear Mixed Models Using Data Cloning

Maximum likelihood estimation for Generalized Linear Mixed Models (GLMM), an important class of statistical models with substantial applications in epidemiology, medical statistics, and many other fields, poses significant computational difficulties. In this article, we use data cloning, a simple computational method that exploits advances in Bayesian computation, in particular the Markov Chain Monte Carlo method, to obtain maximum likelihood estimators of the parameters in these models. This method also leads to a simple estimator of the asymptotic variance of the maximum likelihood estimators. Determining estimability of the parameters in a mixed model is, in general, a very difficult problem. Data cloning provides a simple graphical test to not only check if the full set of parameters is estimable but also, and perhaps more importantly, if a specified function of the parameters is estimable. One of the goals of mixed models is to predict random effects. We suggest a frequentist method to obtain prediction intervals for random effects. We illustrate data cloning in the GLMM context by analyzing the Logistic–Normal model for over-dispersed binary data, and the Poisson–Normal model for repeated and spatial counts data. We consider Normal–Normal and Binary–Normal mixture models to show how data cloning can be used to study estimability of various parameters. We contend that whenever hierarchical models are used, estimability of the parameters should be checked before drawing scientific inferences or making management decisions. Data cloning facilitates such a check on hierarchical models.

Climate change (Communication arising): Regional warming and malaria resurgence

Disease outbreaks are known to be often influenced by local weather, but how changes in disease trends might be affected by long-term global warming is more difficult to establish. In a study of malaria in the African highlands, Hay et al. found no significant change in long-term climate at four locations where malaria incidence has been increasing since 1976. We contend, however, that their conclusions are likely to be flawed by their inappropriate use of a global climate data set. Moreover, the absence of a historical climate signal allows no inference to be drawn about the impact of future climate change on malaria in the region.

The influences of wolf predation, habitat loss, and human activity on caribou and moose in the Alberta oil sands

Woodland caribou (Rangifer tarandus caribou) and moose (Alces alces) populations in the Alberta oil sands region of western Canada are influenced by wolf (Canis lupus) predation, habitat degradation and loss, and anthropogenic activities. Trained domestic dogs were used to locate scat from caribou, moose, and wolves during winter surges in petroleum development. Evidence obtained from collected scat was then used to estimate resource selection, measure physiological stress, and provide individual genetic identification for precise mark–recapture abundance estimates of caribou, moose, and wolves. Strong impacts of human activity were indicated by changes in resource selection and in stress and nutrition hormone levels as human-use measures were added to base resource selection models (including ecological variables, provincial highways, and pre-existing linear features with no human activity) for caribou. Wolf predation and resource selection so heavily targeted deer (Odocoileus virginiana or O hemionus) t...