An extension of an over-dispersion test for count data

While over-dispersion in capture–recapture studies is well known to lead to poor estimation of population size, current diagnostic tools to detect the presence of heterogeneity have not been specifically developed for capture–recapture studies. To address this, a simple and efficient method of testing for over-dispersion in zero-truncated count data is developed and evaluated. The proposed method generalizes an over-dispersion test previously suggested for un-truncated count data and may also be used for testing residual over-dispersion in zero-inflation data. Simulations suggest that the asymptotic distribution of the test statistic is standard normal and that this approximation is also reasonable for small sample sizes. The method is also shown to be more efficient than an existing test for over-dispersion adapted for the capture–recapture setting. Studies with zero-truncated and zero-inflated count data are used to illustrate the test procedures.

Estimating the hidden number of scrapie affected holdings in great Britain using a simple, truncated count model allowing for heterogeneity.

None of the current surveillance streams monitoring the presence of scrapie in Great Britain provide a comprehensive and unbiased estimate of the prevalence of the disease at the holding level. Previous work to estimate the under-ascertainment adjusted prevalence of scrapie in Great Britain applied multiple-list capture–recapture methods. The enforcement of new control measures on scrapie-affected holdings in 2004 has stopped the overlapping between surveillance sources and, hence, the application of multiple-list capture–recapture models. Alternative methods, still under the capture–recapture methodology, relying on repeated entries in one single list have been suggested in these situations. In this article, we apply one-list capture–recapture approaches to data held on the Scrapie Notifications Database to estimate the undetected population of scrapie-affected holdings with clinical disease in Great Britain for the years 2002, 2003, and 2004. For doing so, we develop a new diagnostic tool for indication of heterogeneity as well as a new understanding of the Zelterman and Chao’s lower bound estimators to account for potential unobserved heterogeneity. We demonstrate that the Zelterman estimator can be viewed as a maximum likelihood estimator for a special, locally truncated Poisson likelihood equivalent to a binomial likelihood. This understanding allows the extension of the Zelterman approach by means of logistic regression to include observed heterogeneity in the form of covariates—in case studied here, the holding size and country of origin. Our results confirm the presence of substantial unobserved heterogeneity supporting the application of our two estimators. The total scrapie-affected holding population in Great Britain is around 300 holdings per year. None of the covariates appear to inform the model significantly.

Mixture models for capture-recapture count data

The contribution investigates the problem of estimating the size of a population, also known as the missing cases problem. Suppose a registration system is targeting to identify all cases having a certain characteristic such as a specific disease (cancer, heart disease, ...), disease related condition (HIV, heroin use, ...) or a specific behavior (driving a car without license). Every case in such a registration system has a certain notification history in that it might have been identified several times (at least once) which can be understood as a particular capture-recapture situation. Typically, cases are left out which have never been listed at any occasion, and it is this frequency one wants to estimate. In this paper modelling is concentrating on the counting distribution, e.g. the distribution of the variable that counts how often a given case has been identified by the registration system. Besides very simple models like the binomial or Poisson distribution, finite (nonparametric) mixtures of these are considered providing rather flexible modelling tools. Estimation is done using maximum likelihood by means of the EM algorithm. A case study on heroin users in Bangkok in the year 2001 is completing the contribution.

On the question of proportionality of the count of observed Scrapie cases and the size of holding

Background: The present paper investigates the question of a suitable basic model for the number of scrapie cases in a holding and applications of this knowledge to the estimation of scrapie-ffected holding population sizes and adequacy of control measures within holding. Is the number of scrapie cases proportional to the size of the holding in which case it should be incorporated into the parameter of the error distribution for the scrapie counts? Or, is there a different - potentially more complex - relationship between case count and holding size in which case the information about the size of the holding should be better incorporated as a covariate in the modeling? Methods: We show that this question can be appropriately addressed via a simple zero-truncated Poisson model in which the hypothesis of proportionality enters as a special offset-model. Model comparisons can be achieved by means of likelihood ratio testing. The procedure is illustrated by means of surveillance data on classical scrapie in Great Britain. Furthermore, the model with the best fit is used to estimate the size of the scrapie-affected holding population in Great Britain by means of two capture-recapture estimators: the Poisson estimator and the generalized Zelterman estimator. Results: No evidence could be found for the hypothesis of proportionality. In fact, there is some evidence that this relationship follows a curved line which increases for small holdings up to a maximum after which it declines again. Furthermore, it is pointed out how crucial the correct model choice is when applied to capture-recapture estimation on the basis of zero-truncated Poisson models as well as on the basis of the generalized Zelterman estimator. Estimators based on the proportionality model return very different and unreasonable estimates for the population sizes. Conclusion: Our results stress the importance of an adequate modelling approach to the association between holding size and the number of cases of classical scrapie within holding. Reporting artefacts and speculative biological effects are hypothesized as the underlying causes of the observed curved relationship. The lack of adjustment for these artefacts might well render ineffective the current strategies for the control of the disease.

CAMCR: Computer assisted mixture model analysis for capture-recapture count data

Population size estimation with discrete or nonparametric mixture models is considered, and reliable ways of construction of the nonparametric mixture model estimator are reviewed and set into perspective. Construction of the maximum likelihood estimator of the mixing distribution is done for any number of components up to the global nonparametric maximum likelihood bound using the EM algorithm. In addition, the estimators of Chao and Zelterman are considered with some generalisations of Zelterman’s estimator. All computations are done with CAMCR, a special software developed for population size estimation with mixture models. Several examples and data sets are discussed and the estimators illustrated. Problems using the mixture model-based estimators are highlighted.

Estimating the hidden number of scrapie affected holdings in great Britain using a simple, truncated count model allowing for heterogeneity

None of the current surveillance streams monitoring the presence of scrapie in Great Britain provide a comprehensive and unbiased estimate of the prevalence of the disease at the holding level. Previous work to estimate the under-ascertainment adjusted prevalence of scrapie in Great Britain applied multiple-list capture-recapture methods. The enforcement of new control measures on scrapie-affected holdings in 2004 has stopped the overlapping between surveillance sources and, hence, the application of multiple-list capture-recapture models. Alternative methods, still under the capture-recapture methodology, relying on repeated entries in one single list have been suggested in these situations. In this article, we apply one-list capture-recapture approaches to data held on the Scrapie Notifications Database to estimate the undetected population of scrapie-affected holdings with clinical disease in Great Britain for the years 2002, 2003, and 2004. For doing so, we develop a new diagnostic tool for indication of heterogeneity as well as a new understanding of the Zelterman and Chao's lower bound estimators to account for potential unobserved heterogeneity. We demonstrate that the Zelterman estimator can be viewed as a maximum likelihood estimator for a special, locally truncated Poisson likelihood equivalent to a binomial likelihood. This understanding allows the extension of the Zelterman approach by means of logistic regression to include observed heterogeneity in the form of covariates-in case studied here, the holding size and country of origin. Our results confirm the presence of substantial unobserved heterogeneity supporting the application of our two estimators. The total scrapie-affected holding population in Great Britain is around 300 holdings per year. None of the covariates appear to inform the model significantly.

Equivalence of truncated count mixture distributions and mixtures of truncated count distributions

This article is about modeling count data with zero truncation. A parametric count density family is considered. The truncated mixture of densities from this family is different from the mixture of truncated densities from the same family. Whereas the former model is more natural to formulate and to interpret, the latter model is theoretically easier to treat. It is shown that for any mixing distribution leading to a truncated mixture, a (usually different) mixing distribution can be found so. that the associated mixture of truncated densities equals the truncated mixture, and vice versa. This implies that the likelihood surfaces for both situations agree, and in this sense both models are equivalent. Zero-truncated count data models are used frequently in the capture-recapture setting to estimate population size, and it can be shown that the two Horvitz-Thompson estimators, associated with the two models, agree. In particular, it is possible to achieve strong results for mixtures of truncated Poisson densities, including reliable, global construction of the unique NPMLE (nonparametric maximum likelihood estimator) of the mixing distribution, implying a unique estimator for the population size. The benefit of these results lies in the fact that it is valid to work with the mixture of truncated count densities, which is less appealing for the practitioner but theoretically easier. Mixtures of truncated count densities form a convex linear model, for which a developed theory exists, including global maximum likelihood theory as well as algorithmic approaches. Once the problem has been solved in this class, it might readily be transformed back to the original problem by means of an explicitly given mapping. Applications of these ideas are given, particularly in the case of the truncated Poisson family.

Glycosaminoglycans and protein disulfide isomerase-mediated reduction of HIV Env

Conformational changes within the human immunodeficiency virus-1 (HIV-1) surface glycoprotein gp120 result from binding to the lymphocyte surface receptors and trigger gp41-mediated virus/cell membrane fusion. The triggering of fusion requires cleavage of two of the nine disulfide bonds of gp120 by a cell-surface protein disulfide-isomerase (PDI). Soluble glycosaminoglycans such as heparin and heparan sulfate bind gp120 via V3 and, possibly, a CD4-induced domain. They exert anti-HIV activity by interfering with the HIV envelope glycoprotein ( Env)/cell-surface interaction. Env also binds cell-surface glycosaminoglycans. Here, using surface plasmon resonance, we observed an inverse relationship between heparin binding by gp120 and its thiol content. In vitro, and in conditions in which gp120 could bind CD4, heparin and heparan sulfate reduced PDI-mediated gp120 reduction by approximately 80%. Interaction of Env with the surface of lymphocytes treated using sodium chlorate, an inhibitor of glycosaminoglycan synthesis, led to gp120 reduction. We conclude that besides their capacity to block Env/cell interaction, soluble glycosaminoglycans can effect anti-HIV activity via interference with PDI- mediated gp120 reduction. In contrast, their presence at the cell surface is dispensable for Env reduction during the course of interaction with the lymphocyte surface. This work suggests that the reduction of exofacial proteins in various diseases can be inhibited by compounds targeting the substrates ( not by targeting PDI, as is usually done), and that glycosaminoglycans that primarily protect proteins by preserving them from proteolysis also have a role in preventing reduction.

Protein-disulfide isomerase-mediated reduction of two disulfide bonds of HIV envelope glycoprotein 120 occurs post-CXCR4 binding and is required for fusion

The human immunodeficiency virus (HIV) envelope (Env) glycoprotein (gp) 120 is a highly disulfide-bonded molecule that attaches HIV to the lymphocyte surface receptors CD4 and CXCR4. Conformation changes within gp120 result from binding and trigger HIV/cell fusion. Inhibition of lymphocyte surface-associated protein-disulfide isomerase (PDI) blocks HIV/cell fusion, suggesting that redox changes within Env are required. Using a sensitive assay based on a thiol reagent, we show that (i) the thiol content of gp120, either secreted by mammalian cells or bound to a lymphocyte surface enabling CD4 but not CXCR4 binding, was 0.5-1 pmol SH/pmol gp120 (SH/gp120), whereas that of gp120 after its interaction with a surface enabling both CD4 and CXCR4 binding was raised to 4 SH/gp120; (ii) PDI inhibitors prevented this change; and (iii) gp120 displaying 2 SH/gp120 exhibited CD4 but not CXCR4 binding capacity. In addition, PDI inhibition did not impair gp120 binding to receptors. We conclude that on average two of the nine disulfides of gp120 are reduced during interaction with the lymphocyte surface after CXCR4 binding prior to fusion and that cell surface PDI catalyzes this process. Disulfide bond restructuring within Env may constitute the molecular basis of the post-receptor binding conformational changes that induce fusion competence.

Synthesis and structure-activity relationship studies of CD4 down-modulating cyclotriazadisulfonamide (CADA) analogues

HIV attachment via the CD4 receptor is an important target for developing novel approaches to HIV chemotherapy. Cyclotriazadisulfonamide (CADA) inhibits HIV at submicromolar levels by specifically down-modulating cell-surface and intracellular CD4. An effective five-step synthesis of CADA in 30% overall yield is reported. This synthesis has also been modified to produce more than 50 analogues. Many tail-group analogues have been made by removing the benzyl tail of CADA and replacing it with various alkyl, acyl, alkoxycarbonyl and aminocarbonyl substituents. A series of sidearm analogues, including two unsymmetrical compounds, have also been prepared by modifying the CADA synthesis, replacing the toluenesulfonyl sidearms with other sulfonyl groups. Testing 30 of these compounds in MT-4 cells shows a wide range of CD4 down-modulation potency, which correlates with ability to inhibit HIV-1. Three-dimensional quantitative structure-activity relationship (3D-QSAR) models were constructed using comparative molecular field analysis (CoMFA) and comparative molecular similarity indices analysis (CoMSIA) approaches. The X-ray crystal structures of four compounds, including CADA, show the same major conformation of the central 12-membered ring. The solid-state structure of CADA was energy minimized and used to generate the remaining 29 structures, which were similarly minimized and aligned to produce the 3D-QSAR models. Both models indicate that steric bulk of the tail group, and, to a lesser extent, the sidearms mainly determine CD4 down-modulation potency in this series of compounds.

Cigarette smokers have decreased lymphocyte and platelet alpha-tocopherol levels and increased excretion of the gamma-tocopherol metabolite gamma-carboxyethyl-hydroxychroman (gamma-CEHC)

Cigarette smoking is associated with increased oxidative stress and increased risk of degenerative disease. As the major lipophilic antioxidant, requirements for vitamin E may be higher in smokers due to increased utilisation. In this observational study we have compared vitamin E status in smokers and non-smokers using a holistic approach by measuring plasma, erythrocyte, lymphocyte and platelet alpha- and gamma-tocopherol, as well as the specific urinary vitamin E metabolites alpha- and gamma-carboxyethylhydroxychroman (CEHC). Fifteen smokers (average age 27 years, smoking time 7.5 years) and non-smokers of comparable age, gender and body mass index (BMI) were recruited. Subjects completed a 7-day food diary and on the final day they provided a 24 h urine collection and a 20 ml blood sample for measurement of urinary vitamin E metabolites and total vitamin E in blood components, respectively. No significant differences were found between plasma and erythrocyte alpha- and gamma-tocopherol in smokers and non-smokers. However, smokers had significantly lower ce-tocopherol (mean +/-SD, 1.34+/-0.31 mumol/g protein compared with 1.94+/-0.54, P = 0.001) and gamma-tocopherol (0.19 +/- 0.04 mumol/g protein compared with 0.26 +/- 0.08, P = 0.026) levels in their lymphocytes, as well as significantly lower (alpha-tocopherol levels in platelets (1.09 +/- 0.49 mumol/g protein compared with 1.60 +/- 0.55, P = 0.014; gamma-tocopherol levels were similar). Interestingly smokers also had significantly higher excretion of the urinary gamma-tocopherol metabolite, gamma-CEHC (0.49 +/- 0.25 mg/g creatinine compared with 0.32 +/- 0.16, P = 0.036) compared to non-smokers, while their (alpha-CEHC (metabolite of a-tocopherol) levels were similar. There was no significant difference between plasma ascorbate, urate and F-2-isoprostane levels. Therefore in this population of cigarette smokers (mean age 27 years, mean smoking duration 7.5 years), alterations to vitamin E status can be observed even without the more characteristic changes to ascorbate and F-2-isoprostanes. We suggest that the measurement of lymphocyte and platelet vitamin E may represent a valuable biomarker of vitamin E status in relation to oxidative stress conditions.

Watercress supplementation in diet reduces lymphocyte DNA damage and alters blood antioxidant status in healthy adults

Background: Cruciferous vegetable (CV) consumption is associated with a reduced risk of several cancers in epidemiologic studies. Objective: The aim of this study was to determine the effects of watercress (a CV) supplementation on biomarkers related to cancer risk in healthy adults. Design: A single-blind, randomized, crossover study was conducted in 30 men and 30 women (30 smokers and 30 nonsmokers) with a mean age of 33 y (range: 19-55 y). The subjects were fed 85 g raw watercress daily for 8 wk in addition to their habitual diet. The effect of supplementation was measured on a range of endpoints, including DNA damage in lymphocytes (with the comet assay), activity of detoxifying enzymes (glutathione peroxidase and superoxide dismutase) in erythrocytes, plasma antioxidants (retinol, ascorbic acid, a-tocopherol, lutein, and beta-carotene), plasma total antioxidant status with the use of the ferric reducing ability of plasma assay, and plasma lipid profile. Results: Watercress supplementation (active compared with control phase) was associated with reductions in basal DNA damage (by 17%; P = 0.03), in basal plus oxidative purine DNA damage (by 23.9%; P = 0.002), and in basal DNA damage in response to ex vivo hydrogen peroxide challenge (by 9.4%; P = 0.07). Beneficial changes seen after watercress intervention were greater and more significant in smokers than in nonsmokers. Plasma lutein and P-carotene increased significantly by 100% and 33% (P < 0.001), respectively, after watercress supplementation. Conclusion: The results support the theory that consumption of watercress can be linked to a reduced risk of cancer via decreased damage to DNA and possible modulation of antioxidant status by increasing carotenoid concentrations.

CAMCR: Computer-Assisted Mixture model analysis for Capture–Recapture count data

Population size estimation with discrete or nonparametric mixture models is considered, and reliable ways of construction of the nonparametric mixture model estimator are reviewed and set into perspective. Construction of the maximum likelihood estimator of the mixing distribution is done for any number of components up to the global nonparametric maximum likelihood bound using the EM algorithm. In addition, the estimators of Chao and Zelterman are considered with some generalisations of Zelterman’s estimator. All computations are done with CAMCR, a special software developed for population size estimation with mixture models. Several examples and data sets are discussed and the estimators illustrated. Problems using the mixture model-based estimators are highlighted.