Ratio plot and ratio regression with applications to social and medical sciences

We consider count data modeling, in particular, the zero-truncated case as it arises naturally in capture–recapture modeling as the marginal distribution of the count of identifications of the members of a target population. Whereas in wildlife ecology these distributions are often of a well-defined type, this is less the case for social and medical science applications since study types are often entirely observational. Hence, in these applications, violations of the assumptions underlying closed capture–recapture are more likely to occur than in carefully designed capture–recapture experiments. As a consequence, the marginal count distribution might be rather complex. The purpose of this note is to sketch some of the major ideas in the recent developments in ratio plotting and ratio regression designed to explore the pattern of the distribution underlying the capture process. Ratio plotting and ratio regression are based upon considering the ratios of neighboring probabilities which can be estimated by ratios of observed frequencies. Frequently, these ratios show patterns which can be easily modeled by a regression model. The fitted regression model is then used to predict the frequency of hidden zero counts. Particular attention is given to regression models corresponding to the negative binomial, multiplicative binomial and the Conway–Maxwell–Poisson distribution

A flexible ratio regression approach for zero-truncated capture–recapture counts

Capture–recapture methods are used to estimate the size of a population of interest which is only partially observed. In such studies, each member of the population carries a count of the number of times it has been identified during the observational period. In real-life applications, only positive counts are recorded, and we get a truncated at zero-observed distribution. We need to use the truncated count distribution to estimate the number of unobserved units. We consider ratios of neighboring count probabilities, estimated by ratios of observed frequencies, regardless of whether we have a zero-truncated or an untruncated distribution. Rocchetti et al. (2011) have shown that, for densities in the Katz family, these ratios can be modeled by a regression approach, and Rocchetti et al. (2014) have specialized the approach to the beta-binomial distribution. Once the regression model has been estimated, the unobserved frequency of zero counts can be simply derived. The guiding principle is that it is often easier to find an appropriate regression model than a proper model for the count distribution. However, a full analysis of the connection between the regression model and the associated count distribution has been missing. In this manuscript, we fill the gap and show that the regression model approach leads, under general conditions, to a valid count distribution; we also consider a wider class of regression models, based on fractional polynomials. The proposed approach is illustrated by analyzing various empirical applications, and by means of a simulation study

Estimating the size of undetected cases of the COVID-19 outbreak in Europe: An upper bound estimator

Under embargo until: 2021-12-23Background While the number of detected COVID-19 infections are widely available, an understanding of the extent of undetected cases is urgently needed for an effective tackling of the pandemic. The aim of this work is to estimate the true number of COVID-19 (detected and undetected) infections in several European countries. The question being asked is: How many cases have actually occurred? Methods We propose an upper bound estimator under cumulative data distributions, in an open population, based on a day-wise estimator that allows for heterogeneity. The estimator is data-driven and can be easily computed from the distributions of daily cases and deaths. Uncertainty surrounding the estimates is obtained using bootstrap methods. Results We focus on the ratio of the total estimated cases to the observed cases at April 17th. Differences arise at the country level, and we get estimates ranging from the 3.93 times of Norway to the 7.94 times of France. Accurate estimates are obtained, as bootstrap-based intervals are rather narrow. Conclusions Many parametric or semi-parametric models have been developed to estimate the population size from aggregated counts leading to an approximation of the missed population and/or to the estimate of the threshold under which the number of missed people cannot fall (i.e. a lower bound). Here, we provide a methodological contribution introducing an upper bound estimator and provide reliable estimates on the dark number, i.e. how many undetected cases are going around for several European countries, where the epidemic spreads differently.publishedVersio

Моделювання квазіідеальних полів для тонких просторово викривлених анізотропних пластів

Розглядається задача моделювання квазіідеальної фільтраційної течії у деякому неоднорідному анізотропному пористому просторово викривленому пласті, обмеженому двома еквіпотенціальними поверхнями-стінками та чотирма поверхнями течії. Проведено її апроксимацію деяким ''усередненим'' плоским аналогом. На цій основі і з використанням розроблених числових методів квазіконформних відображень побудовано алгоритм її розв'язання.We consider the modeling of quasiideal flow for a heterogeneous anisotropic porous spatially curved layer, which is restricted by two equipotential surfaces and four stream surfaces. We approximate it by some averaged plane analogue. On this basis with the use of developed numerical methods of quasiconformal mappings, we build an algorithm for its solution

Recent developments in life and social science applications of capture–recapture methods.

Over the last 20 years capture-recapture methods have experienced important developments, in particular in their applications in the life and social sciences. It appears appropriate to take a closer look at some of these developments. A recent conference entitled Recent Developments in Capture-Recapture Methods and their Applications was held in 2007 at The University of Reading. A special issue focusing on applications mainly in the Biological Sciences appeared elsewhere (Böhning 2008), whereas in this special topic we would like to focus more on life and social science applications. The capture-recapture or mark-and-recapture methodology goes back to the Biological/Ecological Sciences with the work of Lincoln and Petersen. About one hundred and ten years ago Petersen (1896) published his landmark paper suggesting what later became known as the Lincoln-Petersen estimator, since it was also independently developed b

Delayed antibiotic prescribing for respiratory tract infections: protocol of an individual patient data meta-analysis

Introduction Delayed prescribing can be a useful strategy to reduce antibiotic prescribing, but it is not clear for whom delayed prescribing might be effective. This protocol outlines an individual patient data (IPD) meta-analysis of randomised controlled trials (RCTs) and observational cohort studies to explore the overall effect of delayed prescribing and identify key patient characteristics that are associated with efficacy of delayed prescribing. Methods and analysis A systematic search of the databases Cochrane Central Register of Controlled Trials, Ovid MEDLINE, Ovid Embase, EBSCO CINAHL Plus and Web of Science was conducted to identify relevant studies from inception to October 2017. Outcomes of interest include duration of illness, severity of illness, complication, reconsultation and patient satisfaction. Study authors of eligible papers will be contacted and invited to contribute raw IPD data. IPD data will be checked against published data, harmonised and aggregated to create one large IPD database. Multilevel regression will be performed to explore interaction effects between treatment allocation and patient characteristics. The economic evaluation will be conducted based on IPD from the combined trial and observational studies to estimate the differences in costs and effectiveness for delayed prescribing compared with normal practice. A decision model will be developed to assess potential savings and cost-effectiveness in terms of reduced antibiotic usage of delayed prescribing and quality-adjusted life years. Ethics and dissemination Ethical approval was obtained from the University of Southampton Faculty of Medicine Research Ethics Committee (Reference number: 30068). Findings of this study will be published in peer-reviewed academic journals as well as General Practice trade journals and will be presented at national and international conferences. The results will have important public health implications, shaping the way in which antibiotics are prescribed in the future and to whom delayed prescriptions are issued

Renewed:Protocol for a randomised controlled trial of a digital intervention to support quality of life in cancer survivors

International audienceIntroduction Low quality of life is common in cancer survivors. Increasing physical activity, improving diet, supporting psychological well-being and weight loss can improve quality of life in several cancers and may limit relapse. The aim of the randomised controlled trial outlined in this protocol is to examine whether a digital intervention (Renewed), with or without human support, can improve quality of life in cancer survivors. Renewed provides support for increasing physical activity, managing difficult emotions, eating a healthier diet and weight management.Methods and analysis A randomised controlled trial is being conducted comparing usual care, access to Renewed or access to Renewed with brief human support. Cancer survivors who have had colorectal, breast or prostate cancer will be identified and invited through general practice searches and mail-outs. Participants are asked to complete baseline measures immediately after screening and will then be randomised to a study group; this is all completed on the Renewed website. The primary outcome is quality of life measured by the European Organization for Research and Treatment of Cancer QLQ-c30. Secondary outcomes include anxiety and depression, fear of cancer recurrence, general well-being, enablement and items relating to costs for a health economics analysis. Process measures include perceptions of human support, intervention usage and satisfaction, and adherence to behavioural changes. Qualitative process evaluations will be conducted with patients and healthcare staff providing support.Ethics and dissemination The trial has been approved by the NHS Research Ethics Committee (Reference 18/NW/0013). The results of this trial will be published in peer-reviewed journals and through conference presentations.Trial registration number ISRCTN96374224; Pre-results

Meta-analysis and meta-modelling for diagnostic problems

BackgroundA proportional hazards measure is suggested in the context of analyzing SROC curves that arise in the meta–analysis of diagnostic studies. The measure can be motivated as a special model: the Lehmann model for ROC curves. The Lehmann model involves study–specific sensitivities and specificities and a diagnostic accuracy parameter which connects the two.MethodsA study–specific model is estimated for each study, and the resulting study-specific estimate of diagnostic accuracy is taken as an outcome measure for a mixed model with a random study effect and other study-level covariates as fixed effects. The variance component model becomes estimable by deriving within-study variances, depending on the outcome measure of choice. In contrast to existing approaches – usually of bivariate nature for the outcome measures – the suggested approach is univariate and, hence, allows easily the application of conventional mixed modelling.ResultsSome simple modifications in the SAS procedure proc mixed allow the fitting of mixed models for meta-analytic data from diagnostic studies. The methodology is illustrated with several meta–analytic diagnostic data sets, including a meta–analysis of the Mini–Mental State Examination as a diagnostic device for dementia and mild cognitive impairment.ConclusionsThe proposed methodology allows us to embed the meta-analysis of diagnostic studies into the well–developed area of mixed modelling. Different outcome measures, specifically from the perspective of whether a local or a global measure of diagnostic accuracy should be applied, are discussed as well. In particular, variation in cut-off value is discussed together with recommendations on choosing the best cut-off value. We also show how this problem can be addressed with the proposed methodology

On the equivalence of one-inflated zero-truncated and zero-truncated one-inflated count data likelihoods

One-inflation in zero-truncated count data has recently found considerable attention. There are currently two views in the literature. In the first approach, the untruncated model is considered as one-inflated whereas in the second approach the truncated model is viewed as one-inflated. Here, we show that both models have identical model spaces as well as identical maximum likelihoods. Consequences of population size estimation are illuminated, and the findings are illustrated at hand of two case studies