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Objective: We examined how probability of conviction affects the maximum plea sentence mock defendants will accept. Hypothesis: Relying on Prospect Theory (Kahneman & Tversky, 1979), we hypothesized that, relative to the expected value of trial, participants would need increasingly better sentences as conviction probability increased and would settle for sentences worse than the expected value of trial when probability was very low. Method: We manipulated conviction probability and potential trial sentence in a series of three between-subjects experiments, with Amazon Mechanical Turk participants assigned to the role of guilty defendants. Participants were majority White (75-82%) and non-Hispanic (92-94%); approximately half (45-51%) identified as female. Study 1 ( N = 681) explored the effects of conviction probability (.05, .15, .50, .85, .90) and potential trial sentence (5, 20 years) on the maximum sentence accepted in exchange for a plea. Study 2 ( N = 343; X¯age = 37.5) clarified results of Study 1 for the upper range of probabilities for two potential trial sentences (5, 10 years). Study 3 ( N = 1,035; X¯age = 37.6) replicated the effects of probability (.05, .10, .15, .50, .85, .90) and potential trial sentence (5, 10 years). Results: Across all three studies, participants wanted increasingly better deals (relative to the expected value of trial) as conviction probability increased. For example, in Study 3, when probability of conviction was 0.90, plea sentences were, on average, 58% better than the expected value of trial; in contrast, when the probability was 0.05, sentences that were nearly 4 times the expected value of trial were acceptable. Conclusions: The most commonly used model of plea decision-making, Shadow of the Trial (SOT) (Mnookin & Kornhauser, 1979), assumes a direct and constant linear relationship between conviction probability and plea sentence. In contrast, our data suggest that the way conviction probability affects mock defendants' appraisals of plea offers may change across the probability spectrum. These results can facilitate development of a more comprehensive model of plea decision-making. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Rationale: Risky choice can be measured using the risky decision task (RDT). In the RDT, animals choose between a large, risky option that is paired with probabilistic foot shock and a small, safe option that is never paired with shock. To date, studies examining the neurochemical basis of decision-making in the RDT have focused primarily on the dopaminergic system but have not focused on the glutamatergic system, which has been implicated in risky decision-making., Objectives: Because glutamate is known to play a critical role in decision-making, we wanted to determine the contribution of the glutamatergic system to performance in the RDT., Methods: In the experiment, 32 rats (16 male; 16 female) were tested in the RDT. The probability of receiving a foot shock increased across the session (ascending schedule) for half of the rats but decreased across the session (descending schedule) for half of the rats. Following training, rats received injections of the N-methyl-D-aspartate (NMDA) receptor competitive antagonist CGS 19755 (0, 1.0, 2.5, 5.0 mg/kg; s.c.) and the GluN2B-selective antagonist Ro 63-1908 (0, 0.1, 0.3, 1.0 mg/kg; s.c.)., Results: CGS 19755 (2.5 and 5.0 mg/kg) increased risky choice in males and females trained on the ascending schedule. Ro 63-1908 (1.0 mg/kg) decreased risky choice, but only in male rats trained on the ascending schedule., Conclusions: Although NMDA receptor antagonists differentially alter risky choice in the RDT, the current results show that NMDA receptors are an important mediator of decision-making involving probabilistic delivery of positive punishment.

There is growing interest in the use of polygenic risk scores based on genetic variants to predict cancer incidence. The type of metric used to evaluate the predictive performance of polygenic risk scores plays a crucial role in their interpretation. I compare 3 metrics for this evaluation: the area under the receiver operating characteristic curve (AUC), the probability of cancer in a high-risk subset divided by the prevalence of cancer in the population, which I call the subset relative risk (SRR), and the minimum test tradeoff, which is the minimum number of genetic variant ascertainments (one per person) for each correct prediction of cancer to yield a positive expected clinical utility. I show that SRR is a relabeling of AUC. I recommend the minimum test tradeoff for the evaluation of polygenic risk scores because, unlike AUC and SRR, it is directly related to the expected clinical utility., (Published by Oxford University Press 2020. This work is written by US Government employees and is in the public domain in the US.)

We provide methods to estimate the confidence interval for the difference between two relative risks. Letting p 0 , p 1 , and p 2 be the probabilities of an event in three groups (i.e. control, treatment 1, treatment 2), our methods estimate a confidence interval for r  =  p 1 / p 0  -  p 2 / p 0 . We highlight that our methods can handle small sample sizes, covariates, and study populations from multiple strata. We specifically developed these methods for vaccine trials to estimate the difference between two vaccine efficacies, where VE 1  = 1 -  p 1 / p 0 , VE 2  = 1 -  p 2 / p 0 and r  = VE 2  - VE 1 . We showcase our methods by using interim data from one of these trials to suggest that one dose of the human papillomavirus vaccine may be as efficacious as two doses of the vaccine.

New cybersecurity technologies, such as commercial antivirus software (AV), sometimes fail to deliver on their promised benefits. This article develops and tests a revised version of risk homeostasis theory, which suggests that new cybersecurity technologies can sometimes have ill effects on security outcomes in the short run and little-to-no effect over the long run. It tests the preliminary plausibility of four predictions from the revised risk homeostasis theory using new survey data from 1,072 respondents. The estimations suggest the plausible operation of a number of risk homeostasis dynamics: (1) commercial AV users are significantly more likely to self-report a cybersecurity event in the past year than nonusers, even after correcting for potential reverse causality and informational mechanisms; (2) nonusers become somewhat less likely to self-report a cybersecurity event as the perceived riskiness of various e-mail-based behaviors increases, while commercial AV users do not; (3) the negative short-run effect of commercial AV use on cybersecurity outcomes fade over time at a predicted rate of about 7.03 percentage points per year of use; and (4) after five years of use, commercial AV users are statistically indistinguishable from nonusers in terms of their probability of self-reporting a cybersecurity event as perceptions of risky e-mail-based behaviors increase., (© 2020 Society for Risk Analysis.)

Graphs are increasingly recommended for improving decision-making and promoting risk-avoidant behaviors. Graphs that depict only the number of people affected by a risk ("foreground-only" displays) tend to increase perceived risk and risk aversion (e.g., willingness to get vaccinated), as compared to graphs that also depict the number of people at risk for harm ("foreground+background" displays). However, previous research examining these "foreground-only effects" has focused on relatively low-probability risks (<10%), limiting generalizability to communications about larger risks. In two experiments, we systematically investigated the moderating role of probability size on foreground-only effects, using a wide range of probability sizes (from 0.1% to 40%). Additionally, we examined the moderating role of the size of the risk reduction, that is, the extent to which a protective behavior reduces the risk. Across both experiments, foreground-only effects on perceived risk and risk aversion were weaker for larger probabilities. Experiment 2 also revealed that foreground-only effects were weaker for smaller risk reductions, while foreground-only displays decreased understanding of absolute risk magnitudes independently of probability size. These findings suggest that the greater effectiveness of foreground-only versus foreground+background displays for increasing perceived risk and risk aversion diminishes with larger probability sizes and smaller risk reductions. Moreover, if the goal is to promote understanding of absolute risk magnitudes, foreground+background displays should be used rather than foreground-only displays regardless of probability size. Our findings also help to refine and extend existing theoretical accounts of foreground-only effects to situations involving a wide range of probability sizes., (© 2020 Society for Risk Analysis.)

A growing body of research has provided evidence for the foreign language effect on thinking, notably decision-making. Our prior work found reduction of recency effect following positive feedback in a foreign language as compared to the native tongue during even-probability gambling. However, the fundamental mechanisms underlying this effect remain unclear. The present study, therefore, aims to probe into this by engaging Chinese-English bilinguals in a functional magnetic resonance imaging version of our gambling task, which required participants to make decisions between playing and leaving equal-odds bets whilst manipulating language and valence of feedback. Results showed fewer 'play' choices following positive feedback presented in English relative to Chinese while no cross-language differences were observed after negative feedback. This valence-dependent language effect on risk-taking behaviour was supported by a language-emotion-decision neural circuit involving interplay between the right lingual gyrus, left fusiform gyrus, and right inferior frontal gyrus. Overall, our findings suggest valence-differential mechanisms of the foreign language effect in the risky decision. That is, the use of a foreign language in feedback presentation attenuates emotional reaction to positive feedback and thus diminishes subsequent risk-taking behaviour. Differently, negative counterparts seem to trigger detachment from negative emotion, leading to dissociation between feedback-encoding and decision-making.

Youth who are lesbian, gay, bisexual, and who identify with other sexual orientations (LGB +) are at higher risk for illicit drug use and have higher rates of mental illness. The current study examined the prevalence of illicit drug use among LGB+ persons and assessed the moderating effect of mental illness. Cross-sectional data from the 2015, 2017, and 2019 Youth Risk Behavioral Surveillance System were aggregated. The outcome was any reported use of cocaine, inhalants, heroin, methamphetamines, ecstasy, or hallucinogens. The primary exposure was self-reported sexual orientation category (i.e. heterosexual, gay/lesbian, bisexual, and not sure). Self-reported depressive symptoms were tested as a moderator. Logistic regression models assessed main and interactive effects. Gay or lesbian students [AOR = 1.87 95% CI: 1.45, 2.43], bisexual students [AOR = 2.07 95% CI: 1.77, 2.42], and those unsure of their sexual orientation [AOR = 1.99 95% CI: 1.65, 2.39] had increased odds of illicit drug use. Odds were higher among LGB+ youth who did not have depressive symptoms (p < 0.001). Odds of illicit substance use was significantly greater in youth identifying as gay and lesbian, bisexual, and students who were not sure about their sexual orientation and among LGB+ youth without depressive symptoms. Targeted, but non-stigmatizing, prevention programs are needed.

There is an enormous interest in identifying the causes of psychiatric disorders but there are considerable challenges in identifying which risks are genuinely causal. Traditionally risk factors have been inferred from observational designs. However, association with psychiatric outcome does not equate to causation. There are a number of threats that clinicians and researchers face in making causal inferences from traditional observational designs because adversities or exposures are not randomly allocated to individuals. Natural experiments provide an alternative strategy to randomized controlled trials as they take advantage of situations whereby links between exposure and other variables are separated by naturally occurring events or situations. In this review, we describe a growing range of different types of natural experiment and highlight that there is a greater confidence about findings where there is a convergence of findings across different designs. For example, exposure to hostile parenting is consistently found to be associated with conduct problems using different natural experiment designs providing support for this being a causal risk factor. Different genetically informative designs have repeatedly found that exposure to negative life events and being bullied are linked to later depression. However, for exposure to prenatal cigarette smoking, while findings from natural experiment designs are consistent with a causal effect on offspring lower birth weight, they do not support the hypothesis that intra-uterine cigarette smoking has a causal effect on attention-deficit/hyperactivity disorder and conduct problems and emerging findings highlight caution about inferring causal effects on bipolar disorder and schizophrenia.

Probabilistic thinking is a structure of thinking characterized by scenarios that allow one to explore reality. Therefore, the characteristic of probabilistic thinking is problem-oriented that will occur in a future full of uncertainty. Nevertheless, few studies examine the students' probabilistic thinking level based on the Stress Tolerance dimensions. Thus, in this study, researchers aim to describe the students' probabilistic thinking level based on the Stress Tolerance dimension in solving probability problems. It is shown that the smallest Stress Tolerance (ST)- Students consider confirming that the first solution is accurate. In contrast, the students with the highest score in ST-dimensions tend to make a simple step in solving the problem. The students' answers to probability problems characterize authentic risk-based decision-making. When we deal with probabilistic situations in everyday life, we all use a series of decision-making in our everyday estimation of probabilities, which sometimes leads to biases. However, the level of probabilistic thinking depends on the stress tolerance of the students. The students with the smallest stress tolerance score tend to get level 4 in probabilistic thinking. In contrast, the students with the highest stress tolerance score tends to reach level 1 in probabilistic thinking.

The well-established a priori probability of illness threshold in medical decision making, introduced by Pauker and Kassirer (N Engl J Med 293:229-234, 1975; N Engl J Med 302:1109-1117, 1980), involves the diagnostic risk only. We generalize the threshold analysis by adding the therapeutic risk, i.e., in accounting for the risk that a treatment might sometimes fail. We derive a priori probability of illness threshold as a function of the probability of successful treatment, as well as the inverted function, where the successful treatment probability threshold is a function of the a priori probability of illness. The thresholds in the general model are higher than those in the special cases where one of the two risks is absent. Applications show that the changes in the thresholds can be substantial. Our general model might explain empirical findings of much higher thresholds than the Pauker-Kassirer model suggests.

Objective: Tree-based models belong to common, assumption-free methods of data analysis. Their application in survival data is narrowed to univariate models, which partition the feature space with axis-parallel hyperplanes, meaning that each internal node involves a single feature. In this paper, I extend the idea of oblique survival tree induction for competing risks by modifying a piecewise-linear criterion function. Additionally, the use of tree-based ensembles to analyze the competing events is proposed., Method and Materials: Two types of competing risks trees are proposed: a single event tree designed for analysis of the event of interest and a composite event tree, in which all the competing events are taken into account. The induction process is similar, except that the calculation of the criterion function is minimized for the individual tree nodes generation. These two tree types were also used for building the ensembles with aggregated cumulative incidence functions as an outcome. Nine real data sets, as well as a simulated data set, were taken to assess performance of the models, while detailed analysis was conducted on the basis of follicular cell lymphoma data., Results: The evaluation was focused on two measures: the prediction error expressed by an integrated Brier score (IBS), and the ranked measure of predictive ability calculated as a time-truncated concordance index (C-index). The proposed techniques were compared with the existing approaches of the Fine-Gray subdistribution hazard model, Fine-Gray regression model with backward elimination, and random survival forest for competing risks. The results for both the IBS and the C-index indicated statistically significant differences between these methods (p < .0001)., Conclusions: The prediction error of the individual trees was similar to the other methods, but the results of the C-index differ in comparison to the Fine-Gray subdistribution hazard model and the Fine-Gray regression with backward elimination. The ensembles prediction ability was comparable to existing algorithms, but their IBS values were better than either random survival forest or Fine-Gray regression with backward elimination., (Copyright © 2018 Elsevier B.V. All rights reserved.)

We present a knowledge-base to represent collated infectious disease risk (IDR) knowledge. The knowledge is about personal and contextual risk of contracting an infectious disease obtained from declarative sources (e.g. Atlas of Human Infectious Diseases). Automated prediction requires encoding this knowledge in a form that can produce risk probabilities (e.g. Bayesian Network - BN). The knowledge-base presented in this paper feeds an algorithm that can auto-generate the BN. The knowledge from 234 infectious diseases was compiled. From this compilation, we designed an ontology and five rule types for modelling IDR knowledge in general. The evaluation aims to assess whether the knowledge-base structure, and its application to three disease-country contexts, meets the needs of personalized IDR prediction system. From the evaluation results, the knowledge-base conforms to the system's purpose: personalization of infectious disease risk.

It remains unclear if participation in moderate-to-vigorous physical activity (MVPA) differs between children with ASD and typically developing children (TDC). We compared daily MVPA, time spent in MVPA during physical education (PE) and recess, and odds of not meeting MVPA recommendation (60 min/day) between children with ASD and TDC. Nine studies reporting accelerometer-measured MVPA were included in the meta-analyses. MVPA was 30 min lower/day, 12% and 8% lower during PE and recess, respectively, in children with ASD, and they had 4 times higher odds of not meeting MVPA recommendation when compared to TDC. Children with ASD engage in daily MVPA less than TDC and below the guidelines. Tailored interventions to increase MVPA in children with ASD are warranted.

This study builds on previous research investigating management organizations (MOs), charter school locations, and closure by examining the effects of MO type (EMO, CMO and freestanding schools), racial enrollment, student achievement, and the community characteristics surrounding each charter school in Ohio's eight largest counties with the largest urban school districts on the likelihood of closure between 2009 and 2018. We conducted a discrete-time survival analysis using life tables and binary logistic regression. Findings indicated that freestanding charter schools experience higher risks of closure than EMO and CMO managed charter schools in those counties. Although they are more likely to close, freestanding schools have higher student achievement in math and reading. Higher math proficiency reduces the likelihood of closure by 2.8%. However, community and enrollment characteristics are not statistically significant predictors of closure.

Objective: Athletic involvement is linked to increased risk for heavy alcohol use among college students. We examined whether student-athletes from diverse racial/ethnic backgrounds differ with respect to heavy drinking and related consequences. Method: Participants were 15,135 student-athlete drinkers (50.7% female) from 170 NCAA member institutions who participated in an online study. Results: Findings from our hierarchical linear models indicated that being a male student-athlete was associated with an increased likelihood of high intensity drinking (10/8 + drinks/per sitting for males/females) for White, Asian American/Pacific Islander, and Black student-athletes, but not for Hispanic student-athletes. Additionally, being a female student-athlete was associated with higher levels of negative alcohol-related consequences across all racial/ethnic groups. Finally, at similar drink quantities, compared to being a White student-athlete, being an Asian American/Pacific Islander student-athlete was associated with higher levels of alcohol-related consequences. Conclusions: Student-athlete drinkers are not homogeneous with respect to heavy drinking and related consequences.

The authors describe an asymmetric information demonstration that assigns students different probabilities of incurring healthcare expenses. In each round, students choose whether to purchase insurance; then, the instructor randomly determines who gets "sick." After computing insurer profits, students help determine a new insurance price to maximize future profit. Within three rounds, students recognize that the provider always incurs losses from adverse selection, opening a discussion of market failures pertaining to health insurance and asymmetric information. The experiment features idiosyncratic, but not systematic, risk as such; the same number of students get "sick" every round. Therefore, the instructor can straightforwardly demonstrate the benefits of risk pooling. The experiment is applicable to economic principles as well as intermediate courses in healthcare economics and microeconomic theory.

The perception ability has attained much recognition in the identification of cognitive processing and decision-making in autism spectrum disorder (ASD) individuals. However, the prior studies have subjectively worked on perception ability using conditioning paradigms that can be intolerable for ASD individuals. The present paper quantitatively investigates the perception ability of ASD individuals by modelling visual judgement and statistical learning. Thirty ASD and typically developing (TD) individuals are selected for experimenting distinguishing animated images related to risk situations with different risk levels. The experimental paradigm-based behavioural measures (reaction time, d' index, and accuracy) revealed that ASD individuals, although performed poorly than TDs, they visually and statistically perceived the risk. Quantitatively, the perception level in ASD is (mean 0.57 ± 0.02) in the range [0 1]. In comparison to TDs, the attenuated visual and statistical learning during the experiment could lead to impaired perception in ASD. However, when statistical learning comes into action (comparing performance in block 1 and block 6), it played a crucial role in improving visual knowledge; thus, the perception ability of ASD individuals. In the future, the studies can implicate the quantitative perception to identify other deficits in the ASD phenotype.

Young children encounter uncertainty and challenges on a daily basis; through their intuitions, experiences and experimentation they construct knowledge, skills and dispositions towards probabilistic concepts. The aim of this exploratory ethnographic study is to identify how young children engage with probabilistic thinking and reasoning while playing outdoors. Twelve 3--4year-old children and two practitioners were observed during free and structured activities outdoors. Critical events, that reflect contexts of probability, chance and uncertainty, were identified for further analysis based on participants' linguistic interactions. Children's probabilistic thinking was mainly expressed in three instances: while solving problems, in creative play, and while considering risk and safety issues. These authentic understandings can become the basis for more instructional pedagogical sequences on probability in early years.

Many researchers report risk ratios of White students to Black students with disabilities to show disproportionality and draw the conclusion discrimination exists. Risk ratios, upon further inspection, have methodological and philosophical problems which challenge the usefulness. A qualitative literature review provides a framework for understanding disproportionality and the use of risk ratios. Four themes underpin disproportionality findings, and a theory for future action was derived from the literature review. Recommendations to improve special education services are presented: universal screening, a standardized process, fidelity and research, and a focus on academic achievement.

The association of autism spectrum disorder (ASD) with self-reported maternal cannabis use from 3 months pre-conception to delivery ("peri-pregnancy") was assessed in children aged 30-68 months, born 2003 to 2011. Children with ASD (N = 1428) were compared to children with other developmental delays/disorders (DD, N = 1198) and population controls (POP, N = 1628). Peri-pregnancy cannabis use was reported for 5.2% of ASD, 3.2% of DD and 4.4% of POP children. Adjusted odds of peri-pregnancy cannabis use did not differ significantly between ASD cases and DD or POP controls. Results were similar for any use during pregnancy. However, given potential risks suggested by underlying neurobiology and animal models, further studies in more recent cohorts, in which cannabis use and perception may have changed, are needed.

The Lorenz curve is a graphical tool that is used widely in econometrics. It represents the spread of a probability distribution, and its traditional use has been to characterize population distributions of wealth or income, or more specifically, inequalities in wealth or income. However, its utility in public health research has not been broadly established. The purpose of this article is to explain its special usefulness for characterizing the population distribution of disease risks, and in particular for identifying the precise disease burden that can be predicted to occur in segments of the population that are known to have especially high (or low) risks, a feature that is important for evaluating the yield of screening or other disease prevention initiatives. We demonstrate that, although the Lorenz curve represents the distribution of predicted risks in a population at risk for the disease, in fact it can be estimated from a case-control study conducted in the population without the need for information on absolute risks. We explore two different estimation strategies and compare their statistical properties using simulations. The Lorenz curve is a statistical tool that deserves wider use in public health research.

In observational studies without random assignment of the treatment, the unadjusted comparison between treatment groups may be misleading due to confounding. One method to adjust for measured confounders is inverse probability of treatment weighting. This method can also be used in the analysis of time to event data with competing risks. Competing risks arise if for some individuals the event of interest is precluded by a different type of event occurring before, or if only the earliest of several times to event, corresponding to different event types, is observed or is of interest. In the presence of competing risks, time to event data are often characterized by cumulative incidence functions, one for each event type of interest. We describe the use of inverse probability of treatment weighting to create adjusted cumulative incidence functions. This method is equivalent to direct standardization when the weight model is saturated. No assumptions about the form of the cumulative incidence functions are required. The method allows studying associations between treatment and the different types of event under study, while focusing on the earliest event only. We present a SAS macro implementing this method and we provide a worked example., (Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.)

With the ascent of modern epidemiology in the Twentieth Century came a new standard model of prediction in public health and clinical medicine. In this article, we describe the structure of the model. The standard model uses epidemiological measures-most commonly, risk measures-to predict outcomes (prognosis) and effect sizes (treatment) in a patient population that can then be transformed into probabilities for individual patients. In the first step, a risk measure in a study population is generalized or extrapolated to a target population. In the second step, the risk measure is particularized or transformed to yield probabilistic information relevant to a patient from the target population. Hence, we call the approach the Risk Generalization-Particularization (Risk GP) Model. There are serious problems at both stages, especially with the extent to which the required assumptions will hold and the extent to which we have evidence for the assumptions. Given that there are other models of prediction that use different assumptions, we should not inflexibly commit ourselves to one standard model. Instead, model pluralism should be standard in medical prediction., (Copyright © 2015 Elsevier Ltd. All rights reserved.)

Student perpetrated violence against teachers is widespread, yet few studies differentiate teacher experiences of violence by school level (i.e., elementary, middle, and high school). This study, based upon 2,558 pre-kindergarten through 12th grade teacher survey responses, revealed differences in types of student aggression against teachers by school level. Middle and high school teachers were more likely to report verbal harassment compared to elementary school teachers. Middle school teachers were most likely to report property offenses. Elementary and middle school teachers were more likely to report physical aggression than high school teachers. Demographic predictors of teacher-directed violence were also examined at each school level. Across all school levels, urban teachers had a greater probability of experiencing a violent incident. For elementary teachers, race/ethnicity and teaching experience were also significant risk factors. Future research, policy, and practice implications and recommendations are discussed.

Current use of vaping products has increased in recent years among youth in the United States. We conducted cross-sectional surveys of vaping product users aged 15-17 in New York in 2017 and 2019 to assess vaping frequency, reported nicotine content of vaping products used, risk perceptions of vaping and openness to vaping cannabis (2019 survey only). Between 2017 and 2019, the proportion of youth vapers who were frequent vaping product users increased from 16.8% to 26.2% (P < 0.05). The proportion of youth vapers who usually used high-nicotine vaping products also increased, from 12.6% to 40.0% (P < 0.05). In both years, the use of high-nicotine vaping products was positively associated with frequent use (P < 0.05). The perceived likelihood of harm from vaping increased (P < 0.05), but respondents' perception of harm from using tobacco-flavored vaping products remained higher than that from using menthol/mint or sweet flavors. In 2019, 60.6% of respondents reported having tried vaping cannabis. Results suggest shifts in youth vaping behavior toward more frequent use and use of higher nicotine vaping products, support previous findings about youth misperceptions about health risks of flavored vaping products and highlight openness to vaping cannabis among youth vaping product users.

There are claims in the literature that the risk difference is a more heterogeneous measure than the odds ratio or risk ratio. These claims are based on surveys of meta-analyses showing that tests reject the null hypothesis of homogeneity more often for the risk difference than for the ratio measures. Discussions of this point have neglected the fact that homogeneity tests can have different levels of statistical power (i.e., different probabilities of rejecting the null when it is false) across different scales. We give hypothetical examples in which there is arguably equal heterogeneity across risk difference and odds ratio measures but in which the risk difference homogeneity test rejects more often, and therefore has higher power, than the odds ratio homogeneity test. These examples suggest that current empirical evidence for the claim that the risk difference is more heterogeneous is not at present satisfactory. Further research could consider other approaches to empirical comparisons of the heterogeneity of the three measures.

In a world of limited resources, scarcity and rivalry are central challenges for decision makers-animals foraging for food, corporations seeking maximal profits, and athletes training to win, all strive against others competing for the same goals. In this article, we establish the role of competitive pressures for the facilitation of optimal decision making in simple sequential binary choice tasks. In two experiments, competition was introduced with a computerized opponent whose choice behavior reinforced one of two strategies: If the opponent probabilistically imitated participant choices, probability matching was optimal; if the opponent was indifferent, probability maximizing was optimal. We observed accurate asymptotic strategy use in both conditions irrespective of the provision of outcome probabilities, suggesting that participants were sensitive to the differences in opponent behavior. An analysis of reinforcement learning models established that computational conceptualizations of opponent behavior are critical to account for the observed divergence in strategy adoption. Our results provide a novel appraisal of probability matching and show how this individually 'irrational' choice phenomenon can be socially adaptive under competition., (Copyright © 2015 Elsevier Inc. All rights reserved.)

Objective: To introduce the competing risk model into outcome prediction of mild cognitive impairment (MCI) of seniors and to explore influencing factors for the prognosis of MCI to Alzheimer's disease (AD)., Methods: Data were collected from six follow-up visits to 600 seniors from communities in Taiyuan city, which were conducted at an interval of six months from October 2010 to May 2013. MCI state was defined as the transient state, AD and death before AD as two absorbing states (death before AD in which was regarded as a competing risk event), building the competing risk model to identify the model parameters, and to explore influencing factors on MCI prognosis to AD. In the meantime, the 3-year MCI-AD transition probability was estimated based on the multi-state Markov model., Results: Based on screening with the multivariate competing risk model analysis, factors such as higher age (estimate HR = 1.56, 95% CI: 1.01-2.39), female gender (HR = 1.72, 95% CI: 1.02-2.92), higher education (HR = 0.64, 95% CI: 0.41-1.00), reading frequently (HR = 0.57, 95% CI: 0.32-0.99), hypertension (HR = 3.43, 95% CI: 1.08-10.85) and high SBP (HR = 1.67, 95% CI: 1.04-2.66), were statistically significant for transition from MCI to AD in three years. 3-year MCI-AD transition probability was 10.7% (95% CI: 8.6%-13.2%)., Conclusion: Age, gender, education, reading and blood pressure were the influencing factors for the prognosis of MCI to AD. Competing risk model was advantageous in studying longitudinal data with multiple potential outcomes.

Direct experiences, we find, influence environmental risk beliefs more than the indirect experiences derived from outcomes to others. This disparity could have a rational basis. Or it could be based on behavioral proclivities in accord with the well-established availability heuristic or the vested-interest heuristic, which we introduce in this article. Using original data from a large, nationally representative sample, this article examines the perception of, and responses to, morbidity risks from tap water. Direct experiences have a stronger and more consistent effect on different measures of risk belief. Direct experiences also boost the precautionary response of drinking bottled water and drinking filtered water, while indirect experiences do not. These results are consistent with the hypothesized neglect of indirect experiences in other risk contexts, such as climate change., (© 2014 Society for Risk Analysis.)

Objectives: To evaluate how often newly developed risk prediction models undergo external validation and how well they perform in such validations., Study Design and Setting: We reviewed derivation studies of newly proposed risk models and their subsequent external validations. Study characteristics, outcome(s), and models' discriminatory performance [area under the curve, (AUC)] in derivation and validation studies were extracted. We estimated the probability of having a validation, change in discriminatory performance with more stringent external validation by overlapping or different authors compared to the derivation estimates., Results: We evaluated 127 new prediction models. Of those, for 32 models (25%), at least an external validation study was identified; in 22 models (17%), the validation had been done by entirely different authors. The probability of having an external validation by different authors within 5 years was 16%. AUC estimates significantly decreased during external validation vs. the derivation study [median AUC change: -0.05 (P < 0.001) overall; -0.04 (P = 0.009) for validation by overlapping authors; -0.05 (P < 0.001) for validation by different authors]. On external validation, AUC decreased by at least 0.03 in 19 models and never increased by at least 0.03 (P < 0.001)., Conclusion: External independent validation of predictive models in different studies is uncommon. Predictive performance may worsen substantially on external validation., (Copyright © 2015 Elsevier Inc. All rights reserved.)

It is now widely accepted that the standard inferential toolkit used by the scientific research community--null-hypothesis significance testing (NHST)--is not fit for purpose. Yet despite the threat posed to the scientific enterprise, there is no agreement concerning alternative approaches for evidence assessment. This lack of consensus reflects long-standing issues concerning Bayesian methods, the principal alternative to NHST. We report on recent work that builds on an approach to inference put forward over 70 years ago to address the well-known "Problem of Priors" in Bayesian analysis, by reversing the conventional prior-likelihood-posterior ("forward") use of Bayes' theorem. Such Reverse-Bayes analysis allows priors to be deduced from the likelihood by requiring that the posterior achieve a specified level of credibility. We summarise the technical underpinning of this approach, and show how it opens up new approaches to common inferential challenges, such as assessing the credibility of scientific findings, setting them in appropriate context, estimating the probability of successful replications, and extracting more insight from NHST while reducing the risk of misinterpretation. We argue that Reverse-Bayes methods have a key role to play in making Bayesian methods more accessible and attractive for evidence assessment and research synthesis. As a running example we consider a recently published meta-analysis from several randomised controlled trials (RCTs) investigating the association between corticosteroids and mortality in hospitalised patients with COVID-19.

To facilitate people using mathematical reasoning to compare risks associated with the COVID-19 pandemic, the National Science Foundation (NSF) funded the COViD-TASER (Creation of Visualizations of Data: The Application of STEM Education Research) research team to create the COVID-19 Relative Risk Tool (RRT). The RRT uses an interactive bar chart to display COVID-19 infection and vaccination risks alongside more familiar risks like driving, contracting breast cancer, playing soccer, and skydiving. To involve students, the authors developed and tested elementary, middle, and high school lesson plans that use the RRT. Each lesson is aligned with the Common Core State Standards for Mathematics (CCSSM; NGA Center and CCSSO 2010) for both content and mathematical practice, and each plan pursues two goals: (1) making comparisons of relative size of quantities, and (2) interpreting these relative sizes to understand COVID-19 data. For teachers who wish to incorporate more real-world contexts in the mathematics classroom and are unsure of how to start, the authors hope that their structured, pretested lessons plans provide a starting place for to help students make connections between the classroom and their everyday lives.

The difference between two proportions, referred to as a risk difference, is a useful measure of effect size in studies where the response variable is dichotomous. Confidence interval methods based on a varying coefficient model are proposed for combining and comparing risk differences from multi-study between-subjects or within-subjects designs. The proposed methods are new alternatives to the popular constant coefficient and random coefficient methods. The proposed varying coefficient methods do not require the constant coefficient assumption of effect size homogeneity, nor do they require the random coefficient assumption that the risk differences from the selected studies represent a random sample from a normally distributed superpopulation of risk differences. The proposed varying coefficient methods are shown to have excellent finite-sample performance characteristics under realistic conditions., (© 2013 The British Psychological Society.)

Competing risks model time to first event and type of first event. An example from hospital epidemiology is the incidence of hospital-acquired infection, which has to account for hospital discharge of non-infected patients as a competing risk. An illness-death model would allow to further study hospital outcomes of infected patients. Such a model typically relies on a Markov assumption. However, it is conceivable that the future course of an infected patient does not only depend on the time since hospital admission and current infection status but also on the time since infection. We demonstrate how a modified competing risks model can be used for nonparametric estimation of transition probabilities when the Markov assumption is violated.

A method based on pseudo-observations has been proposed for direct regression modeling of functionals of interest with right-censored data, including the survival function, the restricted mean and the cumulative incidence function in competing risks. The models, once the pseudo-observations have been computed, can be fitted using standard generalized estimating equation software. Regression models can however yield problematic results if the number of covariates is large in relation to the number of events observed. Guidelines of events per variable are often used in practice. These rules of thumb for the number of events per variable have primarily been established based on simulation studies for the logistic regression model and Cox regression model. In this paper we conduct a simulation study to examine the small sample behavior of the pseudo-observation method to estimate risk differences and relative risks for right-censored data. We investigate how coverage probabilities and relative bias of the pseudo-observation estimator interact with sample size, number of variables and average number of events per variable.

We describe a flexible family of tests for evaluating the goodness of fit (calibration) of a pre-specified personal risk model to the outcomes observed in a longitudinal cohort. Such evaluation involves using the risk model to assign each subject an absolute risk of developing the outcome within a given time from cohort entry and comparing subjects' assigned risks with their observed outcomes. This comparison involves several issues. For example, subjects followed only for part of the risk period have unknown outcomes. Moreover, existing tests do not reveal the reasons for poor model fit when it occurs, which can reflect misspecification of the model's hazards for the competing risks of outcome development and death. To address these issues, we extend the model-specified hazards for outcome and death, and use score statistics to test the null hypothesis that the extensions are unnecessary. Simulated cohort data applied to risk models whose outcome and mortality hazards agreed and disagreed with those generating the data show that the tests are sensitive to poor model fit, provide insight into the reasons for poor fit, and accommodate a wide range of model misspecification. We illustrate the methods by examining the calibration of two breast cancer risk models as applied to a cohort of participants in the Breast Cancer Family Registry. The methods can be implemented using the Risk Model Assessment Program, an R package freely available at http://stanford.edu/~ggong/rmap/., (Copyright © 2014 John Wiley & Sons, Ltd.)

The study measured cortical hemodynamic signals and peripheral correlates of decision makers during a dynamic risky task, the Just One More task (JOM), in which the risky decision entails choosing whether to incrementally increase accumulated earnings at the risk of ruin (going bust ending up with nothing). Twenty subjects participated in multiple instantiations of this task in which the probability of ruin and size of the stakes varied. Physiological correlates were simultaneously quantified by functional near-infrared spectroscopy (fNIRS) over dorsolateral prefrontal cortex (DLPFC) and electrodermal activity (EDA). First, in the task decision phase (i.e., when subjects are contemplating options before making a choice) probability of ruin had a dissociating effect on fNIRS and EDA. fNIRS derived DLPFC hemodynamic signals reflected a subjective value signal, correlating positively with individual risk attitude. Contrary, EDA reflected the probability of ruin in terms of a common affective measure, irrespective of individuals׳ risk attitude. Second, during the task outcome phase (i.e., the time after subjects have made a choice and observed the outcomes) fNIRS and EDA revealed opposite patterns. While fNIRS derived DLPFC hemodynamic signals were larger in response to gains, EDA signals were larger in response to losses; both patterns were statistically independent of individual risk attitude. Lastly, fNIRS derived DLPFC hemodynamic signals in the decision phase correlated positively with the mean round earnings, providing a measure of the quality of the individual decision-making performance. Together with the positive correlation with individual risk attitude, our findings indicate that fNIRS signals, but not EDA, could be taken as a useful method for studying individual risk attitude and task performance in dynamic risky decision-making., (Copyright © 2014 Elsevier B.V. All rights reserved.)

We explored the utility of analyzing within- and between-balloon response patterns on a balloon analogue task (BAT) in relation to overall risk scores, and to a choice between a small guaranteed cash reward and an uncertain reward of the same expected value. Young adults (n = 61) played a BAT, and then were offered a choice between $5 in cash and betting to win $0 to $15. Between groups, pumping was differentially influenced by explosions and by the number of successive unexploded balloons, with risk takers responding increasingly on successive balloons after an explosion. Within-balloons, risk takers showed a characteristic pattern of constant high rate, while non-risk takers showed a characteristic variable lower rate. Overall, results show that the higher number of pumps and explosions that characterize risk takers at a molar level, result from particular forms of adaptation to the positive and negative outcomes of choices seen at a molecular level.

A new definition of risk is that risk is the product of a measure of the size of the hazard and its probability of occurrence. We have some mechanisms that would be make too perception of risk in our mind. These mechanisms are including information processing of risk, binary judgment, and risk perception of low probability area. We are required to have bidirectional communication with other person. So, in order to do good risk communication, we have to establish a trust relationship with other person.

This article describes a simple two-player game which illustrates basic concepts of brinkmanship, to include calculations of probability and expected outcomes, and risk-taking profiles. The game befits a single 50-minute class period with introduction, gameplay, and discussion. The game can supplement the study of conflict from classic Cold War case studies of crisis bargaining, to arms control, or negotiating international protocols for global climate change such as the Paris Agreement. The Brinkmanship Game was developed for the seventh week of a 10-week graduate course called Game Theory and Decisionmaking: Exploring Strategic Situations. The course features a flipped classroom with class time devoted to experimentation, gameplay, and discussion of readings and games; lectures are online. The Brinkmanship Game would be appropriate for students in any advanced undergraduate or graduate level course in international relations, security studies, negotiation, or game theory. The Brinkmanship Game provides an active learning opportunity that can be valuable for encouraging students to come to their own understanding of concepts of mutual risk-taking. The authors have found the game to be effective in the classroom and hope it may prove valuable to those searching for ways to motivate students and to help them learn.

The purpose of this study was to compare and contrast frameworks for evaluating methodological rigor in single case research. Specifically, research on high-probability requests to increase compliance in young children was evaluated. Ten studies were identified and were coded using 4 frameworks. These frameworks were the Council for Exceptional Children Standards for Evidence-based Practices, What Works Clearinghouse, Risk of Bias Assessment for Single Subject Experimental Designs, and Single Case Analysis and Review Framework. Significant differences were found across frameworks, both in the rating of rigor and the study effects. Implications for determining high-quality research and effective practices are discussed.

This study presents results coming from Grade 4 students discussing financial concepts that emerged while learning about probability. Six mathematical learning situations on probability were implemented in an elementary classroom situated in Québec, Canada. These learning situations presented gambling activities as sociocultural contexts to be studied in order to develop probabilistic knowledge and reasoning. This process also involves the use of critical thinking, which supports the development of citizenship competencies. The sociocultural context created an opportunity for students to talk about financial concepts broadly, not just those related to gambling activities. The teaching experiment involved the participation of 27 students. Results showed that students have many representations about financial concepts, more specifically on money, means to have money, consumption, risk, and global economy. Those concepts were conceptualised in the citizenship context, where three kinds of citizens emerged: the personally responsible citizen, the participatory citizen, and the justice-oriented citizen. The results of this study suggest that students need to be financially educated in order to develop citizenship.

We analyzed claims data from the Taiwan National Health Insurance database, which contains data of 23.5 million Taiwan residents. We included children born after January 1, 2000 who had received a diagnosis of autism spectrum disorders (ASD). Patients who were not diagnosed with ASD were included in the control group. The ASD prevalence was 517 in 62,051 (0.83%) children. Neonatal jaundice, hypoglycemia, intrauterine growth retardation (IUGR), and craniofacial anomalies (CFA) differed significantly between the ASD and control groups. After logistic regressive analysis, the adjusted odds ratios of IUGR, CFA, neonatal hypoglycemia, and neonatal jaundice were 8.58, 7.37, 3.83, and 1.32, respectively. Those insidiously perinatal risk factors, namely CFA, IUGR, neonatal hypoglycemia, and neonatal jaundice, could increase the risk of ASD.

This research proposes and implements a new approach to the elicitation and analysis of perceptions of risk. We use best worst scaling (BWS) to elicit the levels of control respondents believe they have over risks and the level of concern those risks prompt. The approach seeks perceptions of control and concern over a large risk set and the elicitation method is structured so as to reduce the cognitive burden typically associated with ranking over large sets. The BWS approach is designed to yield strong discrimination over items. Further, the approach permits derivation of individual-level values, in this case of perceptions of control and worry, and analysis of how these vary over observable characteristics, through estimation of random parameter logit models. The approach is implemented for a set of 20 food and nonfood risks. The results show considerable heterogeneity in perceptions of control and worry, that the degree of heterogeneity varies across the risks, and that women systematically consider themselves to have less control over the risks than men., (© 2013 Society for Risk Analysis.)