Dennis M. Heisey

The abuse of power : The pervasive fallacy of power calculations for data analysis

It is well known that statistical power calculations can be valuable in planning an experiment. There is also a large literature advocating that power calculations be made whenever one performs a statistical test of a hypothesis and one obtains a statistically nonsignificant result. Advocates of such post-experiment power calculations claim the calculations should be used to aid in the interpretation of the experimental results. This approach, which appears in various forms, is fundamentally flawed. We document that the problem is extensive and present arguments to demonstrate the flaw in the logic.

A review of methods to estimate cause-specific mortality in presence of competing risks

Abstract Estimating cause-specific mortality is often of central importance for understanding the dynamics of wildlife populations. Despite such importance, methodology for estimating and analyzing cause-specific mortality has received little attention in wildlife ecology during the past 20 years. The issue of analyzing cause-specific, mutually exclusive events in time is not unique to wildlife. In fact, this general problem has received substantial attention in human biomedical applications within the context of biostatistical survival analysis. Here, we consider cause-specific mortality from a modern biostatistical perspective. This requires carefully defining what we mean by cause-specific mortality and then providing an appropriate hazard-based representation as a competing risks problem. This leads to the general solution of cause-specific mortality as the cumulative incidence function (CIF). We describe the appropriate generalization of the fully nonparametric staggered-entry Kaplan–Meier survival estimator to cause-specific mortality via the nonparametric CIF estimator (NPCIFE), which in many situations offers an attractive alternative to the Heisey–Fuller estimator. An advantage of the NPCIFE is that it lends itself readily to risk factors analysis with standard software for Cox proportional hazards model. The competing risks–based approach also clarifies issues regarding another intuitive but erroneous “cause-specific mortality” estimator based on the Kaplan–Meier survival estimator and commonly seen in the life sciences literature.

Modeling Routes of Chronic Wasting Disease Transmission: Environmental Prion Persistence Promotes Deer Population Decline and Extinction

Chronic wasting disease (CWD) is a fatal disease of deer, elk, and moose transmitted through direct, animal-to-animal contact, and indirectly, via environmental contamination. Considerable attention has been paid to modeling direct transmission, but despite the fact that CWD prions can remain infectious in the environment for years, relatively little information exists about the potential effects of indirect transmission on CWD dynamics. In the present study, we use simulation models to demonstrate how indirect transmission and the duration of environmental prion persistence may affect epidemics of CWD and populations of North American deer. Existing data from Colorado, Wyoming, and Wisconsins CWD epidemics were used to define plausible short-term outcomes and associated parameter spaces. Resulting long-term outcomes range from relatively low disease prevalence and limited host-population decline to host-population collapse and extinction. Our models suggest that disease prevalence and the severity of population decline is driven by the duration that prions remain infectious in the environment. Despite relatively low epidemic growth rates, the basic reproductive number, R 0, may be much larger than expected under the direct-transmission paradigm because the infectious period can vastly exceed the hosts life span. High prion persistence is expected to lead to an increasing environmental pool of prions during the early phases (i.e. approximately during the first 50 years) of the epidemic. As a consequence, over this period of time, disease dynamics will become more heavily influenced by indirect transmission, which may explain some of the observed regional differences in age and sex-specific disease patterns. This suggests management interventions, such as culling or vaccination, will become increasingly less effective as CWD epidemics progress.

Linking process to pattern: estimating spatiotemporal dynamics of a wildlife epidemic from cross-sectional data

Underlying dynamic event processes unfolding in continuous time give rise to spatiotemporal patterns that are sometimes observable at only a few discrete times. Such event processes may be modulated simultaneously over several spatial (e.g., latitude and longitude) and temporal (e.g., age, calendar time, and cohort) dimensions. The ecological challenge is to understand the dynamic latent processes that were integrated over several dimensions (space and time) to produce the observed pattern: a so-called inverse problem. An example of such a problem is characterizing epidemiological rate processes from spatially referenced age-specific prevalence data for a wildlife disease such as chronic wasting disease (CWD). With age-specific prevalence data, the exact infection times are not observed, which complicates the direct estimation of rates. However, the relationship between the observed data and the unobserved rate variables can be described with likelihood equations. Typically, for problems with multiple timescales, the likelihoods are integral equations without closed forms. The complexity of the likelihoods often makes traditional maximum-likelihood approaches untenable. Here, using seven years of hunter-harvest prevalence data from the CWD epidemic in white-tailed deer (Odocoileus virginianus) in Wisconsin, USA, we develop and explore a Bayesian approach that allows for a detailed examination of factors modulating the infection rates over space, age, and time, and their interactions. Our approach relies on the Bayesian ability to borrow strength from neighbors in both space and time. Synthesizing a number of areas of event time analysis (current-status data, age/period/cohort models, Bayesian spatial shared frailty models), our general framework has very broad ecological applicability beyond disease prevalence data to a number of important ecological event time analyses, including general survival studies with multiple time dimensions for which existing methodology is limited. We observed strong associations of infection rates with age, gender, and location. The infection rate appears to be increasing with time. We could not detect growth hotspots, or location by time interactions, which suggests that spatial variation in infection rates is determined primarily by when the disease arrives locally, rather than how fast it grows. We emphasize assumptions and the potential consequences of their violations.

Spatial and temporal patterns of chronic wasting disease: fine- scale mapping of a wildlife epidemic in Wisconsin

Emerging infectious diseases threaten wildlife populations and human health. Understanding the spatial distributions of these new diseases is important for disease management and policy makers; however, the data are complicated by heterogeneities across host classes, sampling variance, sampling biases, and the space-time epidemic process. Ignoring these issues can lead to false conclusions or obscure important patterns in the data, such as spatial variation in disease prevalence. Here, we applied hierarchical Bayesian disease mapping methods to account for risk factors and to estimate spatial and temporal patterns of infection by chronic wasting disease (CWD) in white-tailed deer (Odocoileus virginianus) of Wisconsin, U.S.A. We found significant heterogeneities for infection due to age, sex, and spatial location. Infection probability increased with age for all young deer, increased with age faster for young males, and then declined for some older animals, as expected from disease-associated mortality and age-related changes in infection risk. We found that disease prevalence was clustered in a central location, as expected under a simple spatial epidemic process where disease prevalence should increase with time and expand spatially. However, we could not detect any consistent temporal or spatiotemporal trends in CWD prevalence. Estimates of the temporal trend indicated that prevalence may have decreased or increased with nearly equal posterior probability, and the model without temporal or spatiotemporal effects was nearly equivalent to models with these effects based on deviance information criteria. For maximum interpretability of the role of location as a disease risk factor, we used the technique of direct standardization for prevalence mapping, which we develop and describe. These mapping results allow disease management actions to be employed with reference to the estimated spatial distribution of the disease and to those host classes most at risk. Future wildlife epidemiology studies should employ hierarchical Bayesian methods to smooth estimated quantities across space and time, account for heterogeneities, and then report disease rates based on an appropriate standardization.

Chronic Wasting Disease (CWD) Susceptibility of Several North American Rodents That Are Sympatric with Cervid CWD Epidemics

ABSTRACT Chronic wasting disease (CWD) is a highly contagious always fatal neurodegenerative disease that is currently known to naturally infect only species of the deer family, Cervidae. CWD epidemics are occurring in free-ranging cervids at several locations in North America, and other wildlife species are certainly being exposed to infectious material. To assess the potential for transmission, we intracerebrally inoculated four species of epidemic-sympatric rodents with CWD. Transmission was efficient in all species; the onset of disease was faster in the two vole species than the two Peromyscus spp. The results for inocula prepared from CWD-positive deer with or without CWD-resistant genotypes were similar. Survival times were substantially shortened upon second passage, demonstrating adaptation. Unlike all other known prion protein sequences for cricetid rodents that possess asparagine at position 170, our red-backed voles expressed serine and refute previous suggestions that a serine in this position substantially reduces susceptibility to CWD. Given the scavenging habits of these rodent species, the apparent persistence of CWD prions in the environment, and the inevitable exposure of these rodents to CWD prions, our intracerebral challenge results indicate that further investigation of the possibility of natural transmission is warranted.

Mapping brucellosis increases relative to elk density using hierarchical Bayesian models

The relationship between host density and parasite transmission is central to the effectiveness of many disease management strategies. Few studies, however, have empirically estimated this relationship particularly in large mammals. We applied hierarchical Bayesian methods to a 19-year dataset of over 6400 brucellosis tests of adult female elk (Cervus elaphus) in northwestern Wyoming. Management captures that occurred from January to March were over two times more likely to be seropositive than hunted elk that were killed in September to December, while accounting for site and year effects. Areas with supplemental feeding grounds for elk had higher seroprevalence in 1991 than other regions, but by 2009 many areas distant from the feeding grounds were of comparable seroprevalence. The increases in brucellosis seroprevalence were correlated with elk densities at the elk management unit, or hunt area, scale (mean 2070 km2; range  = [95–10237]). The data, however, could not differentiate among linear and non-linear effects of host density. Therefore, control efforts that focus on reducing elk densities at a broad spatial scale were only weakly supported. Additional research on how a few, large groups within a region may be driving disease dynamics is needed for more targeted and effective management interventions. Brucellosis appears to be expanding its range into new regions and elk populations, which is likely to further complicate the United States brucellosis eradication program. This study is an example of how the dynamics of host populations can affect their ability to serve as disease reservoirs.

MYCOBACTERIOSIS‐ASSOCIATED MORTALITY IN WILD STRIPED BASS (MORONE SAXATILIS) FROM CHESAPEAKE BAY, USA

The striped bass (Morone saxatilis) is an economically and ecologically important finfish species along the Atlantic seaboard of the United States. Recent stock assessments in Chesapeake Bay (U.S.A.) indicate that non-fishing mortality in striped bass has increased since 1999, concomitant with very high (>50%) prevalence of visceral and dermal disease caused by Mycobacterium spp. Current fishery assessment models do not differentiate between disease and other components of non-fishing mortality (e.g., senescence, predation); therefore, disease impact on the striped bass population has not been established. Specific measurement of mortality associated with mycobacteriosis in wild striped bass is complicated because the disease is chronic and mortality is cryptic. Epidemiological models have been developed to estimate disease-associated mortality from cross-sectional prevalence data and have recently been generalized to represent disease processes more realistically. Here, we used this generalized approach to demonstrate disease-associated mortality in striped bass from Chesapeake Bay. To our knowledge this is the first demonstration of cryptic mortality associated with a chronic infectious disease in a wild finfish. This finding has direct implications for management and stock assessment of striped bass, as it demonstrates population-level negative impacts of a chronic disease. Additionally, this research provides a framework by which disease-associated mortality may be specifically addressed within fisheries models for resource management.

Wildlife contact analysis: emerging methods, questions, and challenges

Recent technological advances, such as proximity loggers, allow researchers to collect complete interaction histories, day and night, among sampled individuals over several months to years. Social network analyses are an obvious approach to analyzing interaction data because of their flexibility for fitting many different social structures as well as the ability to assess both direct contacts and indirect associations via intermediaries. For many network properties, however, it is not clear whether estimates based upon a sample of the network are reflective of the entire network. In wildlife applications, networks may be poorly sampled and boundary effects will be common. We present an alternative approach that utilizes a hierarchical modeling framework to assess the individual, dyadic, and environmental factors contributing to variation in the interaction rates and allows us to estimate the underlying process variation in each. In a disease control context, this approach will allow managers to focus efforts on those types of individuals and environments that contribute the most toward super-spreading events. We account for the sampling distribution of proximity loggers and the non-independence of contacts among groups by only using contact data within a group during days when the group membership of proximity loggers was known. This allows us to separate the two mechanisms responsible for a pair not contacting one another: they were not in the same group or they were in the same group but did not come within the specified contact distance. We illustrate our approach with an example dataset of female elk from northwestern Wyoming and conclude with a number of important future research directions.

Use of a Log-Linear Model with the EM Algorithm to Correct Estimates of Stock Composition and to Convert Length to Age

Abstract The EM (expectation-maximization) algorithm was used to develop a general procedure for finding maximum likelihood estimates of population proportions when some observations cannot be assigned unambiguously to a population category. The method can be used to estimate the age composition of fish from length frequencies, to adjust biased estimates of age composition (e.g., scale ages that tend to be too low), and to correct biased estimates of unit stock composition. To implement the method, two samples are obtained. In the first sample, the items are cross-classified by their actual identity and by a second (possibly error-prone) surrogate classifying variable. In the second sample, the items are classified by only the surrogate variable. The information in the two samples is then used to estimate the population proportions in the second sample.