Beyond tail median and conditional tail expectation: Extreme risk estimation using tail Lp-optimization

The conditional tail expectation (CTE) is an indicator of tail behavior that takes into account both the frequency and magnitude of a tail event. However, the asymptotic normality of its empirical estimator requires that the underlying distribution possess a finite variance; this can be a strong restriction in actuarial and financial applications. A valuable alternative is the median shortfall (MS), although it only gives information about the frequency of a tail event. We construct a class of tail L^p-medians encompassing the MS and CTE. For p in (1,2), a tail L^p-median depends on both the frequency and magnitude of tail events, and its empirical estimator is, within the range of the data, asymptotically normal under a condition weaker than a finite variance. We extrapolate this estimator and another technique to extreme levels using the heavy-tailed framework. The estimators are showcased on a simulation study and on real fire insurance data.     

Human Salmonellosis: Estimation of Dose-Illness from Outbreak Data

The quantification of the relationship between the amount of microbial organisms ingested and a specific outcome such as infection, illness, or mortality is a key aspect of quantitative risk assessment. A main problem in determining such dose-response models is the availability of appropriate data. Human feeding trials have been criticized because only young healthy volunteers are selected to participate and low doses, as often occurring in real life, are typically not considered. Epidemiological outbreak data are considered to be more valuable, but are more subject to data uncertainty. In this article, we model the dose-illness relationship based on data of 20 Salmonella outbreaks, as discussed by the World Health Organization. In particular, we model the dose-illness relationship using generalized linear mixed models and fractional polynomials of dose. The fractional polynomial models are modified to satisfy the properties of different types of dose-illness models as proposed by Teunis et al . Within these models, differences in host susceptibility (susceptible versus normal population) are modeled as fixed effects whereas differences in serovar type and food matrix are modeled as random effects. In addition, two bootstrap procedures are presented. A first procedure accounts for stochastic variability whereas a second procedure accounts for both stochastic variability and data uncertainty. The analyses indicate that the susceptible population has a higher probability of illness at low dose levels when the combination pathogen-food matrix is extremely virulent and at high dose levels when the combination is less virulent. Furthermore, the analyses suggest that immunity exists in the normal population but not in the susceptible population.     

Impact of physical activity and sedentary behaviour on fall risks in older people: a systematic review and meta-analysis of observational studies

The objective of this work was to summarise and evaluate the evidence showing that physical activity is a protector factor as regards falls in older people. Relevant studies were identified through a systematic search in the MEDLINE and Cochrane Library, under the keywords of accidental fall/numerical data and risk factors, and with the bibliographies of retrieved papers. The combined odds ratio (OR) [95% confidence interval] for physical activity was 0.75 [0.64, 0.88] with moderate heterogeneity (I ²?=?33%). For fall injury, it was 0.59 [0.47, 0.74] and, for falls in general, it rose to 0.94 [0.76, 1.17] with nil heterogeneity. The combined OR for sedentary factors was 1.14 [1.10, 1.82] with moderate heterogeneity (I ²?=?36%). Regular physical activity in daily life yields significant reduction in falls in older people, especially falls with injuries.     

Being the best or doing the right thing? An investigation of positional,prosocial and conformist preferences in provision of public goods

Based on a simple theoretical framework, we show that when individuals exhibit positional, prosocial or conformist preferences which are endogenous, the end outcomes in terms of private provision of public goods can differ significantly from traditional neo-classical predictions. Indeed, when a given individual selects a specific subset of preferences according to what others do, he/she will contribute positively to the public good provision. We provide anecdotal evidence to support our theoretical analysis by using data from an Internet survey on a sample of French individuals. Analyses of individual responses confirm our theoretical arguments. For instance, we show that relative concerns matter, that is, for several environmental goods, people might prefer polluting more in absolute terms but less than others in society. Moreover, we also test whether people exhibit a social desirability bias and show that they attribute more (less) positional (prosocial) concerns to others in society.     

Reporting Errors in Siblings’ Survival Histories and Their Impact on Adult Mortality Estimates: Results From a Record Linkage Study in Senegal

Estimates of adult mortality in countries with limited vital registration (e.g., sub-Saharan Africa) are often derived from information about the survival of a respondent’s siblings. We evaluated the completeness and accuracy of such data through a record linkage study conducted in Bandafassi, located in southeastern Senegal. We linked at the individual level retrospective siblings’ survival histories (SSH) reported by female respondents (n = 268) to prospective mortality data and genealogies collected through a health and demographic surveillance system (HDSS). Respondents often reported inaccurate lists of siblings. Additions to these lists were uncommon, but omissions were frequent: respondents omitted 3.8 % of their live sisters, 9.1 % of their deceased sisters, and 16.6 % of their sisters who had migrated out of the DSS area. Respondents underestimated the age at death of the siblings they reported during the interview, particularly among siblings who had died at older ages (≥45 years). Restricting SSH data to person-years and events having occurred during a recent reference period reduced list errors but not age and date errors. Overall, SSH data led to a 20 % underestimate of ₄₅ q ₁₅ relative to HDSS data. Our study suggests new quality improvement strategies for SSH data and demonstrates the potential use of HDSS data for the validation of “unconventional” demographic techniques.     

Local influence diagnostics for incomplete overdispersed longitudinal counts

We develop local influence diagnostics to detect influential subjects when generalized linear mixed models are fitted to incomplete longitudinal overdispersed count data. The focus is on the influence stemming from the dropout model specification. In particular, the effect of small perturbations around an MAR specification are examined. The method is applied to data from a longitudinal clinical trial in epileptic patients. The effect on models allowing for overdispersion is contrasted with that on models that do not.     

Integrated nested Laplace approximation for the analysis of count data via the combined model: A simulation study

The combined model accounts for different forms of extra-variability and has traditionally been applied in the likelihood framework, or in the Bayesian setting via Markov chain Monte Carlo. In this article, integrated nested Laplace approximation is investigated as an alternative estimation method for the combined model for count data, and compared with the former estimation techniques. Longitudinal, spatial, and multi-hierarchical data scenarios are investigated in three case studies as well as a simulation study. As a conclusion, integrated nested Laplace approximation provides fast and precise estimation, while avoiding convergence problems often seen when using Markov chain Monte Carlo.     

Local influence diagnostics for generalized linear mixed models with overdispersion

Since the seminal paper by Cook and Weisberg [9 R.D. Cook and S. Weisberg, Residuals and Influence in Regression, Chapman &; Hall, London, 1982. [Google Scholar]], local influence, next to case deletion, has gained popularity as a tool to detect influential subjects and measurements for a variety of statistical models. For the linear mixed model the approach leads to easily interpretable and computationally convenient expressions, not only highlighting influential subjects, but also which aspect of their profile leads to undue influence on the model's fit [17 E. Lesaffre and G. Verbeke, Local influence in linear mixed models, Biometrics 54 (1998), pp. 570–582. doi: 10.2307/3109764[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]]. Ouwens et al. [24 M.J.N.M. Ouwens, F.E.S. Tan, and M.P.F. Berger, Local influence to detect influential data structures for generalized linear mixed models, Biometrics 57 (2001), pp. 1166–1172. doi: 10.1111/j.0006-341X.2001.01166.x[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]] applied the method to the Poisson-normal generalized linear mixed model (GLMM). Given the model's nonlinear structure, these authors did not derive interpretable components but rather focused on a graphical depiction of influence. In this paper, we consider GLMMs for binary, count, and time-to-event data, with the additional feature of accommodating overdispersion whenever necessary. For each situation, three approaches are considered, based on: (1) purely numerical derivations; (2) using a closed-form expression of the marginal likelihood function; and (3) using an integral representation of this likelihood. Unlike when case deletion is used, this leads to interpretable components, allowing not only to identify influential subjects, but also to study the cause thereof. The methodology is illustrated in case studies that range over the three data types mentioned.     

Twinning Rates in Developed Countries: Trends and Explanations

The twinning rate has increased dramatically over the last four decades in developed countries. Two main factors account for this increase: delayed childbearing, as older women tend to have twins more frequently than younger ones, and the expansion of medically assisted reproduction (MAR), which carries an increased probability of multiple births. Using civil registration data, we estimate the share of the increase in twinning rates attributable to the rise in the age at childbearing and to MAR. The effect of MAR is estimated to be about three times as important as the effect of delayed childbearing. Negative health outcomes associated with multiple births and the cost of MAR have raised concerns. We find that in one‐quarter of developed countries with the relevant data, the twinning rate reached a plateau around the early 2000s and decreased thereafter. We examine the reasons for this reversal, in particular changes in MAR policies and practices.