A Measurement Error Model for Heterogeneous Capture Probabilities in Mark-Recapture Experiments: An Estimating Equation Approach

Logistic models for capture probabilities that depend on covariates are effective if the covariates can be measured exactly. If there is measurement error so that a surrogate for the covariate is observed rather than the covariate itself, simple adjustments may be made if the parameters of joint distribution of the covariate and the surrogate are known. Here we consider the case when a surrogate is observed whenever an individual is captured and the parameters must also be estimated from the data. An estimating equation regression calibration approach is developed and it is illustrated on a real dataset where the surrogate is an individual bird's wing-length, which varies from occasion to occasion. This article has supplementary material online

A Varying Coefficient Model to Measure the Effectiveness of Mass Media Anti-Smoking Campaigns in Generating Calls to a Quitline

Background: Anti-smoking advertisements are an effective population-based smoking reduction strategy. The Quitline telephone service provides a first point of contact for adults considering quitting. Because of data complexity, the relationship between anti-smoking advertising placement, intensity, and time trends in total call volume is poorly understood. In this study we use a recently developed semi-varying coefficient model to elucidate this relationship. Methods: Semi-varying coefficient models comprise parametric and nonparametric components. The model is fitted to the daily number of calls to Quitline in Victoria, Australia to estimate a nonparametric long-term trend and parametric terms for day-of-the-week effects and to clarify the relationship with target audience rating points (TARPs) for the Quit and nicotine replacement advertising campaigns. Results: The number of calls to Quitline increased with the TARP value of both the Quit and other smoking cessation advertisement; the TARP values associated with the Quit program were almost twice as effective. The varying coefficient term was statistically significant for peak periods with little or no advertising. Conclusions: Semi-varying coefficient models are useful for modeling public health data when there is little or no information on other factors related to the at-risk population. These models are well suited to modeling call volume to Quitline, because the varying coefficient allowed the underlying time trend to depend on fixed covariates that also vary with time, thereby explaining more of the variation in the call model

Application of semiparametric regression models in the analysis of capture-recapture experiments

If the capture probabilities in a capture-recapture experiment depend on covariates, parametric models may be fitted and the population size may then be estimated. Here a semiparametric model for the capture probabilities that allows both continuous and categorical covariates is developed. Kernel smoothing and profile estimating equations are used to estimate the nonparametric and parametric components. Analytic forms of the standard errors are derived, which allows an empirical bias bandwidth selection procedure to be used to estimate the bandwidth. The method is evaluated in simulations and is applied to a real data set concerning captures of Prinia flaviventris, which is a common bird species in Southeast Asia

Non-parametric estimation of population size from capture-recapture data when the capture probability depends on a covariate

In capture-recapture experiments the capture probabilities may depend on individual covariates such as an individual's weight or age. Typically this dependence is modelled through simple parametric functions of the covariates. Here we first demonstrate that misspecification of the model can produce biased estimates and subsequently develop a non-parametric procedure to estimate the functional relationship between the probability of capture and a single covariate. This estimator is then incorporated in a Horvitz-Thompson estimator to estimate the size of the population. The resulting estimators are evaluated in a simulation study and applied to a data set on captures of the Mountain Pygmy Possum

A SEMIPARAMETRIC MODEL FOR A FUNCTIONAL BEHAVIOURAL RESPONSE TO CAPTURE IN CAPTURE-RECAPTURE EXPERIMENTS

Capturerecapture experiments are commonly used to estimate the size of a closed population. However, the associated estimators of the population size are well known to be highly sensitive to misspecification of the capture probabilities. To address this, we present a general semiparametric framework for the analysis of capturerecapture experiments when the capture probability depends on individual characteristics, time effects and behavioural response. This generalizes well-known general parametric capturerecapture models and extends previous semiparametric models in which there is no time dependence or behavioural response. The method is evaluated in simulations and applied to two real data sets

Consistent estimation of species abundance from a presence-absence map

The estimation of the abundance of a species using the presence or absence of the species over a grid of cells simplifies data collection but the resulting statistical analysis is challenging. Several estimators have been proposed but their properties are unknown. Here we consider a generalized gamma-Poisson model which allows dependencies across the grid and develop a new estimator for this model. It is shown that this estimator is consistent, allowing us to conclude that it is indeed possible to estimate abundance from presence-absence maps. (C) 2011 Elsevier B.V. All rights reserved

A Review of the Use of Conditional Likelihood in Capture-Recapture Experiments

We present a modern perspective of the conditional likelihood approach to the analysis of capture-recapture experiments, which shows the conditional likelihood to be a member of generalized linear model (GLM). Hence, there is the potential to apply the full range of GLM methodologies. To put this method in context, we first review some approaches to capture-recapture experiments with heterogeneous capture probabilities in closed populations, covering parametric and non-parametric mixture models and the use of covariates. We then review in more detail the analysis of capture-recapture experiments when the capture probabilities depend on a covariate

Heterogeneous Capture-Recapture Models with Covariates: A Partial Likelihood Approach for Closed Populations

In practice, when analyzing data from a capturerecapture experiment it is tempting to apply modern advanced statistical methods to the observed capture histories. However, unless the analysis takes into account that the data have only been collected from individuals who have been captured at least once, the results may be biased. Without the development of new software packages, methods such as generalized additive models, generalized linear mixed models, and simulationextrapolation cannot be readily implemented. In contrast, the partial likelihood approach allows the analysis of a capturerecapture experiment to be conducted using commonly available software. Here we examine the efficiency of this approach and apply it to several data sets