The recalibrated HellenicSCORE based on newly derived risk factors from the Hellenic National Nutrition and Health Survey (HNNHS); the HellenicSCORE II

BackgroundBecause of the increased burden of cardiovascular disease (CVD), country specific risk prediction models to forecast future CVD events and mortality are recommended, for primary prevention. The aim of this study was to recalibrate the HellenicSCORE, to accurately estimate the 10-year risk CVD mortality of Greek adults.MethodsData from the Hellenic National Nutrition and Health Survey (HNNHS) were used (N = 1012; 37.9% males). Information on age, smoking, systolic blood pressure (SBP), and total blood cholesterol from adults >40 years of age were derived following validated health survey protocols. Individual scores were calculated using these data and beta-coefficients derived from ESC SCORE.ResultsBoth updated HellenicSCORE II charts had lower risk estimates compared to the older version and were closer to the ESC SCORE charts, particularly at the extremes. No significant age difference by sex was observed (mean 59.5 (SD 13.1) years in total) in the population. Women had a significant higher mean total cholesterol compared to men [212.9 (39.5) vs 204.6 (41.2) mg/dl, respectively; p = 0.0343], but smoking prevalence and mean SBP was significantly higher in men [p for all, <0.001]. The mean population HellenicSCORE II score level was between 5.6% (0.2) and 7.9% (3.2) depending on the chart used, with no significant sex differences.ConclusionAlthough the HellenicSCORE II charts were lower, the mean population score was moderately high. This is of great importance because according to ESC guidelines, lifestyle intervention, and drug treatment should be based on an individuals’ total cardiovascular risk.     

Competing Risk of Death: An Important Consideration in Studies of Older Adults

Clinical studies often face the difficult problem of how to account for participants who die without experiencing the study outcome of interest. In a geriatric population with considerable comorbidities, the competing risk of death is especially high. Traditional approaches to describe risk of disease include Kaplan‐Meier survival analysis and Cox proportional hazards regression, but these methods can overestimate risk of disease by failing to account for the competing risk of death. This report discusses traditional survival analysis and competing risk analysis as used to estimate risk of disease in geriatric studies. Furthermore, it illustrates a competing risk approach to estimate risk of second hip fracture in the Framingham Osteoporosis Study and compares the results with traditional survival analysis. In this example, survival analysis overestimated the 5‐year risk of second hip fracture by 37% and the 10‐year risk by 75% compared with competing risk estimates. In studies of older individuals in which a substantial number of participants die during a long follow‐up, the cumulative incidence competing risk estimate and competing risk regression should be used to determine incidence and effect estimates. Use of a competing risk approach is critical to accurately determining disease risk for elderly individuals and therefore best inform clinical decision‐making.     

Adverse cardiac events after surgery

OBJECTIVE: To establish rates of and risk factors for cardiac complications after noncardiac surgery in veterans. DESIGN: Prospective cohort study. SETTING: A large urban veterans affairs hospital. PARTICIPANTS: One thousand patients with known or suspected cardiac problems undergoing 1,121 noncardiac procedures. MEASUREMENTS: Patients were assessed preoperatively for important clinical variables. Postoperative evaluation was done by an assessor blinded to preoperative status with a daily physical examination, electrocardiogram, and creatine kinase with MB fraction until postoperative day 6, day of discharge, death, or reoperation (whichever occurred earliest). Serial electrocardiograms, enzymes, and chest radiographs were obtained as indicated. Severe cardiac complications included cardiac death, cardiac arrest, myocardial infarction, ventricular tachycardia, and fibrillation and pulmonary edema. Serious cardiac complications included the above, heart failure, and unstable angina. MAIN RESULTS: Severe and serious complications were seen in 24% and 32% of aortic, 8.3% and 10% of carotid, 11.8% and 14.7% of peripheral vascular, 9.0% and 13.1% of intraabdominal/intrathoracic, 2.9% and 3.3% of intermediate-risk (head and neck and major orthopedic procedures), and 0.27% and 1.1% of low-risk procedures respectively. The five associated patient-specific risk factors identified by logistic regression are: myocardial infarction < 6 months (odds ratio [OR], 4.5; 95% confidence interval [CI], 1.9 to 12.9), emergency surgery (OR, 2.6; 95% CI, 1.2 to 5.6), myocardial infarction > 6 months (OR, 2.2; 95% CI, 1.4 to 3.5), heart failure ever (OR, 1.9; 95% CI, 1.2 to 3.0), and rhythm other than sinus (OR, 1.7; 95% CI, 0.9 to 3.2). Inclusion of the planned operative procedure significantly improves the predictive ability of our risk model. CONCLUSIONS: Five patient-specific risk factors are associated with high risk for cardiac complications in the perioperative period of noncardiac surgery in veterans. Inclusion of the operative procedure significantly improves the predictive ability of the risk model. Overall cardiac complication rates (pretest probabilities) are established for these patients. A simple nomogram is presented for calculation of post-test probabilities by incorporating the operative procedure.     

Priming Effects of HIV Risk Assessments on Related Perceptions and Behavior: An Experimental Field Study

HIV-AIDS prevention research requires assessment administration formats that do not enhance response bias or risk sensitization. In the present study, reactivity of self-reported sexual history measures used in HIV prevention research was examined in a sample of 158 African American women. Sexual history assessments were administered in one of three formats: self-administration, administration assisted by overhead projections of measures explaining items while participants completed their own assessment instruments, or face-to-face interviews, with follow-up assessments completed 2 weeks later. Consistent with previous research, test-retest coefficients indicated moderate stability of the sexual behavior measures. We also found that participants who self-administered measures were less likely to return for the 2-week follow-up. Tests for measurement reactivity showed that self-administered questionnaires and face-to-face interviews primed sensitization to personal risk and intentions to change risk behaviors to a greater extent than did the projector-assisted assessments. We conclude that sexual behaviors can be assessed with moderate test-retest stability in inner-city women and some administration procedures may enhance preparedness to change HIV risk behaviors.     

新的心血管危险标志物的评估标准

个体心血管危险的准确评估是做出临床决策的必要条件。随着新的心血管危险标志物的不断出现,对其进行系统而规范的评价显得日益重要。对新标志物的正确评估及评估方法的改善,将有助于优化临床决策和实践,提高心血管疾病的综合防治水平。     

老年性痴呆的简易预测模型

目的尝试建立老年性痴呆(阿尔茨海默病)的简易预测模型。方法通过病例对照研究获得老年性痴呆的主要影响因素及其回归系数,以回归系数为基础建立riskscore(风险评分)预测模型,并考核其预测效果。结果 52个病例、70个对照的Logistic回归分析显示,年龄(OR=1.39)、文化程度(OR=0.65)、婚姻状况(OR=1.12)、高血压史(OR=1.25)、血铝水平(OR=3.71)、血硒水平(OR=0.52)为老年性痴呆的主要影响因素。通过使用风险评分模型计算各研究对象所得风险总分并绘制受试者工作曲线(ROC),曲线下的面积为0.838(P0.001)。当风险总分切点选择为216.6时,该模型的灵敏度为80.8%,特异度为75.7%,粗一致率为75.9%,其在一般人群中的阳性预测值和阴性预测值分别为14.1%和98.8%。结论通过使用年龄、文化程度、婚姻状况、高血压史、血铝水平、血硒水平作为老年性痴呆预测因子的riskscore预测模型可能对老年性痴呆具有一定的预测效果。     

Assessing and evaluating the combined impact of behavioural and biological risk factors for HIV seroconversion in a cohort of South African women

In this prospective study, we aimed to investigate and evaluate the impact of combinations of behavioural and biological risk factors on HIV acquisition in a cohort of women. Demographic, sexual and biologic risk factors including HIV seroconversion results from 1485 HIV negative women who were enrolled in a HIV prevention trial were used. First, Cox regression models were used to create a prediction model and weighted scoring system. Second, internal validation data-set was used to evaluate the performance characteristics of the model prospectively. In the prediction model, an increasing number of lifetime sexual partners, women who were classified as in a "high risk behavior" group, and those who were not cohabitating with their partners were consistently associated with increased risk of HIV acquisition. Among the baseline biological factors, genital epithelial disruption, genital signs and symptoms, genital discharge and detecting edema, erythma or warts in vulva were all associated with HIV seroconversion. High scores were associated with increased risk of HIV seroconversion. A cut-point score of 15 (out of 44) or higher distinguished an "increased risk" group with a sensitivity of 88%. This study presents reasonable robust analyses for investigating and evaluating epidemiological measures on HIV infection. Results from this study may be included as part of a health promotion to prompt those who are at increased risk of HIV infection which may potentially lead to increased uptake and frequency of testing.     

The perception of health care risk: patients, health care staff and society

Introduction

The Nuovo Zingarelli, dictionary of the Italian language, defines risk as “the possibility of harmful or negative consequences following not always predictable circumstances”. A statistical-epidemiological type of definition is far removed from the social and psychological conception that the population attributes to the risk of harm, which is related to interior processes and emotional reactions. Information on risks interacts with knowledge, personal values and beliefs to produce a subjective expression that is perception.

Materials and methods

Two years after instituting the Hospital Quality and Risk Management Unit at S. Giovanni Battista Molinette Hospital (Turin, Italy) it became clear that it was necessary to determine the perception of health care risk among nursing staff. Therefore, nursing teams from eight sub-departmental units in six departments were invited to participate in an assessment project.

Results

The project was undertaken by four nursing teams composed of four head nurses (project representatives) and 45 professional nurses. The aims of the project were understood by all four groups; three participated with interest, one only in part. Three groups considered that it would be useful to continue the project, while the other group did not discuss this point.

Conclusions

The project on the perception of health care risk by nursing staff revealed that mistaken identification of the patient, errors during the administration of treatment and poor communication among colleagues and with doctors and patients were the risks of error perceived as most important by nurses. Heavy work loads, staff shortages, technical and structural problems, and gaps in professional knowledge were identified as the factors related to the occurrence of adverse events. These data differed from management’s perception because no incident report forms had ever been received from these nursing teams.     

Risk Perception and Sexual Risk Behaviors Among HIV-Positive Men on Antiretroviral Therapy

There are reports of increased sexual risk behavior among people on highly active antiretroviral therapy (HAART) due to beliefs about risk of HIV transmission when on HAART. In a cross-sectional study (Seropositive Urban Mens Study), we examined the relationship between risk perception and sexual risk behavior among sexually active, culturally diverse HIV positive men who have sex with men (N = 456). Less than twenty-five percent engaged in unprotected anal sex (either with an HIV negative, or unknown-status partner, or an HIV positive partner) within the past 3 months. Most men believed there was significant health risk (to partner or self) associated with unprotected sex when on HAART. There was no increased risk behavior associated with being on HAART, although the perception of negative health consequences, including HIV transmission, when on HAART was significantly lower for the relatively small subset of men who reported unprotected sex. Prevention strategies need to be tailored to address risk perception associated with HAART.     

Communicating benefit and risk

Improved reporting of clinical trials and greater engagement by patients in treatment decisions requires that clinicians have a working knowledge of estimates of benefit and risk and how to communicate these measures. A basic understanding of study design and analysis is often neglected by clinicians in training, and recent analyses indicate that inadequate reporting and design are associated with biassed estimates of treatment effects. Communicating likely treatment results to patients requires presentation of information as absolute rather than relative risk, using common denominators or probabilities, and explaining risk with reference to a proposed treatment duration. Conveying uncertainty in relation to estimates of likelihood is particularly difficult when discussing outcomes with patients and often the clinician is still left with phrases such as ' best guess '.     

Cross-sectionally assessed carotid intima-media thickness relates to long-term risk of stroke, coronary heart disease and death as estimated by available risk functions

OBJECTIVE: To relate cross-sectionally assessed indicators of carotid atherosclerosis measured in participants of the Rotterdam Study to absolute 10-12 year risks of stroke, coronary heart disease and death estimated by risk functions available from other studies. SETTING: General population living in the suburb of Ommoord in Rotterdam, The Netherlands. SUBJECTS: A sample of men and women (n = 1683), aged 55 years or over, drawn from participants from the Rotterdam Study (n = 7983). MAIN OUTCOMES MEASURES: Three risk scores were used to estimate for each individual the absolute risk of stroke, coronary heart disease and death within 10-12 years as a function of their cardiovascular risk factor profile. Cross-sectionally measured indicators of carotid atherosclerosis (presence of atherosclerotic lesions and common carotid intima-media thickness) were subsequently related to these risk scores. RESULTS: The 10-year absolute risk of stroke increased linearly from 4.8% (95% CI = 3.8, 5.8) for subjects in the lowest quintile to 16.1% (12.3, 21.9) for subjects in the highest quintile of common carotid intima-media thickness distribution. Similarly, the 10-year absolute risk for coronary heart disease rose from 13.1% (95% CI = 12.0, 14.2) to 23.4% (95% CI = 21.4, 25.4), whereas the risk of death within 11.5 years rose from 15.0% (95% CI = 12.8, 17.4) in the lowest quintile to 46.0% (42.8, 49.3) in the upper quintile. The absolute risks of stroke, coronary heart disease or death rose from 8.8, 15.8 and 26.9% to 14.3, 19.8 and 40.9%, respectively, when plaques in the common carotid artery were present. Similar findings were observed for plaques in the carotid bifurcation. CONCLUSION: Common carotid intima-media thickness and carotid plaques are markers for increased risk of stroke, coronary heart disease and death within 10-12 years.     

Use of risk scores to identify lower and higher risk subsets among COMPASS‐eligible patients with chronic coronary syndromes. Insights from the CLARIFY registry

BackgroundThe COMPASS trial showed a reduction of ischemic events with low‐dose rivaroxaban and aspirin in chronic coronary syndromes (CCS) compared with aspirin alone, at the expense of increased bleeding.HypothesisThe CHA₂DS₂VaSc Score, REACH Recurrent Ischemic (RIS), and REACH Bleeding Risk Score (BRS) could identify patients with a favorable trade‐off between ischemic and bleeding events, among COMPASS‐eligible patients.MethodsWe identified the COMPASS‐eligible population within the CLARIFY registry (>30.000 patients with CCS). High‐bleeding risk patients (REACH BRS > 10) were excluded, as in the COMPASS trial. Patients were categorized as low (0–1) or high (≥ 2) CHA₂DS₂VaSc; low (0–12) or intermediate (13–19) REACH RIS, and low (0–6) or intermediate (7–10) REACH BRS. Ischemic outcome was the composite of cardiovascular death, myocardial infarction or stroke. Bleeding was defined as serious bleeding (haemorrhagic stroke, hospitalization for bleeding, transfusion).ResultsThe COMPASS‐eligible population comprised 5.142 patients with ischemic and bleeding outcome of 2.3 (2.1–2.5) and 0.5 (0.4–0.6) per 100 patient‐years, respectively. Patients with intermediate REACH RIS (n = 1934 [37.6%]) had the higher ischemic risk (3.0 [2.6–3.4]) with similar bleeding risk (0.5 [0.4–0.7]) as the overall population. Patients with low CHA₂DS₂VaSc (n = 229 [4.4%]) had a very low ischemic risk (0.6 [0.3–1.3]) with similar bleeding risk (0.5 [0.2–1.1]).ConclusionsIntermediate REACH RIS identified potential optimal candidates for adjunction of low‐dose rivaroxaban while patients with low CHA₂DS₂VaSc score .appears unlikely to benefit from the COMPASS regimen. None of the three risk scores predicted the occurrence of serious bleeding.     

Coronary heart disease incidence in northern and southern European populations: a reanalysis of the seven countries study for a European coronary risk chart

OBJECTIVE—A systematic reanalysis of 10 year coronary heart disease incidence data from the northern and the southern European cohorts of the seven countries study, to contribute indirectly to the production of a European coronary risk chart.
DESIGN AND SETTING—Men aged 40-59 years at entry were studied in three northern European cohorts based in Finland and Netherlands (n = 2213); and in 10 southern European cohorts based in Italy, former Yugoslavia, and Greece (n = 5897). Multiple logistic models for the prediction of coronary deaths, coronary incidence (hard criteria), and coronary incidence (any criterion) were solved for the two geographical groups and their pool. Risk factors fed into the models were age, systolic blood pressure, serum total cholesterol, and cigarette smoking.
RESULTS—10 year coronary heart disease mortality and incidence were higher in northern than in southern Europe, with ratios around 2.65. Ratios among the three coronary heart disease manifestations were identical in the two cultural groupings. Coefficients of the multiple logistic models were similar and not significantly different between the two groupings. When applying the coefficients back to the same or the opposite population, the relative risk was large and similar in the different cultures. Relative risk was larger for more severe coronary heart disease manifestations. The absolute risk was overestimated when applying the northern European model to southern European populations and vice versa, with ratios of about 1.5 and 0.5, respectively. Coronary risk charts created to reproduce the shape of those incorporated in recent European guidelines confirmed the excess of absolute risk in the northern compared with the southern European cohorts, all else being equal.
CONCLUSIONS—In theory, a more appropriate European coronary risk chart could be produced by adopting coefficients to correct for different background incidence rates in different cultures. Other coefficients could appropriately be used to transform mortality risk into incidence risk.


Keywords: coronary heart disease; risk factors; risk estimate     

Risk stratification and management of sudden cardiac death: a new paradigm

Risk Stratification and Management of SCD. Management of SCD is undergoing radical change in direction. It is becoming increasingly appreciated that besides depressed left ventricular systolic function and the conventional risk stratification tools, new markers for plaque vulnerability, enhanced thrombogenesis, specific genetic alterations of the autonomic nervous system, cardiac sarcolemmal and contractile proteins, and familial clustering may better segregate patients with atherosclerotic coronary artery disease who are at high risk for SCD from those who may suffer from nonfatal ischemic events. Better understanding of pathophysiologic processes, such as postmyocardial infarction remodeling, the transition from compensated hypertrophy to heart failure, and the increased cardiovascular risk of coronary artery disease in the presence of diabetes or even a prediabetic state will help to improve both risk stratification and management. The rapidly developing fields of microchips technology and proteomics may allow rapid and cost-effective mass screening of multiple risk factors for SCD. The ultimate goal is to identify novel methods for risk stratification, risk modification, and prevention of SCD that could be applied to the general public at large.     

Evolved attitudes to risk and the demand for equity

The equity premium puzzle refers to the observation that people invest far less in the stock market than is implied by measures of their risk aversion in other contexts. Here, we argue that light on this puzzle can be shed by the hypothesis that human risk attitudes were at least partly shaped by our evolutionary history. In particular, a simple evolutionary model shows that natural selection will, over the long haul, favor a greater aversion to aggregate than to idiosyncratic risk. We apply this model—via both a static model of portfolio choice and a dynamic model that allows for intertemporal tradeoffs—to show that an aversion to aggregate risk that is derived from biology may help explain the equity premium puzzle. The type of investor favored in our model would indeed invest less in equities than other common observations of risk-taking behavior from outside the stock market would imply, while engaging in reasonable tradeoffs over time.

This paper lies in lightly explored territory between biology and economics, in which the utility functions used in economics are informed by results on biological evolution. This approach contrasts with the conventional axiomatic approach in economics. Consider, for example, the human fondness for sweet or fatty foods. These preferences presumably arose among our distant ancestors and plausibly reflect the nutritional and fitness value of such foods in an often difficult and unpredictable environment. These preferences are not, however, always appropriate in present postagricultural and wealthy societies. But the existence of such preferences is plausible evidence that our biological histories shape some of our preferences and aversions. (This argument is drawn from ref. 1.)The aspects of preferences that are the most promising candidates for biological explanation are aspects that are basic and so would have been important for humans throughout our history (2). One of these aspects concerns time preference (see ref. 3, for example). Another aspect concerns attitudes to risk, which is the focus here.The Evolutionary Context.We hypothesize that attitudes to risk are at least partly hardwired and so persist even if there is no longer a strong link, or any link at all, between material success and fitness. (See ref. 4 for evidence that risk attitudes are also shaped by culture.) What attitudes toward risk might then be favored by natural selection? A specific and striking evolutionary prediction is that individuals ought to be more averse to aggregate risk—where a single public coin generates the same outcome for everyone—than they are to comparable idiosyncratic risk—where multiple independent coins generate the outcomes (1). We will argue that this provides a novel resolution of the “equity premium puzzle”—the “excessive” aversion investors typically display to stock market risk.We follow the basic approach of Robson (1), which involves perhaps the simplest possible biological model. Risk-taking behavior in a random environment is controlled by alternative genes (alleles) at a single “locus.” These alleles induce different risk behaviors and so compete to fill this locus. The model is haploid and asexual and features discrete generations with no carrying capacity or density dependence. (A species is haploid if it carries a single copy of each gene, and it is asexual if there is no mixing of genetic material inherited from two parents when producing gametes.) A branching process model that allows extinction shows, among other things, that the type that maximizes the expected logarithm of offspring number over the environments encountered ultimately dominates the population.Several of Robson’s results reflect findings from the economic literature—for example, on portfolios that maximize wealth in the distant future (5). His results also echo those from the biological literature on the population genetics of evolution in random environments—in particular, the classical “geometric mean principle.”^* In a two-allele haploid model where fitness (probability of survival) fluctuates randomly through time—–reflecting random environments encountered over discrete generations—the allele with the higher geometric mean fitness will tend to ultimately displace the other allele (7–9). (Apparent “balancing” selection arising from temporal variation in fitness cannot, therefore, maintain both alleles in a haploid population; i.e., see ref. 9.)Although the allele with the higher geometric mean fitness tends to dominate the population over the long haul, its expected frequency does not always increase; rather, this depends on current allele frequencies. See ref. 10 for this and other concerns about the universality of the geometric mean principle.In the end, the extent to which evolution has endowed us with particular attitudes to risk is an empirical question. Here, we merely ask if the simple evolutionary scenario described above sheds light on the equity premium puzzle.^†Evolved Attitudes to Aggregate and Idiosyncratic Risk. The differential impact of aggregate and idiosyncratic economic gambles on biological success is considered in ref. 1.^‡ These results can best be illustrated by examples. Consider two types of individuals within an asexual species in a discrete-time setting.In each period, Type 1 has either 1 or 2 offspring, each with probability 1/2, and this risk is “idiosyncratic,” that is, independent across all individuals and periods. Assume that there is no density dependence, that the population has size 1 at t=0, but the population is “large,” so that the per period growth factor is always exactly 3/2. It follows that the number of Type 1 individuals at t is then x(t)=(3/2)t. As a purely formal matter, although this is a discrete-time setting, it is convenient to use the equivalent continuous time growth rate ln⁡x(t)t=ln(3/2).On the other hand, although Type 2 individuals again have either 1 or 2 offspring, each with probability 1/2, the risk is now “aggregate,” in that all individuals in each period either have 1 offspring or all of them have 2.Suppose that the initial population of Type 2 at t=0 is also 1. Even if this population is also “large,” the number of Type 2’s at period t is necessarily random, given by y~(t)=2ñ(t), where ñ(t) is the random number of heads in t flips of a fair coin. It follows from the strong law of large numbers that a limiting continuous growth rate exists since lny~(t)t=ñ(t)tln⁡2→ln2<ln(3/2), with probability 1, as t→∞.The evolutionary dominance of Type 1 over Type 2 then follows from the relationship between the limiting growth rates. We have ln⁡x(t)/y~(t)t=ln⁡x(t)t−lny~(t)t→ln(3/2)−ln(2)>0, with probability 1, so that x(t)y~(t)→∞, with probability 1, as t→∞. Hence, Type 1 is the unambiguous evolutionary winner in the long run.Although this race is simple in that it lacks interactions between the types, it shows how certain preferences may be favored by evolution. Given the choice, individuals should strictly prefer idiosyncratic risk over aggregate risk with the same distribution. (These findings are related to those from population genetics on “genotypic homeostasis” in a fluctuating environment; i.e., see ref. 10.)It is worth noting that, although Type 2 is unambiguously beaten in terms of a compelling criterion, it does not always simply lag behind Type 1. Indeed, the mean of Type 2 keeps pace with Type 1. That is, since Ey~(t)=(3/2)t, for all t, it follows that ln⁡Ey~(t)t=ln(3/2) for all t.^§ Hence, for finite t, there are many outcomes where y~(t)>x(t). There must then be sequences with substantially more 2s than 1s, in order to maintain the growth rate of the mean of the Type 2 population at ln(3/2). In the limit, however, the probability of all sequences that do not have a precisely equal number of 1s and 2s tends to 0, and the limiting growth rate of the Type 2 population is only ln2. (Similar results in a biological context are in ref. 12; they are applied in economics in ref. 13.)Perhaps the simplest way of converting this biological argument to an economic example is to suppose that expected offspring are produced as Ψ(c), where c≥0 is consumption and the nondecreasing Ψ is a biological production function. Suppose that Ψ(c1)=1 and Ψ(c2)=2. The present example then implies that individuals who experience an idiosyncratic gamble over consumption levels c1 and c2 will outperform those who experience an aggregate gamble over c1 and c2, where, in both cases, c1 and c2 have equal probability.More explicitly, suppose these consumption outcomes c1 and c2 for Type 2 are generated by aggregate states A and B, respectively, where these occur independently across periods. The Type 1 population, however, is unaffected by the state, so that c1 and c2 occur independently across individuals with equal probability in either state. If the individual can choose between the idiosyncratic gamble over consumption and the aggregate gamble, she should strictly prefer the former, despite the two gambles being identical from a purely individualistic point of view.This example can be sharpened, so that Type 2 has one offspring with probability p and two offspring with probability 1 – p. That is, there exists p < 1/2 such that Type 1 still outdoes Type 2. From a strictly individualistic point of view, this contradicts first-order stochastic dominance or probabilistic sophistication, more generally. The most successful type is not individualistic but takes the outcomes of others into account. (See refs. 1 and 3 for further discussion of the issues this raises.)This example can also be dramatized in a way that is relevant to the present application. Although zero offspring is bad from an idiosyncratic point of view, it is catastrophic from an aggregate point of view. Suppose, that is, that Type 1 has either zero offspring, with probability p∈(0,1/2), or two offspring, with probability 1 – p. The expected number of offspring is then 2(1 – p) > 1 and the limiting continuous time growth rate is ln(2(1 – p)) > 0.^¶ Type 2 also has zero offspring, with probability p∈(0,1/2), or two offspring, with probability 1 – p, but these outcomes are aggregate. The limiting growth rate for Type 2 is then p⁡ln⁡0+(1−p)ln⁡2=−∞. This reflects the inevitable extinction of Type 2, which happens in the first period that all individuals generate zero offspring. (The evolutionary dominance of Type 1 over Type 2 holds if Type 2 has any probability q>0 of zero offspring.)The most general case treated in ref. 1 is as follows. Suppose that there are random aggregate states denoted by s. These states are drawn independently from a given distribution in each of an infinite number of periods. In each such state s, consumption outcomes are random and independent across individuals conditional on the state s. Suppose that Ψ(x) is the expected offspring produced by any x. Expected offspring in state s is then EΨ(x)|s. The limiting growth rate of the population is then the expectation over the states of the logarithm of the expected offspring conditional on the state:ln⁡EΨ(x)|s<ln⁡EEΨ(x)|s=lnEΨ(x).[1]The inequality reflects that the individual prefers aggregate risk to be converted to comparable idiosyncratic risk. The biological reason for this preference is that idiosyncratic risk can be diversified within the population, but aggregate risk cannot. When this distinction is embedded in preferences, the mere possibility of such biological diversification generates less risk aversion for idiosyncratic risks than for aggregate risks for the individual.Although this distinction arises in a dynamic setting—reflecting how aggregate outcomes compound over time—the appropriate criterion has a formally static representation. This particular representation arises because the age structure of the population is degenerate with only one adult age. (We sketch an extension below in A Simple Dynamic Model to a population with two adult ages, where the criterion is explicitly dynamic.)However, ref. 14 shows that the distinction between aggregate and idiosyncratic risk disappears in a continuous time model, where consumption and offspring are treated as “rates.” They assume that there is no variation with age in mortality or fertility.In continuous time with a general age structure, ref. 15 shows that the distinction between aggregate and idiosyncratic risk remains as long as mortality or fertility vary with age, although the simplicity of the criterion from ref. 1 is generally lost. Indeed, it is possible that an individual even prefers aggregate risk to strictly comparable idiosyncratic risk. One simple case where there remains greater aversion to aggregate risk than to idiosyncratic risk is where there is a lag to first reproduction, or menarche. This lag plays the role of the period in discrete time.The model outlined above generates a distinction between idiosyncratic and aggregate risk that is captured by a logarithmic transformation of Ψ for the latter case. This is a specific tilt in favor of idiosyncratic risk. What is crucial is not the precise shape of the logarithmic function but that it reflect the disastrous aggregate consequences of offspring levels near zero. This qualitative property will hold for many other functions.Convex–Concave Ψ in Biology and Economics.The second key element of the model here is the assumption that the biological production function Ψ is at first convex and then concave. It is important then to defend the empirical plausibility of an initial convex range, in particular. We do this with evidence first from biology and then from economics.A convex–concave production function is not canonical in biology, but it has been invoked in several scenarios. Perhaps the best known of these is a behavioral ecological scenario. This concerns an organism that confronts an environment that either meets its energetic (nutritional) needs for survival on average or an environment that does not.In the latter case, the optimal foraging strategy is risk-loving: if one does not expect, for example, to survive the day on the nutrients typically available, then risky foraging behaviors are favored as one may get lucky, obtaining a large enough payoff in food to survive. Reductions in food are essentially inconsequential as one did not expect to survive anyway. Alternatively, if one does expect to survive the day, then risk-averse foraging behaviors are favored, as now the downside with a potential failure to survive is highly consequential.Mathematically, these intuitions are captured in the behavioral ecology literature via a convex–concave production function (16–18). A large empirical literature provides some support for this model (reviewed in refs. 16 and 19). However, complications have been noted, and alternative hypotheses have been proposed. (See ref. 20 for a critical review of this and related literature.)An evolutionary account of attitudes to risk in economics is provided in ref. 21. In particular, this hypothesizes that risk-taking at low levels of wealth would be evolutionarily advantageous if such levels already preclude obtaining a mate, so that a loss would be inconsequential, whereas sufficiently large gains would enable a mate to be obtained.In economics, there is also evidence of human economic risk-preferring behavior among poorer individuals (22). Demand for state lotteries, which are actuarially unfair, is highest among those with the lowest incomes. As incomes rise, individuals shift to stocks. This is not evidence of risk-loving, of course, since the stock market is actuarially advantageous.Finally, a convex–concave payoff function is a salient feature of prospect theory, where a reference point marks the transition from the convex range to the concave. This theory is advocated in ref. 23 and buttressed with rich empirical evidence. The endogeneity of the reference point is a key part of prospect theory. It may ultimately be useful to make the transition here endogenous also but this is left for future work.Equity Premium Puzzle.Since we argue that the distinction between idiosyncratic and aggregate risk can help resolve the equity premium puzzle, we now describe this puzzle and previous attempts to resolve it.There is a profound difficulty in reconciling long-run data on the stock and bond markets with economic theory, as vividly established in ref. 24. That is, in a basic additive model of preferences for consumption over time and risk, it is very difficult to explain why people hold any bonds at all given the vastly superior average return on stocks (Fig. 1).^#Open in a separate windowFig. 1.US equity risk premium 1927 to 2019.Although stocks are clearly riskier than bonds, an implausible degree of risk aversion is needed to achieve a reconciliation. The implausibility arises because other evidence on attitudes to risk implies more moderate estimates of risk aversion. Some evidence on more moderate risk aversion derives from property or liability insurance. For example, ref. 26, using US data on property and liability insurance, estimates that the coefficient of relative risk aversion is between 1.2 and 1.8. We argue that it is important to observe that the property or liability insurance considered in ref. 26 largely concerns idiosyncratic risk for a single property or business. Only a small fraction of the total premiums paid for property insurance, for example, covers earthquakes, hurricanes, or multiple properties.The standard additive model of preferences tightly links attitudes to risk and intertemporal tradeoffs, which makes it more difficult to evaluate the source of the problem posed by the equity premium puzzle. That is, imposing a high degree of risk aversion may also distort intertemporal choice.A pioneering approach is taken in ref. 27, which constructs a recursive nonadditive model of preferences over consumption streams that allows risk aversion and intertemporal inequality aversion to be independently chosen. However, the best estimates in ref. 28 are that the elasticity of intertemporal substitution is less than 1 and the coefficient of relative risk aversion is close to 1. They do not then claim to resolve the equity premium puzzle.Another approach to untying risk aversion and intertemporal choice is taken in ref. 29. The author makes the illuminating observation (p. 414) that the difficulty in explaining the equity premium using this model stems from the need to use an implausibly high coefficient of relative risk aversion (CRRA). That is, the model fits the data well with a CRRA of 45, a plausible elasticity of intertemporal substitution and a plausible discount factor.The present simplified model, which predicts a flexible degree of greater risk aversion to aggregate risks, then represents a promising avenue. A more general dynamic version of the present model should be calibrated on data for stocks and bonds. It would be worthwhile if it could ultimately contribute an element to any final resolution of the puzzle.An important approach in the literature that addresses the equity premium puzzle involves the introduction of ambiguity—uncertainty about the underlying distribution of risks. The notion of ambiguity allows the individual to be averse to such higher-order uncertainty. That is, the individual may consider such a two-tiered structure as less desirable than the reduced form, one-tier risk obtained in a straightforward fashion by combining the probabilities from the two tiers.A key paper that accounts for ambiguity aversion is ref. 30. The criterion proposed there is formally similar to the biological criterion discussed in Evolved Attitudes to Aggregate and Idiosyncratic Risk. The role played by aggregate risk here is played by ambiguity there, although the function ln here is replaced by a more general concave function capturing the differential aversion to ambiguity. Aggregate risk and ambiguity may sometimes be difficult to distinguish empirically.^∥ To the extent this is so, the current biological approach could be viewed as providing a biological foundation for ambiguity aversion.The model of ref. 31 permits independent specification of attitudes to risk, attitudes to ambiguity, and intertemporal inequality. (The recursive intertemporal model of ref. 32 also generalizes ref. 27 to allow for ambiguity aversion and ref. 30 to allow for intertemporal substitution.)When this generalized model is applied to the equity premium puzzle, however, a high level of ambiguity aversion is still needed. (The parameter η in ref. 31 is an elasticity measuring ambiguity aversion and is estimated to be 8.86.) There is not much evidence on the level of ambiguity aversion in other contexts, but the plausibility of this resolution depends on such evidence also yielding comparably high estimates of ambiguity aversion.A common feature of many resolutions of the equity premium puzzle is indeed that they raise issues concerning whether behavior outside the context of the stock market would be consistent with the estimated model, whether the resolution builds in a high level of ambiguity aversion, or a high level of risk aversion, with respect to stocks.^**The partial resolution of the puzzle offered here argues that humans may have evolved to be more averse to the aggregate risk generated by stocks than to other idiosyncratic risk. Our argument holds even if individuals are aware, for example, of the distribution of persistent growth rates or of the extremes of the distribution of stock market collapses.Present Contribution.The purpose of the present paper is to demonstrate how aggregate risk might entail an arbitrarily large degree of extra risk aversion relative to idiosyncratic risk. In a simple pedagogic atemporal setting, we show that an individual should have less exposure to stocks—where there is aggregate risk—than would be suggested by her attitudes to idiosyncratic risk (property loss, for example).Indeed, under plausible assumptions on the function Ψ, the difference in the effect of the two types of risk on portfolio choice can be arbitrarily large. Hence, this can reconcile evidence of a coefficient of relative risk aversion near 1 when considering property loss, for example, with evidence of a coefficient of relative risk aversion that is an order of magnitude or more greater when considering exposure to the stock market.^†† We further show that these results can be extended to a simple dynamic model that allows for intertemporal substitution. This simple model maintains an arbitrarily large gap between attitudes to aggregate and idiosyncratic risk but generates plausible elasticities of intertemporal substitution.