Bayesian analysis of one-inflated models for elusive population size estimation

The identification and treatment of “one‐inflation” in estimating the size of an elusive population has received increasing attention in capture–recapture literature in recent years. The phenomenon occurs when the number of units captured exactly once clearly exceeds the expectation under a baseline count distribution. Ignoring one‐inflation has serious consequences for estimation of the population size, which can be drastically overestimated. In this paper we propose a Bayesian approach for Poisson, geometric, and negative binomial one‐inflated count distributions. Posterior inference for population size will be obtained applying a Gibbs sampler approach. We also provide a Bayesian approach to model selection. We illustrate the proposed methodology with simulated and real data and propose a new application in official statistics to estimate the number of people implicated in the exploitation of prostitution in Italy.

Continuous time-interaction processes for population size estimation, with an application to drug dealing in Italy

We introduce a time-interaction point process where the occurrence of an event can increase (self-excitement) or reduce (self-correction) the probability of future events. Self-excitement and self-correction are allowed to be triggered by the same event, at different time scales; other effects such as those of covariates, unobserved heterogeneity, and temporal dependence are also allowed in the model. We focus on capture-recapture data, as our work is motivated by an original example about estimation of the total number of drug dealers in Italy. To do so, we derive a conditional likelihood formulation where only subjects with at least one capture are involved in the inference process. The result is a novel and flexible continuous-time population size estimator. A simulation study and the analysis of our motivating example illustrate the validity of our approach in several scenarios. This article is protected by copyright. All rights reserved.

Population size estimation with interval censored counts and external information: Prevalence of multiple sclerosis in Rome

We discuss Bayesian log-linear models for incomplete contingency tables with both missing and interval censored cells, with the aim of obtaining reliable population size estimates. We also discuss use of external information on the censoring probability, which may substantially reduce uncertainty. We show in simulation that information on lower bounds and external information can each improve the mean squared error of population size estimates, even when the external information is not completely accurate. We conclude with an original example on estimation of prevalence of multiple sclerosis in the metropolitan area of Rome, where five out of six lists have interval censored counts. External information comes from mortality rates of multiple sclerosis patients.

Molecular neuroscience at its "high": bibliometric analysis of the most cited papers on endocannabinoid system, cannabis and cannabinoids

BACKGROUND

Cannabis, cannabinoids and endocannabinoids are heavily investigated topics with many articles published every year. We aimed to identify the 100 most cited manuscripts among the vast literature and analyze their contents.

METHODS

Web of Science (WoS) Core Collection was searched to identify the 100 most cited relevant manuscripts, which were analyzed with reference to (1) authorship, (2) institution, (3) country, (4) document type, (5) journal, (6) publication year, (7) WoS category, and (8) citation count. Semantic content and citation data of the manuscripts were analyzed with VOSviewer.

RESULTS

The most cited manuscripts were published between 1986 and 2016, with the majority being published in the 2000s (n = 51). The number of citations for the top 100 articles ranged from 469 to 3651, with a median citation count of 635.5. The most prolific authors were Vincenzo Di Marzo (n = 11) and Daniele Piomelli (n = 11). The major contributing countries were USA (n = 49), Italy (n = 22), UK (n = 19), and France (n = 11). The most prolific institutions were University of California (n = 14), National Research Council of Italy (n = 12) and National Institutes of Health USA (n = 12). The manuscripts consisted of original articles (n = 75), reviews (n = 24) and a note (n = 1). The most dominant journal was Nature (n = 15). The major WoS categories associated were Multidisciplinary sciences (n = 31), Neurosciences (n = 20), Pharmacology / Pharmacy (n = 16), and General / Internal Medicine (n = 11).

CONCLUSIONS

The top-ranked manuscripts among the 100 were concerning analgesia, weight loss, long-term potentiation, depolarization-induced suppression of inhibition, opiates and other topics. Cannabinoid type 1 (CB1) receptor was studied by more of the top 100 papers in comparison to cannabinoid type 2 (CB2) receptor. The most frequently mentioned chemicals in these publications were 2-arachidonoylglycerol, tetrahydrocannabinol, and anandamide. Together, these manuscripts comprise the most highly cited publications in the topic, literally the molecular neuroscience at its "high".

One-inflation and unobserved heterogeneity in population size estimation

We present the one-inflated zero-truncated negative binomial (OIZTNB) model, and propose its use as the truncated count distribution in Horvitz-Thompson estimation of an unknown population size. In the presence of unobserved heterogeneity, the zero-truncated negative binomial (ZTNB) model is a natural choice over the positive Poisson (PP) model; however, when one-inflation is present the ZTNB model either suffers from a boundary problem, or provides extremely biased population size estimates. Monte Carlo evidence suggests that in the presence of one-inflation, the Horvitz-Thompson estimator under the ZTNB model can converge in probability to infinity. The OIZTNB model gives markedly different population size estimates compared to some existing truncated count distributions, when applied to several capture-recapture data that exhibit both one-inflation and unobserved heterogeneity.

On the design of closed recapture experiments

We propose a method to plan the number of occasions of recapture experiments for population size estimation. We do so by fixing the smallest number of capture occasions so that the expected length of the profile confidence interval is less than or equal to a fixed threshold. In some cases, we solve the optimization problem in closed form. For more complex models we use numerical optimization. We detail models assuming homogeneous, time-varying, subject-specific capture probabilities, behavioral response to capture, and combining behavioral response with subject-specific effects. The principle we propose can be extended to plan any other model specification. We formally show the validity of the approach by proving distributional convergence. We illustrate with simulations and challenging examples in epidemiology and ecology. We report that in many cases adding as few as two sampling occasions may substantially reduce the length of confidence intervals.

A general class of recapture models based on the conditional capture probabilities

We propose an Mhotb model for population size estimation in capture-recapture studies. The tb part is based on equality constraints for the conditional capture probabilities, leading to an extremely rich model class. Observed and unobserved heterogeneity are dealt with by means of a logistic parameterization. In order to explore the model class, we introduce a penalized version of the likelihood. The conditional likelihood and penalized conditional likelihood are maximized by means of efficient EM algorithms. Simulations and two real data examples illustrate the approach.

Integrated survival analysis using an event-time approach in a Bayesian framework

Event-time or continuous-time statistical approaches have been applied throughout the biostatistical literature and have led to numerous scientific advances. However, these techniques have traditionally relied on knowing failure times. This has limited application of these analyses, particularly, within the ecological field where fates of marked animals may be unknown. To address these limitations, we developed an integrated approach within a Bayesian framework to estimate hazard rates in the face of unknown fates. We combine failure/survival times from individuals whose fates are known and times of which are interval-censored with information from those whose fates are unknown, and model the process of detecting animals with unknown fates. This provides the foundation for our integrated model and permits necessary parameter estimation. We provide the Bayesian model, its derivation, and use simulation techniques to investigate the properties and performance of our approach under several scenarios. Lastly, we apply our estimation technique using a piece-wise constant hazard function to investigate the effects of year, age, chick size and sex, sex of the tending adult, and nesting habitat on mortality hazard rates of the endangered mountain plover (Charadrius montanus) chicks. Traditional models were inappropriate for this analysis because fates of some individual chicks were unknown due to failed radio transmitters. Simulations revealed biases of posterior mean estimates were minimal (≤ 4.95%), and posterior distributions behaved as expected with RMSE of the estimates decreasing as sample sizes, detection probability, and survival increased. We determined mortality hazard rates for plover chicks were highest at <5 days old and were lower for chicks with larger birth weights and/or whose nest was within agricultural habitats. Based on its performance, our approach greatly expands the range of problems for which event-time analyses can be used by eliminating the need for having completely known fate data.