A comparison of three different models for estimating relative risk in meta-analysis of clinical trials under unobserved heterogeneity

We focus on the comparison of three statistical models used to estimate the treatment effect in metaanalysis when individually pooled data are available. The models are two conventional models, namely a multi-level and a model based upon an approximate likelihood, and a newly developed model, the profile likelihood model which might be viewed as an extension of the Mantel-Haenszel approach. To exemplify these methods, we use results from a meta-analysis of 22 trials to prevent respiratory tract infections. We show that by using the multi-level approach, in the case of baseline heterogeneity, the number of clusters or components is considerably over-estimated. The approximate and profile likelihood method showed nearly the same pattern for the treatment effect distribution. To provide more evidence two simulation studies are accomplished. The profile likelihood can be considered as a clear alternative to the approximate likelihood model. In the case of strong baseline heterogeneity, the profile likelihood method shows superior behaviour when compared with the multi-level model. Copyright (C) 2006 John Wiley & Sons, Ltd.

Effects of presenting the baseline risk when communicating absolute and relative risk reductions

This study compares relative and absolute forms of presenting risk information about influenza and the need for vaccination. It investigates whether differences in people's risk estimates and their evaluations of risk information, as a result of the different presentation formats, are still apparent when they are provided with information about the baseline level of risk. The results showed that, in the absence of baseline information, the relative risk format resulted in higher ratings of satisfaction, perceived effectiveness of vaccination, and likelihood of being vaccinated. However, these differences were not apparent when baseline information was presented. Overall, provision of baseline information resulted in more accurate risk estimates and more positive evaluations of the risk messages. It is recommended that, in order to facilitate shared and fully informed decision making, information about baseline level of risk should be included in all health communications specifying risk reductions, irrespective of the particular format adopted.

Expressing medicine side effects: assessing the effectiveness of absolute risk, relative risk, and number needed to harm, and the provision of baseline risk information

Objective: To assess the effectiveness of absolute risk, relative risk, and number needed to harm formats for medicine side effects, with and without the provision of baseline risk information. Methods: A two factor, risk increase format (relative, absolute and NNH) x baseline (present/absent) between participants design was used. A sample of 268 women was given a scenario about increase in side effect risk with third generation oral contraceptives, and were required to answer written questions to assess their understanding, satisfaction, and likelihood of continuing to take the drug. Results: Provision of baseline information significantly improved risk estimates and increased satisfaction, although the estimates were still considerably higher than the actual risk. No differences between presentation formats were observed when baseline information was presented. Without baseline information, absolute risk led to the most accurate performance. Conclusion: The findings support the importance of informing people about baseline level of risk when describing risk increases. In contrast, they offer no support for using number needed to harm. Practice implications: Health professionals should provide baseline risk information when presenting information about risk increases or decreases. More research is needed before numbers needed to harm (or treat) should be given to members of the general populations. (c) 2005 Elsevier Ireland Ltd. All rights reserved.

Estimating Relative Risk Aversion, Risk-Neutral and Real-World Densities using Brazilian Real Currency Options

Building Risk-Neutral Densities (RND) from options data can provide market-implied expectations about the future behavior of a financial variable. And market expectations on financial variables may influence macroeconomic policy decisions. It can be useful also for corporate and financial institutions decision making. This paper uses the Liu et all (2007) approach to estimate the option-implied Risk-neutral densities from the Brazilian Real/US Dollar exchange rate distribution. We then compare the RND with actual exchange rates, on a monthly basis, in order to estimate the relative risk-aversion of investors and also obtain a Real-world density for the exchange rate. We are the first to calculate relative risk-aversion and the option-implied Real World Density for an emerging market currency. Our empirical application uses a sample of Brazilian Real/US Dollar options traded at BM&F-Bovespa from 1999 to 2011. The RND is estimated using a Mixture of Two Log-Normals distribution and then the real-world density is obtained by means of the Liu et al. (2007) parametric risktransformations. The relative risk aversion is calculated for the full sample. Our estimated value of the relative risk aversion parameter is around 2.7, which is in line with other articles that have estimated this parameter for the Brazilian Economy, such as Araújo (2005) and Issler and Piqueira (2000). Our out-of-sample evaluation results showed that the RND has some ability to forecast the Brazilian Real exchange rate. Abe et all (2007) found also mixed results in the out-of-sample analysis of the RND forecast ability for exchange rate options. However, when we incorporate the risk aversion into RND in order to obtain a Real-world density, the out-of-sample performance improves substantially, with satisfactory results in both Kolmogorov and Berkowitz tests. Therefore, we would suggest not using the “pure” RND, but rather taking into account risk aversion in order to forecast the Brazilian Real exchange rate.

Relative risk of death for ejected occupants in fatal traffic accidents. Technical report.

Mode of access: Internet.

The report of the Strategic Options Subcommittee : relative risk reduction project : Reducing risk, appendix C.

"September 1990."

The report of the Ecology and Welfare Subcommittee : relative risk reduction project : Reducing risk, appendix A.

"September 1990."

Refining the risk-benefit equation for thrombolysis: How to identity the low risk patient before administering thrombolytic therapy

In view of the relative risk of intracranial haemorrhage and major bleeding with thrombolytic therapy, it is important ro identify as early as possible the low risk patient who may not have a net clinical benefit from thrombolysis in the setting of acute myocardial infarction. An analysis of 5434 hospital-treated patients with myocardial infarction in the Perth MONICA study showed that age below 60 and absence of previous infarction or diabetes, shock, pulmonary oedema, cardiac arrest and Q-wave or left bundle branch block on the initial ECG identified a large group of patients with a 28 day mortality of only 1%, and one year mortality of only 2%. Identification of baseline risk in this way helps refine the risk-benefit equation for thrombolytic therapy, and may help avoid unnecessary use of thrombolysis in those unlikely to benefit.

Risk premiums and benefit measures for generalized-expected-utility theories

Standard tools for the analysis of economic problems involving uncertainty, including risk premiums, certainty equivalents and the notions of absolute and relative risk aversion, are developed without making specific assumptions on functional form beyond the basic requirements of monotonicity, transitivity, continuity, and the presumption that individuals prefer certainty to risk. Individuals are not required to display probabilistic sophistication. The approach relies on the distance and benefit functions to characterize preferences relative to a given state-contingent vector of outcomes. The distance and benefit functions are used to derive absolute and relative risk premiums and to characterize preferences exhibiting constant absolute risk aversion (CARA) and constant relative risk aversion (CRRA). A generalization of the notion of Schur-concavity is presented. If preferences are generalized Schur concave, the absolute and relative risk premiums are generalized Schur convex, and the certainty equivalents are generalized Schur concave.

Response to price and production risk: The case of Australian wheat

A model of Australian wheat grower supply response was specified under the constraints of price and yield uncertainty, risk aversion, partial adjustment, and quadratic costs. The model was solved to obtain area planted. The results of estimation indicate that risk arising from prices and climate have had a significant influence on producer decision making. The coefficient of relative risk aversion and short-run and long-run elasticities of supply with respect to price were calculated. Wheat growers' risk premium, expected at the start of the season for exposed price and yield risk, was 2.8 percent of revenue or 10.4 percent of profit as measured by producer surplus. (C) 2000 John Wiley & Sons, Inc.

Current smoking and the risk of non-fatal myocardial infarction in the WHO MONICA Project populations

Background: Cohort studies have shown that smoking has a substantial influence on coronary heart disease mortality in young people. Population based data on non-fatal events have been sparse, however. Objective: To study the impact of smoking on the risk of non-fatal acute myocardial infarction (MI) in young middle age people. Methods: From 1985 to 1994 all non-fatal MI events in the age group 35 - 64 were registered in men and women in the WHO MONICA ( multinational monitoring of trends and determinants in cardiovascular disease) project populations ( 18 762 events in men and 4047 in women from 32 populations from 21 countries). In the same populations and age groups 65 741 men and 66 717 women participated in the surveys of risk factors ( overall response rate 72%). The relative risk of non-fatal MI for current smokers was compared with non-smokers, by sex and five year age group. Results: The prevalence of smoking in people aged 35 - 39 years who experienced non-fatal MI events was 81% in men and 77% in women. It declined with increasing age to 45% in men aged 60 - 64 years and 36% in women, respectively. In the 35 - 39 years age group the relative risk of non-fatal MI for smokers was 4.9 (95% confidence interval (CI) 3.9 to 6.1) in men and 5.3 ( 95% CI 3.2 to 8.7) in women, and the population attributable fractions were 65% and 55%, respectively. Conclusions: During the study period more than half of the non-fatal MIs occurring in young middle age people can be attributed to smoking.

Prevalence of peripheral arterial disease: persistence of excess risk in former smokers

Objective: To determine the age-standardised prevalence of peripheral arterial disease (PAD) and associated risk factors, particularly smoking. Method: Design: Cross-sectional survey of a randomly selected population. Setting: Metropolitan area of Perth, Western Australia. Participants: Men aged between 65-83 years. Results: The adjusted response fraction was 77.2%. Of 4,470 men assessed, 744 were identified as having PAD by the Edinburgh Claudication Questionnaire and/or the ankle-brachial index of systolic blood pressure, yielding an age-standardised prevalence of PAD of 15.6% (95% confidence intervals (CI): 14.5%, 16.6%). The main risk factors identified in univariate analyses were increasing age, smoking current (OR=3.9, 95% CI 2.9-5.1) or former (OR=2.0, 95% CI 1.6-2.4), physical inactivity (OR=1.4, 95% CI 1.2-1.7), a history of angina (OR=2.2, 95% CI 1.8-2.7) and diabetes mellitus (OR=2.1, 95% CI 1.7-2.6). The multivariate analysis showed that the highest relative risk associated with PAD was current smoking of 25 or more cigarettes daily (OR=7.3, 95% CI 4.2-12.8). In this population, 32% of PAD was attributable to current smoking and a further 40% was attributable to past smoking by men who did not smoke currently. Conclusions: This large observational study shows that PAD is relatively common in older, urban Australian men. In contrast with its relationship to coronary disease and stroke, previous smoking appears to have a long legacy of increased risk of PAD. Implications: This research emphasises the importance of smoking as a preventable cause of PAD.

Hormone replacement therapy and breast cancer risk in California

Numerous studies have documented increased breast cancer risks with hormone replacement therapy (HRT), but these do not give a woman her specific absolute risk for the remainder of her life. This article estimates the magnitude of the effect of HRT on breast cancer incidence in California and calculates a woman's cumulative risk of breast cancer with different formulations and durations of HRT use. The effects of HRT on the underlying breast cancer incidence were estimated using the attributable fraction method, applying HRT prevalence data from the 2001 California Health Interview Survey and published rates of higher relative risk (RR) from HRT use from the Women's Health Initiative (WHI) study and Million Women's Survey (MWS). The annual number of breast cancers potentially attributable to HRT in California was estimated, along with individual cumulative risk of breast cancer for various ages to 79 years according to HRT use, duration, and formulation. Using the WHI data, 829 of 19,000 breast cancers (4.3%) in California may be attributable to HRT This figure increases to 3401 (17.4%) when the MWS RRs are applied. Use of estrogen-only HRT or short-term (approximately 5 years) use of combined HRT has a minimal effect on the cumulative risk calculated to the age of 79 years; application of the MWS data to a Californian woman commencing HRT at the age of 50 years (no HRT, 8.5%; estrogen only, 8.6%; combined, 9.1%). Prolonged (approximately 10 years) use of combined HRT increases the cumulative risk to 10.3%. This article demonstrates that HRT will generate a small additional risk of breast cancer in an individual. The reduction in perimenopausal symptoms may be considered sufficient to warrant this extra risk. However, this view needs to be balanced because the small increases in individual risk will be magnified, producing a noticeable change in population cancer caseload where HRT use is high.

Overweight and obesity increase the risk of coronary heart disease: A pooled analysis of 30 prospective studies

The importance of overweight as a risk factor for coronary heart disease (CHD) remains unsettled. We estimated the relative risk (RR) for CHD associated with underweight (body mass index, BMI < 20 kg/m2), overweight (25 – 30 kg/m2) and obesity (= 30 kg/m2), compared with normal weight (20 – 25 kg/m2) in a random effects meta-analysis of 30 prospective studies, including 389,239 healthy, predominantly Caucasian persons. We also explored sources of heterogeneity between studies and examined effects of systematic adjustment for confounding and intermediary variables. Pooled age-, sex- and smoking-adjusted RRs (95% confidence interval) for overweight, obesity and underweight compared with normal weight were 1.33 (1.24 – 1.43), 1.69 (1.44 – 1.99) and 1.01 (0.85 – 1.20), respectively. Stratified analyses showed that pooled RRs for BMI were higher for studies with longer follow-up (= vs. < 15 years) and younger populations (< vs. = 60 years). Additional adjustment for blood pressure, cholesterol levels and physical activity decreased the RR per 5 BMI units from 1.28 (1.21 – 1.34) to 1.16 (1.11 – 1.21). We conclude that overweight and obesity are associated with a substantially increased CHD risk in Caucasians, whereas underweight is not. Prevention and reduction of overweight and obesity, therefore, remain of importance for preventing CHD.