ABSTRACT. We investigate non-parametric estimation of a monotone baseline hazard and a decreasing baseline density within the Cox model. Two estimators of a non-decreasing baseline hazard function are proposed. We derive the non-parametric maximum likelihood estimator and consider a Grenander type estimator, defined as the left-hand slope of the greatest convex minorant of the Breslow estimator. We demonstrate that the two estimators are strongly consistent and asymptotically equivalent and derive their common limit distribution at a fixed point. Both estimators of a non-increasing baseline hazard and their asymptotic properties are obtained in a similar manner. Furthermore, we introduce a Grenander type estimator for a non-increasing baseline density, defined as the left-hand slope of the least concave majorant of an estimator of the baseline cumulative distribution function, derived from the Breslow estimator. We show that this estimator is strongly consistent and derive its asymptotic distribution at a fixed point.

Expert elicitation is deployed when data are absent or uninformative and critical decisions must be made. In designing an expert elicitation, most practitioners seek to achieve best practice while balancing practical constraints. The choices made influence the required time and effort investment, the quality of the elicited data, experts' engagement, the defensibility of results, and the acceptability of resulting decisions. This piece outlines some of the common choices practitioners encounter when designing and conducting an elicitation. We discuss the evidence supporting these decisions and identify research gaps. This will hopefully allow practitioners to better navigate the literature, and will inspire the expert judgement research community to conduct well powered, replicable experiments that properly address the research gaps identified.

Illnesses transmitted by food and water cause a major disease burden in the United States despite advancements in food safety, water treatment, and sanitation. We report estimates from a structured expert judgment study using 48 experts who applied Cooke’s classical model of the proportion of disease attributable to 5 major transmission pathways (foodborne, waterborne, person-to-person, animal contact, and environmental) and 6 subpathways (food handler–related, under foodborne; recreational, drinking, and nonrecreational/nondrinking, under waterborne; and presumed person-to-person-associated and presumed animal contact-associated, under environmental). Estimates for 33 pathogens were elicited, including bacteria such as Salmonella enterica, Campylobacter spp., Legionella spp., and Pseudomonas spp.; protozoa such as Acanthamoeba spp., Cyclospora cayetanensis , and Naegleria fowleri ; and viruses such as norovirus, rotavirus, and hepatitis A virus. The results highlight the importance of multiple pathways in the transmission of the included pathogens and can be used to guide prioritization of public health interventions.

Although estimates of regression coefficients depend on other independent variables, there is no assumed dependence relationship between coefficient estimators and the change in value of other variables as in the case of BNs. Nonetheless, this analysis suggests that regression is still more accurate or at least as accurate as BNs for risk estimation for both LRRs and SP tumors.

The age of researchers is a critical factor necessary to study the bibliometric characteristics of the scholars that produce new knowledge. In bibliometric studies, the age of scientific authors is generally missing; however, the year of the first publication is frequently considered as a proxy of the age of researchers. In this article, we investigate what are the most important bibibliometric factors that can be used to predict the age of researchers (birth and PhD age). Using a dataset of 3574 researchers from Québec for whom their Web of Science publications, year of birth and year of their PhD are known, our analysis falls under the linear regression setting and focuses on investigating the predictive power of various regression models rather than data fitting, considering also a breakdown by fields. The year of first publication proves to be the best linear predictor for the age of researchers. When using simple linear regression models, predicting birth and PhD years result in an error of about 3.7 years and 3.9 years, respectively. Including other bibliometric data marginally improves the predictive power of the regression models. A validation analysis for the field breakdown shows that the average length of the prediction intervals vary from 2.5 years for Basic Medical Sciences (for birth years) up to almost 10 years for Education (for PhD years). The average models perform significantly better than the models using individual observations. Nonetheless, the high variability of data and the uncertainty inherited by the models advice to caution when using linear regression models for predicting the age of researchers.

Research careers are typically envisioned as a single path in which researchers start being one of a large number of researchers working under the guidance of one or more experienced scientists and, if they are successful, end with the individual leading their own research group and training future generations of scientists. Here we study the author contribution statements of published research papers in order to explore possible biases and disparities in career trajectories in science. We used Bayesian networks to train a prediction model based on a dataset of 70,694 publications from PLoS journals, which included 347,136 distinct authors and their associated contribution statements. This model was used to predict the contributions of 222,925 authors in 6,236,239 publications, and to apply a robust archetypal analysis to profile scientists across four career stages: junior, early-career, mid-career and late-career. All three of the archetypes we found - leader, specialized, and supporting - were encountered for early-career and mid-career researchers. Junior researchers displayed only two archetypes (specialized, and supporting), as did late-career researchers (leader and supporting). Scientists assigned to the leader and specialized archetypes tended to have longer careers than those assigned to the supporting archetype. We also observed consistent gender bias at all stages: the majority of male scientists belonged to the leader archetype, while the larger proportion of women belonged to the specialized archetype, especially for early-career and mid-career researchers.

The Classical Model (CM) or Cooke's method for performing Structured Expert Judgment (SEJ) is the best known method that promotes expert performance evaluation when aggregating experts assessments of uncertain quantities. Assessing experts' performance in quantifying uncertainty involves two scores in CM, the calibration score (or statistical accuracy) and the information score. The two scores combine into overall scores, which, in turn, yield weights for a performance-based aggregation of experts' opinion. The method is fairly demanding, and therefore carrying out a SEJ elicitation with CM requires careful consideration. This chapter aims to address methodological and practical aspects of CM into a comprehensive overview of the CM elicitation process. It complements the chapter "Elicitation in the Classical Model" in the book Elicitation [27]. Nonetheless, we regard this chapter as a stand-alone material, hence some concepts and definitions will be repeated, for the sake of completeness.

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