Properties of a risk measure derived from ruin theory

This paper studies a risk measure inherited from ruin theory and investigates some of its properties. Specifically, we consider a value-at-risk (VaR)-type risk measure defined as the smallest initial capital needed to ensure that the ultimate ruin probability is less than a given level. This VaR-type risk measure turns out to be equivalent to the VaR of the maximal deficit of the ruin process in infinite time. A related Tail-VaR-type risk measure is also discussed.

Risk prediction of prevalent diabetes in a Swiss population using a weighted genetic score--the CoLaus Study.

AIMS/HYPOTHESIS: Several susceptibility genes for type 2 diabetes have been discovered recently. Individually, these genes increase the disease risk only minimally. The goals of the present study were to determine, at the population level, the risk of diabetes in individuals who carry risk alleles within several susceptibility genes for the disease and the added value of this genetic information over the clinical predictors. METHODS: We constructed an additive genetic score using the most replicated single-nucleotide polymorphisms (SNPs) within 15 type 2 diabetes-susceptibility genes, weighting each SNP with its reported effect. We tested this score in the extensively phenotyped population-based cross-sectional CoLaus Study in Lausanne, Switzerland (n = 5,360), involving 356 diabetic individuals. RESULTS: The clinical predictors of prevalent diabetes were age, BMI, family history of diabetes, WHR, and triacylglycerol/HDL-cholesterol ratio. After adjustment for these variables, the risk of diabetes was 2.7 (95% CI 1.8-4.0, p = 0.000006) for individuals with a genetic score within the top quintile, compared with the bottom quintile. Adding the genetic score to the clinical covariates improved the area under the receiver operating characteristic curve slightly (from 0.86 to 0.87), yet significantly (p = 0.002). BMI was similar in these two extreme quintiles. CONCLUSIONS/INTERPRETATION: In this population, a simple weighted 15 SNP-based genetic score provides additional information over clinical predictors of prevalent diabetes. At this stage, however, the clinical benefit of this genetic information is limited.

Scores to predict major bleeding risk during oral anticoagulation therapy: a prospective validation study.

BACKGROUND: Clinical scores may help physicians to better assess the individual risk/benefit of oral anticoagulant therapy. We aimed to externally validate and compare the prognostic performance of 7 clinical prediction scores for major bleeding events during oral anticoagulation therapy. METHODS: We followed 515 adult patients taking oral anticoagulants to measure the first major bleeding event over a 12-month follow-up period. The performance of each score to predict the risk of major bleeding and the physician's subjective assessment of bleeding risk were compared with the C statistic. RESULTS: The cumulative incidence of a first major bleeding event during follow-up was 6.8% (35/515). According to the 7 scoring systems, the proportions of major bleeding ranged from 3.0% to 5.7% for low-risk, 6.7% to 9.9% for intermediate-risk, and 7.4% to 15.4% for high-risk patients. The overall predictive accuracy of the scores was poor, with the C statistic ranging from 0.54 to 0.61 and not significantly different from each other (P=.84). Only the Anticoagulation and Risk Factors in Atrial Fibrillation score performed slightly better than would be expected by chance (C statistic, 0.61; 95% confidence interval, 0.52-0.70). The performance of the scores was not statistically better than physicians' subjective risk assessments (C statistic, 0.55; P=.94). CONCLUSION: The performance of 7 clinical scoring systems in predicting major bleeding events in patients receiving oral anticoagulation therapy was poor and not better than physicians' subjective assessments.

Prognostic value of sentinel node biopsy in 327 prospective melanoma patients from a single institution

AIM: To confirm the accuracy of sentinel node biopsy (SNB) procedure and its morbidity, and to investigate predictive factors for SN status and prognostic factors for disease-free survival (DFS) and disease-specific survival (DSS). MATERIALS AND METHODS: Between October 1997 and December 2004, 327 consecutive patients in one centre with clinically node-negative primary skin melanoma underwent an SNB by the triple technique, i.e. lymphoscintigraphy, blue-dye and gamma-probe. Multivariate logistic regression analyses as well as the Kaplan-Meier were performed. RESULTS: Twenty-three percent of the patients had at least one metastatic SN, which was significantly associated with Breslow thickness (p<0.001). The success rate of SNB was 99.1% and its morbidity was 7.6%. With a median follow-up of 33 months, the 5-year DFS/DSS were 43%/49% for patients with positive SN and 83.5%/87.4% for patients with negative SN, respectively. The false-negative rate of SNB was 8.6% and sensitivity 91.4%. On multivariate analysis, DFS was significantly worsened by Breslow thickness (RR=5.6, p<0.001), positive SN (RR=5.0, p<0.001) and male sex (RR=2.9, p=0.001). The presence of a metastatic SN (RR=8.4, p<0.001), male sex (RR=6.1, p<0.001), Breslow thickness (RR=3.2, p=0.013) and ulceration (RR=2.6, p=0.015) were significantly associated with a poorer DSS. CONCLUSION: SNB is a reliable procedure with high sensitivity (91.4%) and low morbidity. Breslow thickness was the only statistically significant parameter predictive of SN status. DFS was worsened in decreasing order by Breslow thickness, metastatic SN and male gender. Similarly DSS was significantly worsened by a metastatic SN, male gender, Breslow thickness and ulceration. These data reinforce the SN status as a powerful staging procedure

Cardiovascular risk estimation and eligibility for statin therapy using different scoring systems in Europe: a population-based study in Switzerland

BACKGROUND: Recommendations for statin use for primary prevention of coronary heart disease (CHD) are based on estimation of the 10- year CHD risk. We compared the 10-year CHD risk assessments and eligibility percentages for statin therapy using three scoring algorithms currently used in Europe. METHODS: We studied 5683 women and men, aged 35-75, without overt cardiovascular disease (CVD), in a population-based study in Switzerland. We compared the 10-year CHD risk using three scoring schemes, i.e., the Framingham risk score (FRS) from the U.S. National Cholesterol Education Program's Adult Treatment Panel III (ATP III), the PROCAM scoring scheme from the International Atherosclerosis Society (IAS), and the European risk SCORE for low-risk countries, without and with extrapolation to 60 years as recommended by the European Society of Cardiology guidelines (ESC). With FRS and PROCAM, high-risk was defined as a 10- year risk of fatal or non-fatal CHD>20% and a 10-year risk of fatal CVD≥5% with SCORE. We compared the proportions of high-risk participants and eligibility for statin use according to these three schemes. For each guideline, we estimated the impact of increased statin use from current partial compliance to full compliance on potential CHD deaths averted over 10 years, using a success proportion of 27% for statins. RESULTS: Participants classified at high-risk (both genders) were 5.8% according to FRS and 3.0% to the PROCAM, whereas the European risk SCORE classified 12.5% at high-risk (15.4% with extrapolation to 60 years). For the primary prevention of CHD, 18.5% of participants were eligible for statin therapy using ATP III, 16.6% using IAS, and 10.3% using ESC (13.0% with extrapolation) because ESC guidelines recommend statin therapy only in high-risk subjects. In comparison with IAS, agreement to identify eligible adults for statins was good with ATP III, but moderate with ESC. Using a population perspective, a full compliance with ATP III guidelines would reduce up to 17.9% of the 24′ 310 CHD deaths expected over 10 years in Switzerland, 17.3% with IAS and 10.8% with ESC (11.5% with extrapolation). CONCLUSIONS: Full compliance with guidelines for statin therapy would result in substantial health benefits, but proportions of high-risk adults and eligible adults for statin use varied substantially depending on the scoring systems and corresponding guidelines used for estimating CHD risk in Europe.

Subclinical hyperthyroidism and the risk of coronary heart disease and mortality.

BACKGROUND: Data from prospective cohort studies regarding the association between subclinical hyperthyroidism and cardiovascular outcomes are conflicting.We aimed to assess the risks of total and coronary heart disease (CHD) mortality, CHD events, and atrial fibrillation (AF) associated with endogenous subclinical hyperthyroidism among all available large prospective cohorts. METHODS: Individual data on 52 674 participants were pooled from 10 cohorts. Coronary heart disease events were analyzed in 22 437 participants from 6 cohorts with available data, and incident AF was analyzed in 8711 participants from 5 cohorts. Euthyroidism was defined as thyrotropin level between 0.45 and 4.49 mIU/L and endogenous subclinical hyperthyroidism as thyrotropin level lower than 0.45 mIU/L with normal free thyroxine levels, after excluding those receiving thyroid-altering medications. RESULTS: Of 52 674 participants, 2188 (4.2%) had subclinical hyperthyroidism. During follow-up, 8527 participants died (including 1896 from CHD), 3653 of 22 437 had CHD events, and 785 of 8711 developed AF. In age- and sex-adjusted analyses, subclinical hyperthyroidism was associated with increased total mortality (hazard ratio[HR], 1.24, 95% CI, 1.06-1.46), CHD mortality (HR,1.29; 95% CI, 1.02-1.62), CHD events (HR, 1.21; 95%CI, 0.99-1.46), and AF (HR, 1.68; 95% CI, 1.16-2.43).Risks did not differ significantly by age, sex, or preexisting cardiovascular disease and were similar after further adjustment for cardiovascular risk factors, with attributable risk of 14.5% for total mortality to 41.5% forAF in those with subclinical hyperthyroidism. Risks for CHD mortality and AF (but not other outcomes) were higher for thyrotropin level lower than 0.10 mIU/L compared with thyrotropin level between 0.10 and 0.44 mIU/L(for both, P value for trend, .03). CONCLUSION: Endogenous subclinical hyperthyroidism is associated with increased risks of total, CHD mortality, and incident AF, with highest risks of CHD mortality and AF when thyrotropin level is lower than 0.10 mIU/L.

Modifiable and nonmodifiable risk factors for postoperative delirium after cardiac surgery with cardiopulmonary bypass.

Postoperative delirium after cardiac surgery is associated with increased morbidity and mortality as well as prolonged stay in both the intensive care unit and the hospital. The authors sought to identify modifiable risk factors associated with the development of postoperative delirium in elderly patients after elective cardiac surgery in order to be able to design follow-up studies aimed at the prevention of delirium by optimizing perioperative management. A post hoc analysis of data from patients enrolled in a randomized controlled trial was performed. A single university hospital. One hundred thirteen patients aged 65 or older undergoing elective cardiac surgery with cardiopulmonary bypass. None. MEASUREMENTS AND MAINS RESULTS: Screening for delirium was performed using the Confusion Assessment Method (CAM) on the first 6 postoperative days. A multivariable logistic regression model was developed to identify significant risk factors and to control for confounders. Delirium developed in 35 of 113 patients (30%). The multivariable model showed the maximum value of C-reactive protein measured postoperatively, the dose of fentanyl per kilogram of body weight administered intraoperatively, and the duration of mechanical ventilation to be independently associated with delirium. In this post hoc analysis, larger doses of fentanyl administered intraoperatively and longer duration of mechanical ventilation were associated with postoperative delirium in the elderly after cardiac surgery. Prospective randomized trials should be performed to test the hypotheses that a reduced dose of fentanyl administered intraoperatively, the use of a different opioid, or weaning protocols aimed at early extubation prevent delirium in these patients.

The optimal dividend barrier in the Gamma-Omega model

In the traditional actuarial risk model, if the surplus is negative, the company is ruined and has to go out of business. In this paper we distinguish between ruin (negative surplus) and bankruptcy (going out of business), where the probability of bankruptcy is a function of the level of negative surplus. The idea for this notion of bankruptcy comes from the observation that in some industries, companies can continue doing business even though they are technically ruined. Assuming that dividends can only be paid with a certain probability at each point of time, we derive closed-form formulas for the expected discounted dividends until bankruptcy under a barrier strategy. Subsequently, the optimal barrier is determined, and several explicit identities for the optimal value are found. The surplus process of the company is modeled by a Wiener process (Brownian motion).

Comparison of clinical and angiographic prognostic risk scores in elderly patients presenting with acute coronary syndrome and referred for percutaneous coronary intervention.

BACKGROUND: Multiple risk prediction models have been validated in all-age patients presenting with acute coronary syndrome (ACS) and treated with percutaneous coronary intervention (PCI); however, they have not been validated specifically in the elderly. METHODS: We calculated the GRACE (Global Registry of Acute Coronary Events) score, the logistic EuroSCORE, the AMIS (Acute Myocardial Infarction Swiss registry) score, and the SYNTAX (Synergy between Percutaneous Coronary Intervention with TAXUS and Cardiac Surgery) score in a consecutive series of 114 patients ≥75 years presenting with ACS and treated with PCI within 24 hours of hospital admission. Patients were stratified according to score tertiles and analysed retrospectively by comparing the lower/mid tertiles as an aggregate group with the higher tertile group. The primary endpoint was 30-day mortality. Secondary endpoints were the composite of death and major adverse cardiovascular events (MACE) at 30 days, and 1-year MACE-free survival. Model discrimination ability was assessed using the area under receiver operating characteristic curve (AUC). RESULTS: Thirty-day mortality was higher in the upper tertile compared with the aggregate lower/mid tertiles according to the logistic EuroSCORE (42% vs 5%; odds ratio [OR] = 14, 95% confidence interval [CI] = 4-48; p <0.001; AUC = 0.79), the GRACE score (40% vs 4%; OR = 17, 95% CI = 4-64; p <0.001; AUC = 0.80), the AMIS score (40% vs 4%; OR = 16, 95% CI = 4-63; p <0.001; AUC = 0.80), and the SYNTAX score (37% vs 5%; OR = 11, 95% CI = 3-37; p <0.001; AUC = 0.77). CONCLUSIONS: In elderly patients presenting with ACS and referred to PCI within 24 hours of admission, the GRACE score, the EuroSCORE, the AMIS score, and the SYNTAX score predicted 30 day mortality. The predictive value of clinical scores was improved by using them in combination.

Optimal dividend strategies for a compound Poisson risk process under transaction costs and power utility

We characterize the value function of maximizing the total discounted utility of dividend payments for a compound Poisson insurance risk model when strictly positive transaction costs are included, leading to an impulse control problem. We illustrate that well known simple strategies can be optimal in the case of exponential claim amounts. Finally we develop a numerical procedure to deal with general claim amount distributions.

Reduction in the use of diagnostic tests in infants with risk factors for early-onset neonatal sepsis does not delay antibiotic treatment.

Despite a low positive predictive value, diagnostic tests such as complete blood count (CBC) and C-reactive protein (CRP) are commonly used to evaluate whether infants with risk factors for early-onset neonatal sepsis (EOS) should be treated with antibiotics. We investigated the impact of implementing a protocol aiming at reducing the number of diagnostic tests in infants with risk factors for EOS in order to compare the diagnostic performance of repeated clinical examination with CBC and CRP measurement. The primary outcome was the time between birth and the first dose of antibiotics in infants treated for suspected EOS. Among the 11,503 infants born at ≥35 weeks during the study period, 222 were treated with antibiotics for suspected EOS. The proportion of infants receiving antibiotics for suspected EOS was 2.1% and 1.7% before and after the change of protocol (p = 0.09). Reduction of diagnostic tests was associated with earlier antibiotic treatment in infants treated for suspected EOS (hazard ratio 1.58; 95% confidence interval [CI] 1.20-2.07; p <0.001), and in infants with neonatal infection (hazard ratio 2.20; 95% CI 1.19-4.06; p = 0.01). There was no difference in the duration of hospital stay nor in the proportion of infants requiring respiratory or cardiovascular support before and after the change of protocol. Reduction of diagnostic tests such as CBC and CRP does not delay initiation of antibiotic treatment in infants with suspected EOS. The importance of clinical examination in infants with risk factors for EOS should be emphasised.