A covariate adjustment for zero-truncated approaches to estimating the size of hidden and elusive populations

In this paper we consider the estimation of population size from onesource capture–recapture data, that is, a list in which individuals can potentially be found repeatedly and where the question is how many individuals are missed by the list. As a typical example, we provide data from a drug user study in Bangkok from 2001 where the list consists of drug users who repeatedly contact treatment institutions. Drug users with 1, 2, 3, . . . contacts occur, but drug users with zero contacts are not present, requiring the size of this group to be estimated. Statistically, these data can be considered as stemming from a zero-truncated count distribution.We revisit an estimator for the population size suggested by Zelterman that is known to be robust under potential unobserved heterogeneity. We demonstrate that the Zelterman estimator can be viewed as a maximum likelihood estimator for a locally truncated Poisson likelihood which is equivalent to a binomial likelihood. This result allows the extension of the Zelterman estimator by means of logistic regression to include observed heterogeneity in the form of covariates. We also review an estimator proposed by Chao and explain why we are not able to obtain similar results for this estimator. The Zelterman estimator is applied in two case studies, the first a drug user study from Bangkok, the second an illegal immigrant study in the Netherlands. Our results suggest the new estimator should be used, in particular, if substantial unobserved heterogeneity is present.

Modifying willingness to pay estimates where respondents mis-report their preferences

The likelihood for the Logit model is modified, so as to take account of uncertainty associated with mis-reporting in stated preference experiments estimating willingness to pay (WTP). Monte Carlo results demonstrate the bias imparted to estimates where there is mis-reporting. The approach is applied to a data set examining consumer preferences for food produced employing a nonpesticide technology. Our modified approach leads to WTP that are substantially downwardly revised.

The use of bootstrapped Malmquist indices to reassess productivity change findings: an application to a sample of Polish farms

This article assesses the extent to which sampling variation affects findings about Malmquist productivity change derived using data envelopment analysis (DEA), in the first stage by calculating productivity indices and in the second stage by investigating the farm-specific change in productivity. Confidence intervals for Malmquist indices are constructed using Simar and Wilson's (1999) bootstrapping procedure. The main contribution of this article is to account in the second stage for the information in the second stage provided by the first-stage bootstrap. The DEA SEs of the Malmquist indices given by bootstrapping are employed in an innovative heteroscedastic panel regression, using a maximum likelihood procedure. The application is to a sample of 250 Polish farms over the period 1996 to 2000. The confidence intervals' results suggest that the second half of 1990s for Polish farms was characterized not so much by productivity regress but rather by stagnation. As for the determinants of farm productivity change, we find that the integration of the DEA SEs in the second-stage regression is significant in explaining a proportion of the variance in the error term. Although our heteroscedastic regression results differ with those from the standard OLS, in terms of significance and sign, they are consistent with theory and previous research.

A longitudinal study of sero-conversion to tick-borne pathogens in smallholder dairy youngstock in Tanzania

A longitudinal study of sero-conversion of youngstock to the tick-borne pathogens Theileria parva, T mutans, Anaplasma marginale, Babesia bigemina and B. bovis was conducted over two years on smallholder dairy farms in Tanga region, Tanzania. There was evidence of maternal antibodies to all tick-borne pathogens in animals less than 18 weeks of age. Seroprevalence increased as expected with age in animals older than this but seroprevalence profiles underestimated the force of infection due to waning antibody levels between samplings. By the end of the 2-year study, less than 50% of study animals had seroconverted to each of the tick-borne pathogens investigated, consistent with the low levels of tick attachment observed on the study animals. Some associations between seroconversion to tick-borne pathogens, and counts of their known tick vectors on the animals, were identified as expected. However, some were not, suggesting that counts of some tick species may act as an index of rates of attachment of other vector species. Variation in acaricide treatment frequencies was not associated with variations in tick-borne pathogen seroprevalence suggesting that acaricides may be used more frequently than necessary on many farms. Most animals were zero-grazed, a management system associated with a significantly lower likelihood that animals seroconverted to any tick-borne pathogen exceptA. marginale. Seroprevalence varied locally with farm location (particularly for Babesia spp.) but was not well predicted by indices of ecological conditions. Our findings suggest that attempts to achieve a state of 'endemic stability' for tick-bome pathogens may be unreasonable on the smallholder dairy farms studied but reductions in the frequency of use of acaricides may be possible following prospective studies of effects on mortality and morbidity due to tick-bome pathogens. (c) 2005 Elsevier B.V. All rights reserved.

Mutations in H5N1 influenza virus hemagglutinin that confer binding to human tracheal airway epithelium

The emergence in 2009 of a swine-origin H1N1 influenza virus as the first pandemic of the 21st Century is a timely reminder of the international public health impact of influenza viruses, even those associated with mild disease. The widespread distribution of highly pathogenic H5N1 influenza virus in the avian population has spawned concern that it may give rise to a human influenza pandemic. The mortality rate associated with occasional human infection by H5N1 virus approximates 60%, suggesting that an H5N1 pandemic would be devastating to global health and economy. To date, the H5N1 virus has not acquired the propensity to transmit efficiently between humans. The reasons behind this are unclear, especially given the high mutation rate associated with influenza virus replication. Here we used a panel of recombinant H5 hemagglutinin (HA) variants to demonstrate the potential for H5 HA to bind human airway epithelium, the predominant target tissue for influenza virus infection and spread. While parental H5 HA exhibited limited binding to human tracheal epithelium, introduction of selected mutations converted the binding profile to that of a current human influenza strain HA. Strikingly, these amino-acid changes required multiple simultaneous mutations in the genomes of naturally occurring H5 isolates. Moreover, H5 HAs bearing intermediate sequences failed to bind airway tissues and likely represent mutations that are an evolutionary "dead end." We conclude that, although genetic changes that adapt H5 to human airways can be demonstrated, they may not readily arise during natural virus replication. This genetic barrier limits the likelihood that current H5 viruses will originate a human pandemic.

Extending Zelterman’s approach for robust estimation of population size to zero-truncated clustered data

Estimation of population size with missing zero-class is an important problem that is encountered in epidemiological assessment studies. Fitting a Poisson model to the observed data by the method of maximum likelihood and estimation of the population size based on this fit is an approach that has been widely used for this purpose. In practice, however, the Poisson assumption is seldom satisfied. Zelterman (1988) has proposed a robust estimator for unclustered data that works well in a wide class of distributions applicable for count data. In the work presented here, we extend this estimator to clustered data. The estimator requires fitting a zero-truncated homogeneous Poisson model by maximum likelihood and thereby using a Horvitz-Thompson estimator of population size. This was found to work well, when the data follow the hypothesized homogeneous Poisson model. However, when the true distribution deviates from the hypothesized model, the population size was found to be underestimated. In the search of a more robust estimator, we focused on three models that use all clusters with exactly one case, those clusters with exactly two cases and those with exactly three cases to estimate the probability of the zero-class and thereby use data collected on all the clusters in the Horvitz-Thompson estimator of population size. Loss in efficiency associated with gain in robustness was examined based on a simulation study. As a trade-off between gain in robustness and loss in efficiency, the model that uses data collected on clusters with at most three cases to estimate the probability of the zero-class was found to be preferred in general. In applications, we recommend obtaining estimates from all three models and making a choice considering the estimates from the three models, robustness and the loss in efficiency. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Constrained models of evolution lead to improved prediction of functional linkage from correlated gain and loss of genes

Motivation: We compare phylogenetic approaches for inferring functional gene links. The approaches detect independent instances of the correlated gain and loss of pairs of genes from species' genomes. We investigate the effect on results of basing evidence of correlations on two phylogenetic approaches, Dollo parsminony and maximum likelihood (ML). We further examine the effect of constraining the ML model by fixing the rate of gene gain at a low value, rather than estimating it from the data. Results: We detect correlated evolution among a test set of pairs of yeast (Saccharomyces cerevisiae) genes, with a case study of 21 eukaryotic genomes and test data derived from known yeast protein complexes. If the rate at which genes are gained is constrained to be low, ML achieves by far the best results at detecting known functional links. The model then has fewer parameters but it is more realistic by preventing genes from being gained more than once. Availability: BayesTraits by M. Pagel and A. Meade, and a script to configure and repeatedly launch it by D. Barker and M. Pagel, are available at http://www.evolution.reading.ac.uk .

A note on the accuracy of PAC-likelihood inference with microsatellite data

Stephens and Donnelly have introduced a simple yet powerful importance sampling scheme for computing the likelihood in population genetic models. Fundamental to the method is an approximation to the conditional probability of the allelic type of an additional gene, given those currently in the sample. As noted by Li and Stephens, the product of these conditional probabilities for a sequence of draws that gives the frequency of allelic types in a sample is an approximation to the likelihood, and can be used directly in inference. The aim of this note is to demonstrate the high level of accuracy of "product of approximate conditionals" (PAC) likelihood when used with microsatellite data. Results obtained on simulated microsatellite data show that this strategy leads to a negligible bias over a wide range of the scaled mutation parameter theta. Furthermore, the sampling variance of likelihood estimates as well as the computation time are lower than that obtained with importance sampling on the whole range of theta. It follows that this approach represents an efficient substitute to IS algorithms in computer intensive (e.g. MCMC) inference methods in population genetics. (c) 2006 Elsevier Inc. All rights reserved.

A practical approach to a multi-level analysis with a sparse binary outcome within a large surgical trial

Objectives: To assess the potential source of variation that surgeon may add to patient outcome in a clinical trial of surgical procedures. Methods: Two large (n = 1380) parallel multicentre randomized surgical trials were undertaken to compare laparoscopically assisted hysterectomy with conventional methods of abdominal and vaginal hysterectomy; involving 43 surgeons. The primary end point of the trial was the occurrence of at least one major complication. Patients were nested within surgeons giving the data set a hierarchical structure. A total of 10% of patients had at least one major complication, that is, a sparse binary outcome variable. A linear mixed logistic regression model (with logit link function) was used to model the probability of a major complication, with surgeon fitted as a random effect. Models were fitted using the method of maximum likelihood in SAS((R)). Results: There were many convergence problems. These were resolved using a variety of approaches including; treating all effects as fixed for the initial model building; modelling the variance of a parameter on a logarithmic scale and centring of continuous covariates. The initial model building process indicated no significant 'type of operation' across surgeon interaction effect in either trial, the 'type of operation' term was highly significant in the abdominal trial, and the 'surgeon' term was not significant in either trial. Conclusions: The analysis did not find a surgeon effect but it is difficult to conclude that there was not a difference between surgeons. The statistical test may have lacked sufficient power, the variance estimates were small with large standard errors, indicating that the precision of the variance estimates may be questionable.

Likelihood-based estimation of microsatellite mutation rates

Microsatellites are widely used in genetic analyses, many of which require reliable estimates of microsatellite mutation rates, yet the factors determining mutation rates are uncertain. The most straightforward and conclusive method by which to study mutation is direct observation of allele transmissions in parent-child pairs, and studies of this type suggest a positive, possibly exponential, relationship between mutation rate and allele size, together with a bias toward length increase. Except for microsatellites on the Y chromosome, however, previous analyses have not made full use of available data and may have introduced bias: mutations have been identified only where child genotypes could not be generated by transmission from parents' genotypes, so that the probability that a mutation is detected depends on the distribution of allele lengths and varies with allele length. We introduce a likelihood-based approach that has two key advantages over existing methods. First, we can make formal comparisons between competing models of microsatellite evolution; second, we obtain asymptotically unbiased and efficient parameter estimates. Application to data composed of 118,866 parent-offspring transmissions of AC microsatellites supports the hypothesis that mutation rate increases exponentially with microsatellite length, with a suggestion that contractions become more likely than expansions as length increases. This would lead to a stationary distribution for allele length maintained by mutational balance. There is no evidence that contractions and expansions differ in their step size distributions.

Perspectives on experiences of innovation: the development of an assessment methodology appropriate to construction project organizations

The UK construction industry is in the process of trying to adopt a new culture based on the large-scale take up of innovative practices. Through the Demonstration Project process many organizations are implementing changed practices and learning from the experiences of others. This is probably the largest experiment in innovation in any industry in recent times. The long-term success will be measured by the effectiveness of embedding the new practices in the organization. As yet there is no recognized approach to measuring the receptivity of the organization to the innovation process as an indication of the likelihood of long-term development. The development of an appropriate approach is described here. Existing approaches to the measurement of the take up of innovation were reviewed and where appropriate used as the base for the development of a questionnaire. The questionnaire could be applicable to multi-organizational construction project situations such that the output could determine an individual organization's innovative practices via an innovation scorecard, a project team's approach or it could be used to survey a wide cross-section of the industry.

Comparison of two methods of presenting risk information to patients about the side effects of medicines

Objective: To determine whether the use of verbal descriptors suggested by the European Union (EU) such as "common" (1-10% frequency) and "rare" (0.01-0.1%) effectively conveys the level of risk of side effects to people taking a medicine. Design: Randomised controlled study with unconcealed allocation. Participants: 120 adults taking simvastatin or atorvastatin after cardiac surgery or myocardial infarction. Setting: Cardiac rehabilitation clinics at two hospitals in Leeds, UK. Intervention: A written statement about one of the side effects of the medicine (either constipation or pancreatitis). Within each side effect condition half the patients were given the information in verbal form and half in numerical form (for constipation, "common" or 2.5%; for pancreatitis, "rare" or 0.04%). Main outcome measure: The estimated likelihood of the side effect occurring. Other outcome measures related to the perceived severity of the side effect, its risk to health, and its effect on decisions about whether to take the medicine. Results: The mean likelihood estimate given for the constipation side effect was 34.2% in the verbal group and 8.1% in the numerical group; for pancreatitis it was 18% in the verbal group and 2.1% in the numerical group. The verbal descriptors were associated with more negative perceptions of the medicine than their equivalent numerical descriptors. Conclusions: Patients want and need understandable information about medicines and their risks and benefits. This is essential if they are to become partners in medicine taking. The use of verbal descriptors to improve the level of information about side effect risk leads to overestimation of the level of harm and may lead patients to make inappropriate decisions about whether or not they take the medicine.

Research into anxiety of childhood: playing catch-up (to Olympic standard)

This special issue is the culmination of an ESRC seminar series grant awarded to the authors of this editorial. We named the seminar series CATTS (Child Anxiety, Theory and Treatment Seminars) and it took the form of six highly stimulating, one-day seminars on the subject of child anxiety, with participants from clinical and academic backgrounds and from Great Britain, Europe, the USA and Australia. Most of the authors in this publication, and a sister special issue in Cognitions and Emotion (2008), participated in the CATTS series.

Expressing medicine side effects: assessing the effectiveness of absolute risk, relative risk, and number needed to harm, and the provision of baseline risk information

Objective: To assess the effectiveness of absolute risk, relative risk, and number needed to harm formats for medicine side effects, with and without the provision of baseline risk information. Methods: A two factor, risk increase format (relative, absolute and NNH) x baseline (present/absent) between participants design was used. A sample of 268 women was given a scenario about increase in side effect risk with third generation oral contraceptives, and were required to answer written questions to assess their understanding, satisfaction, and likelihood of continuing to take the drug. Results: Provision of baseline information significantly improved risk estimates and increased satisfaction, although the estimates were still considerably higher than the actual risk. No differences between presentation formats were observed when baseline information was presented. Without baseline information, absolute risk led to the most accurate performance. Conclusion: The findings support the importance of informing people about baseline level of risk when describing risk increases. In contrast, they offer no support for using number needed to harm. Practice implications: Health professionals should provide baseline risk information when presenting information about risk increases or decreases. More research is needed before numbers needed to harm (or treat) should be given to members of the general populations. (c) 2005 Elsevier Ireland Ltd. All rights reserved.