Estimation of jump-diffusion processes via empirical characteristic functions

Preface The starting point for this work and eventually the subject of the whole thesis was the question: how to estimate parameters of the affine stochastic volatility jump-diffusion models. These models are very important for contingent claim pricing. Their major advantage, availability T of analytical solutions for characteristic functions, made them the models of choice for many theoretical constructions and practical applications. At the same time, estimation of parameters of stochastic volatility jump-diffusion models is not a straightforward task. The problem is coming from the variance process, which is non-observable. There are several estimation methodologies that deal with estimation problems of latent variables. One appeared to be particularly interesting. It proposes the estimator that in contrast to the other methods requires neither discretization nor simulation of the process: the Continuous Empirical Characteristic function estimator (EGF) based on the unconditional characteristic function. However, the procedure was derived only for the stochastic volatility models without jumps. Thus, it has become the subject of my research. This thesis consists of three parts. Each one is written as independent and self contained article. At the same time, questions that are answered by the second and third parts of this Work arise naturally from the issues investigated and results obtained in the first one. The first chapter is the theoretical foundation of the thesis. It proposes an estimation procedure for the stochastic volatility models with jumps both in the asset price and variance processes. The estimation procedure is based on the joint unconditional characteristic function for the stochastic process. The major analytical result of this part as well as of the whole thesis is the closed form expression for the joint unconditional characteristic function for the stochastic volatility jump-diffusion models. The empirical part of the chapter suggests that besides a stochastic volatility, jumps both in the mean and the volatility equation are relevant for modelling returns of the S&P500 index, which has been chosen as a general representative of the stock asset class. Hence, the next question is: what jump process to use to model returns of the S&P500. The decision about the jump process in the framework of the affine jump- diffusion models boils down to defining the intensity of the compound Poisson process, a constant or some function of state variables, and to choosing the distribution of the jump size. While the jump in the variance process is usually assumed to be exponential, there are at least three distributions of the jump size which are currently used for the asset log-prices: normal, exponential and double exponential. The second part of this thesis shows that normal jumps in the asset log-returns should be used if we are to model S&P500 index by a stochastic volatility jump-diffusion model. This is a surprising result. Exponential distribution has fatter tails and for this reason either exponential or double exponential jump size was expected to provide the best it of the stochastic volatility jump-diffusion models to the data. The idea of testing the efficiency of the Continuous ECF estimator on the simulated data has already appeared when the first estimation results of the first chapter were obtained. In the absence of a benchmark or any ground for comparison it is unreasonable to be sure that our parameter estimates and the true parameters of the models coincide. The conclusion of the second chapter provides one more reason to do that kind of test. Thus, the third part of this thesis concentrates on the estimation of parameters of stochastic volatility jump- diffusion models on the basis of the asset price time-series simulated from various "true" parameter sets. The goal is to show that the Continuous ECF estimator based on the joint unconditional characteristic function is capable of finding the true parameters. And, the third chapter proves that our estimator indeed has the ability to do so. Once it is clear that the Continuous ECF estimator based on the unconditional characteristic function is working, the next question does not wait to appear. The question is whether the computation effort can be reduced without affecting the efficiency of the estimator, or whether the efficiency of the estimator can be improved without dramatically increasing the computational burden. The efficiency of the Continuous ECF estimator depends on the number of dimensions of the joint unconditional characteristic function which is used for its construction. Theoretically, the more dimensions there are, the more efficient is the estimation procedure. In practice, however, this relationship is not so straightforward due to the increasing computational difficulties. The second chapter, for example, in addition to the choice of the jump process, discusses the possibility of using the marginal, i.e. one-dimensional, unconditional characteristic function in the estimation instead of the joint, bi-dimensional, unconditional characteristic function. As result, the preference for one or the other depends on the model to be estimated. Thus, the computational effort can be reduced in some cases without affecting the efficiency of the estimator. The improvement of the estimator s efficiency by increasing its dimensionality faces more difficulties. The third chapter of this thesis, in addition to what was discussed above, compares the performance of the estimators with bi- and three-dimensional unconditional characteristic functions on the simulated data. It shows that the theoretical efficiency of the Continuous ECF estimator based on the three-dimensional unconditional characteristic function is not attainable in practice, at least for the moment, due to the limitations on the computer power and optimization toolboxes available to the general public. Thus, the Continuous ECF estimator based on the joint, bi-dimensional, unconditional characteristic function has all the reasons to exist and to be used for the estimation of parameters of the stochastic volatility jump-diffusion models.

Determinants of the omega-3 index in a Mediterranean population at increased risk for CHD.

The omega-3 index, defined as the sum of EPA and DHA in erythrocyte membranes expressed as a percentage of total fatty acids, has been proposed as both a risk marker and risk factor for CHD death. A major determinant of the omega-3 index is EPA þ DHA intake, but the impact of other dietary fatty acids has not been investigated. In a cross-sectional study on 198 subjects (102 men and 96 women, mean age 66 years) at high cardiovascular risk living in Spain, the country with low rates of cardiac death despite a high prevalence of cardiovascular risk factors, dietary data were acquired from FFQ and blood cell membrane fatty acid composition was measured by GC. The average consumption of EPA þ DHA was 0·9 g/d and the mean omega-3 index was 7·1%. In multivariate models, EPA þ DHA intake was the main predictor of the omega-3 index but explained only 12% of its variability (P,0·001). No associations with other dietary fatty acids were observed. Although the single most influential determinant of the omega-3 index measured here was the intake of EPA þ DHA, it explained little of the former"s variability; hence, the effects of other factors (genetic, dietary and lifestyle) remain to be determined. Nevertheless, the high omega-3 index could at least partially explain the paradox of low rates of fatal CHD in Spain despite a high background prevalence of cardiovascular risk factors.

Determinants of the omega-3 index in a Mediterranean population at increased risk for CHD.

The omega-3 index, defined as the sum of EPA and DHA in erythrocyte membranes expressed as a percentage of total fatty acids, has been proposed as both a risk marker and risk factor for CHD death. A major determinant of the omega-3 index is EPA þ DHA intake, but the impact of other dietary fatty acids has not been investigated. In a cross-sectional study on 198 subjects (102 men and 96 women, mean age 66 years) at high cardiovascular risk living in Spain, the country with low rates of cardiac death despite a high prevalence of cardiovascular risk factors, dietary data were acquired from FFQ and blood cell membrane fatty acid composition was measured by GC. The average consumption of EPA þ DHA was 0·9 g/d and the mean omega-3 index was 7·1%. In multivariate models, EPA þ DHA intake was the main predictor of the omega-3 index but explained only 12% of its variability (P,0·001). No associations with other dietary fatty acids were observed. Although the single most influential determinant of the omega-3 index measured here was the intake of EPA þ DHA, it explained little of the former"s variability; hence, the effects of other factors (genetic, dietary and lifestyle) remain to be determined. Nevertheless, the high omega-3 index could at least partially explain the paradox of low rates of fatal CHD in Spain despite a high background prevalence of cardiovascular risk factors.

Isolated limb perfusion: distinct tourniquet and tumor necrosis factor effects on the early hemodynamic response.

HYPOTHESIS: Recent evidence indicates that tumor response rates after isolated limb perfusion (ILP) are improved when tumor necrosis factor (TNF) is added to the locoregional perfusion of high doses of chemotherapy. Other factors, related to the patient or the ILP procedure, may interfere with the specific role of TNF in the early hemodynamic response after ILP with TNF and high-dose chemotherapy. DESIGN: Case-control study. SETTING: Tertiary care university hospital. PATIENTS: Thirty-eight patients with a locoregionally advanced tumor of a limb treated by ILP with TNF and high-dose chemotherapy (TNF group) were compared with 31 similar patients treated by ILP with high-dose chemotherapy alone (non-TNF group). INTERVENTIONS: Swan-Ganz catheter hemodynamic recordings, patients' treatment data collection, and TNF and interleukin 6 plasma level measurements at regular intervals during the first 36 hours following ILP. MAIN OUTCOME MEASURES: Hemodynamic profile and total fluid and catecholamine administration. RESULTS: In the TNF group, significant changes were observed (P<.006): the mean arterial pressure and the systemic vascular resistance index decreased, and the temperature, heart rate, and cardiac index increased. These hemodynamic alterations started when the ILP tourniquet was released (ie, when or shortly after the systemic TNF levels were the highest). The minimal mean arterial pressure, the minimal systemic vascular resistance index, the maximal cardiac index, the intensive care unit stay, and the interleukin 6 maximal systemic levels were significantly (P<.001 for all) correlated to the log(10) of the systemic TNF level. In the non-TNF group, only a brief decrease in the blood pressure following tourniquet release and an increase in the temperature and in the heart rate were statistically significant (P<.006). Despite significantly more fluid and catecholamine administration in the TNF group, the mean arterial pressure and the systemic vascular resistance index were significantly (P<.001) lower than in the non-TNF group. CONCLUSIONS: Release of the tourniquet induces a blood pressure decrease that lasts less than 1 hour in the absence of TNF and that is distinct from the septic shock-like hemodynamic profile following TNF administration. The systemic TNF levels are correlated to this hemodynamic response, which can be observed even at low TNF levels.

Determinants of the omega-3 index in a Mediterranean population at increased risk for CHD.

The omega-3 index, defined as the sum of EPA and DHA in erythrocyte membranes expressed as a percentage of total fatty acids, has been proposed as both a risk marker and risk factor for CHD death. A major determinant of the omega-3 index is EPA þ DHA intake, but the impact of other dietary fatty acids has not been investigated. In a cross-sectional study on 198 subjects (102 men and 96 women, mean age 66 years) at high cardiovascular risk living in Spain, the country with low rates of cardiac death despite a high prevalence of cardiovascular risk factors, dietary data were acquired from FFQ and blood cell membrane fatty acid composition was measured by GC. The average consumption of EPA þ DHA was 0·9 g/d and the mean omega-3 index was 7·1%. In multivariate models, EPA þ DHA intake was the main predictor of the omega-3 index but explained only 12% of its variability (P,0·001). No associations with other dietary fatty acids were observed. Although the single most influential determinant of the omega-3 index measured here was the intake of EPA þ DHA, it explained little of the former"s variability; hence, the effects of other factors (genetic, dietary and lifestyle) remain to be determined. Nevertheless, the high omega-3 index could at least partially explain the paradox of low rates of fatal CHD in Spain despite a high background prevalence of cardiovascular risk factors.

FTO genotype is associated with phenotypic variability of body mass index.

There is evidence across several species for genetic control of phenotypic variation of complex traits, such that the variance among phenotypes is genotype dependent. Understanding genetic control of variability is important in evolutionary biology, agricultural selection programmes and human medicine, yet for complex traits, no individual genetic variants associated with variance, as opposed to the mean, have been identified. Here we perform a meta-analysis of genome-wide association studies of phenotypic variation using ∼170,000 samples on height and body mass index (BMI) in human populations. We report evidence that the single nucleotide polymorphism (SNP) rs7202116 at the FTO gene locus, which is known to be associated with obesity (as measured by mean BMI for each rs7202116 genotype), is also associated with phenotypic variability. We show that the results are not due to scale effects or other artefacts, and find no other experiment-wise significant evidence for effects on variability, either at loci other than FTO for BMI or at any locus for height. The difference in variance for BMI among individuals with opposite homozygous genotypes at the FTO locus is approximately 7%, corresponding to a difference of ∼0.5 kilograms in the standard deviation of weight. Our results indicate that genetic variants can be discovered that are associated with variability, and that between-person variability in obesity can partly be explained by the genotype at the FTO locus. The results are consistent with reported FTO by environment interactions for BMI, possibly mediated by DNA methylation. Our BMI results for other SNPs and our height results for all SNPs suggest that most genetic variants, including those that influence mean height or mean BMI, are not associated with phenotypic variance, or that their effects on variability are too small to detect even with samples sizes greater than 100,000.

Evaluation of a multicomponent worksite health promotion program for cardiovascular risk factors-correcting for the regression towards the mean effect.

BACKGROUND: We assessed the impact of a multicomponent worksite health promotion program for0 reducing cardiovascular risk factors (CVRF) with short intervention, adjusting for regression towards the mean (RTM) affecting such nonexperimental study without control group. METHODS: A cohort of 4,198 workers (aged 42 +/- 10 years, range 16-76 years, 27% women) were analyzed at 3.7-year interval and stratified by each CVRF risk category (low/medium/high blood pressure [BP], total cholesterol [TC], body mass index [BMI], and smoking) with RTM and secular trend adjustments. Intervention consisted of 15 min CVRF screening and individualized counseling by health professionals to medium- and high-risk individuals, with eventual physician referral. RESULTS: High-risk groups participants improved diastolic BP (-3.4 mm Hg [95%CI: -5.1, -1.7]) in 190 hypertensive patients, TC (-0.58 mmol/l [-0.71, -0.44]) in 693 hypercholesterolemic patients, and smoking (-3.1 cig/day [-3.9, -2.3]) in 808 smokers, while systolic BP changes reflected RTM. Low-risk individuals without counseling deteriorated TC and BMI. Body weight increased uniformly in all risk groups (+0.35 kg/year). CONCLUSIONS: In real-world conditions, short intervention program participants in high-risk groups for diastolic BP, TC, and smoking improved their CVRF, whereas low-risk TC and BMI groups deteriorated. Future programs may include specific advises to low-risk groups to maintain a favorable CVRF profile.

Reference values and factors associated with renal resistive index in a family-based population study.

Increased renal resistive index (RRI) has been recently associated with target organ damage and cardiovascular or renal outcomes in patients with hypertension and diabetes mellitus. However, reference values in the general population and information on familial aggregation are largely lacking. We determined the distribution of RRI, associated factors, and heritability in a population-based study. Families of European ancestry were randomly selected in 3 Swiss cities. Anthropometric parameters and cardiovascular risk factors were assessed. A renal Doppler ultrasound was performed, and RRI was measured in 3 segmental arteries of both kidneys. We used multilevel linear regression analysis to explore the factors associated with RRI, adjusting for center and family relationships. Sex-specific reference values for RRI were generated according to age. Heritability was estimated by variance components using the ASSOC program (SAGE software). Four hundred women (mean age±SD, 44.9±16.7 years) and 326 men (42.1±16.8 years) with normal renal ultrasound had mean RRI of 0.64±0.05 and 0.62±0.05, respectively (P<0.001). In multivariable analyses, RRI was positively associated with female sex, age, systolic blood pressure, and body mass index. We observed an inverse correlation with diastolic blood pressure and heart rate. Age had a nonlinear association with RRI. We found no independent association of RRI with diabetes mellitus, hypertension treatment, smoking, cholesterol levels, or estimated glomerular filtration rate. The adjusted heritability estimate was 42±8% (P<0.001). In a population-based sample with normal renal ultrasound, RRI normal values depend on sex, age, blood pressure, heart rate, and body mass index. The significant heritability of RRI suggests that genes influence this phenotype.

A Swiss neighbourhood index of socioeconomic position: Development and Association with Mortality

Background Area-based measures of socioeconomic position (SEP) suitable for epidemiological research are lacking in Switzerland. The authors developed the Swiss neighbourhood index of SEP (Swiss-SEP). Methods Neighbourhoods of 50 households with overlapping boundaries were defined using Census 2000 and road network data. Median rent per square metre, proportion households headed by a person with primary education or less, proportion headed by a person in manual or unskilled occupation and the mean number of persons per room were analysed in principle component analysis. The authors compared the index with independent income data and examined associations with mortality from 2001 to 2008. Results 1.27 million overlapping neighbourhoods were defined. Education, occupation and housing variables had loadings of 0.578, 0.570 and 0.362, respectively, and median rent had a loading of −0.459. Mean yearly equivalised income of households increased from SFr42 000 to SFr72 000 between deciles of neighbourhoods with lowest and highest SEP. Comparing deciles of neighbourhoods with lowest to highest SEP, the age- and sex-adjusted HR was 1.38 (95% CI 1.36 to 1.41) for all-cause mortality, 1.83 (95% CI 1.71 to 1.95) for lung cancer, 1.48 (95% CI 1.44 to 1.51) for cardiovascular diseases, 2.42 (95% CI 1.94 to 3.01) for traffic accidents, 0.93 (95% CI 0.85 to 1.02) for breast cancer and 0.86 (95% CI 0.78 to 0.95) for suicide. Conclusions Developed using a novel approach to define neighbourhoods, the Swiss-SEP index was strongly associated with household income and some causes of death. It will be useful for clinical- and population-based studies, where individual-level socioeconomic data are often missing, and to investigate the effects on health of the socioeconomic characteristics of a place.

Prepregnancy body mass index and resting metabolic rate during pregnancy.

AIM: The resting metabolic rate (RMR) varies among pregnant women. The factors responsible for this variability are unknown. This study aimed to assess the influence of the prepregnancy body mass index (BMI) on the RMR during late pregnancy. METHODS: RMR, height, weight, and total (TEE) and activity (AEE) energy expenditures were measured in 46 healthy women aged 31 ± 5 years (mean ± SD) with low (<19.8), normal (19.8-26.0), and high (>26.0) prepregnancy BMI at 38.2 ± 1.5 weeks of gestation (t(gest)) and 40 ± 7 weeks postpartum (t(post)) (n = 27). RESULTS: The mean t(gest) RMR for the low-, normal-, and high-BMI groups was 1,373, 1,807, and 2,191 kcal/day, respectively (p = 0.001). The overall mean t(gest) RMR was 316 ± 183 kcal/day (21%), higher than the overall mean t(post) value and this difference was correlated with gestational weight gain (r = 0.78, p < 0.001). The scaled metabolic rate by allometry (RMR/kilograms⁰·⁷³) was similar in the low-, normal-, and high-BMI groups, respectively (p = 0.45). Changes in t(gest) TEE closely paralleled changes in t(gest) RMR (r = 0.84, p < 0.001). AEE was similar among the BMI groups. CONCLUSION: The RMR is significantly increased in the third trimester of pregnancy. The absolute gestational RMR is higher in women with high prepregnancy BMI due to increased body weight. The scaled metabolic rate (RMR/kilograms⁰·⁷³) is similar among the BMI groups of pregnant women.

Development of an activity index for adult eosinophilic esophagitis: international experts propose dysphagia, withish exudates on endoscopy and peripheral eosinophilia as items with closest association to EoE activity

Background and Aims: Eosinophilic Esophagitis (EoE) is reported with increasing frequency over the last two decades. However, it is still unknown whether this reflects a true increase in incidence or just an increased awareness by gastroenterologists. Therefore, we evaluated the incidence and cumulative prevalence of EoE in Olten county over the last 20 years. Methods: Olten county is an area of approximately 91,000 inhabitants without pronounced demographic changes in the last two decades. EoE evaluation is based upon two gastroenterology centers and one pathology center. No public programs for increased EoE awareness were implemented in this region. All EoE patients diagnosed from 1989 to 2009 were entered prospectively into the Olten county database. Results: Fourty-six patients (76% males, mean age 41±16 yrs) were diagnosed with EoE from 1989 to 2009. Ninety-four percent presented with dysphagia. In 70% of the patients concomitant allergies were found. The number of upper endoscopies per year was stable during the entire observation period. An average annual incidence rate of 2/100,000 was found (range 0-8) with a marked increase in the period from 2001 to 2009. A current cumulative EoE prevalence of 43/100,000 inhabitants was calculated. The mean diagnostic delay (time from first symptoms to diagnosis) was 4.3 years from 1989 to 1998 and 4.8 years from 1999 to 2009. Conclusions: Over the last 20 years, a significant increase in EoE incidence was found in a stable indicator region of Switzerland. The constant rate of upper endoscopies, the constant diagnostic delay, as well as the lack of EoE awareness programs in Olten county indicate a true increase in EoE incidence.

4B.05: Plasma Lasma copeptin is associated with insulin resistance in a Swiss population-based study

OBJECTIVE: Previous studies suggest that arginine vasopressin may have a role in metabolic syndrome (MetS) and diabetes by altering liver glycogenolysis, insulin, and glucagon secretion and pituitary ACTH release. We tested whether plasma copeptin, the stable C-terminal fragment of arginine vasopressin prohormone, was associated with insulin resistance and MetS in a Swiss population-based study. DESIGN AND METHOD: We analyzed data from the population-based Swiss Kidney Project on Genes in Hypertension. Copeptin was assessed by an immunoluminometric assay. Insulin resistance was derived from the HOMA model and calculated as follows: (FPI x FPG)/22.5, where FPI is fasting plasma insulin concentration (mU/L) and FPG fasting plasma glucose (mmol/L). Subjects were classified as having the MetS according to the National Cholesterol Education Program Adult Treatment Panel III criteria. Mixed multivariate linear regression models were built to explore the association of insulin resistance with copeptin. In addition, multivariate logistic regression models were built to explore the association between MetS and copeptin. In the two analyses, adjustment was done for age, gender, center, tobacco and alcohol consumption, socioeconomic status, physical activity, intake of fruits and vegetables and 24 h urine flow rate. Copeptin was log-transformed for the analyses. RESULTS: Among the 1,089 subjects included in this analysis, 47% were male. Mean (SD) age and body mass index were 47.4 (17.6) years 25.0 (4.5) kg/m2. The prevalence of MetS was 10.5%. HOMA-IR was higher in men (median 1.3, IQR 0.7-2.1) than in women (median 1.0, IQR 0.5-1.6,P < 0.0001). Plasma copeptin was higher in men (median 5.2, IQR 3.7-7.8 pmol/L) than in women (median 3.0, IQR 2.2-4.3 pmol/L), P < 0.0001. HOMA-IR was positively associated with log-copeptin after full adjustment (β (95% CI) 0.19 (0.09-0.29), P < 0.001). MetS was not associated with copeptin after full adjustment (P = 0.92). CONCLUSIONS: Insulin resistance, but not MetS, was associated with higher copeptin levels. Further studies should examine whether modifying pharmacologically the arginine vasopressin system might improve insulin resistance, thereby providing insight into the causal nature of this association.

1D.03: Inactive matrix GLA protein is associated with renal resistive index in a population-based study

OBJECTIVE: Renal resistive index (RRI) varies directly with renal vascular stiffness and pulse pressure. RRI correlates positively with arteriolosclerosis in damaged kidneys and predicts progressive renal dysfunction. Matrix Gla-protein (MGP) is a vascular calcification inhibitor that needs vitamin K to be activated. Inactive MGP, known as desphospho-uncarboxylated MGP (dp-ucMGP), can be measured in plasma and has been associated with various cardiovascular (CV) markers, CV outcomes and mortality. In this study we hypothesize that increased RRI is associated with high levels of dp-ucMGP. DESIGN AND METHOD: We recruited participants via a multi-center family-based cross-sectional study in Switzerland exploring the role of genes and kidney hemodynamics in blood pressure regulation. Dp-ucMGP was quantified in plasma samples by sandwich ELISA. Renal doppler sonography was performed using a standardized protocol to measure RRIs on 3 segmental arteries in each kidney. The mean of the 6 measures was reported. Multiple regression analysis was performed to estimate associations between RRI and dp-ucMGP adjusting for sex, age, pulse pressure, mean pressure, renal function and other CV risk factors. RESULTS: We included 1035 participants in our analyses. Mean values were 0.64 ± 0.06 for RRI and 0.44 ± 0.21 (nmol/L) for dp-ucMGP. RRI was positively associated with dp-ucMGP both before and after adjustment for sex, age, body mass index, pulse pressure, mean pressure, heart rate, renal function, low and high density lipoprotein, smoking status, diabetes, blood pressure and cholesterol lowering drugs, and history of CV disease (P < 0.001). CONCLUSIONS: RRI is independently and positively associated with high levels of dp-ucMGP after adjustment for pulse pressure and common CV risk factors. Further studies are needed to determine if vitamin K supplementation can have a positive effect on renal vascular stiffness and kidney function.

Multi-institutional validation of the prognostic value of Ki-67 labeling index in patients treated with radical prostatectomy.

OBJECTIVE: Several smaller single-center studies have reported a prognostic role for Ki-67 labeling index in prostate cancer. Our aim was to test whether Ki-67 is an independent prognostic marker of biochemical recurrence (BCR) in a large international cohort of patients treated with radical prostatectomy (RP). METHODS: Ki-67 immunohistochemical staining on prostatectomy specimens from 3,123 patients who underwent RP for prostate cancer was retrospectively performed. Univariable and multivariable Cox regression models were used to assess the association of Ki-67 status with BCR. RESULTS: Ki-67 positive status was observed in 762 (24.4 %) patients and was associated with lymph node involvement (LNI) (p = 0.039). Six hundred and twenty-one (19.9 %) patients experienced BCR. The estimated 3-year biochemical-free survivals were 85 % for patients with negative Ki-67 status and 82.1 % for patients with positive Ki-67 status (log-rank test, p = 0.014). In multivariable analysis that adjusted for the effects of age, preoperative PSA, RP Gleason sum, seminal vesicle invasion, extracapsular extension, positive surgical margins, lymphovascular invasion, and LNI, Ki-67 was significantly associated with BCR (HR = 1.19; p = 0.019). Subgroup analysis revealed that Ki-67 is associated with BCR in patients without LNI (p = 0.004), those with RP Gleason sum 7 (p = 0.015), and those with negative surgical margins (p = 0.047). CONCLUSION: We confirmed Ki-67 as an independent predictor of BCR after RP. Ki-67 could be particularly informative in patients with favorable pathologic characteristics to help in the clinical decision-making regarding adjuvant therapy and optimized follow-up scheduling.

Trends in adult body-mass index in 200 countries from 1975 to 2014: a pooled analysis of 1698 population-based measurement studies with 19·2 million participants.

BACKGROUND: Underweight and severe and morbid obesity are associated with highly elevated risks of adverse health outcomes. We estimated trends in mean body-mass index (BMI), which characterises its population distribution, and in the prevalences of a complete set of BMI categories for adults in all countries. METHODS: We analysed, with use of a consistent protocol, population-based studies that had measured height and weight in adults aged 18 years and older. We applied a Bayesian hierarchical model to these data to estimate trends from 1975 to 2014 in mean BMI and in the prevalences of BMI categories (<18·5 kg/m(2) [underweight], 18·5 kg/m(2) to <20 kg/m(2), 20 kg/m(2) to <25 kg/m(2), 25 kg/m(2) to <30 kg/m(2), 30 kg/m(2) to <35 kg/m(2), 35 kg/m(2) to <40 kg/m(2), ≥40 kg/m(2) [morbid obesity]), by sex in 200 countries and territories, organised in 21 regions. We calculated the posterior probability of meeting the target of halting by 2025 the rise in obesity at its 2010 levels, if post-2000 trends continue. FINDINGS: We used 1698 population-based data sources, with more than 19·2 million adult participants (9·9 million men and 9·3 million women) in 186 of 200 countries for which estimates were made. Global age-standardised mean BMI increased from 21·7 kg/m(2) (95% credible interval 21·3-22·1) in 1975 to 24·2 kg/m(2) (24·0-24·4) in 2014 in men, and from 22·1 kg/m(2) (21·7-22·5) in 1975 to 24·4 kg/m(2) (24·2-24·6) in 2014 in women. Regional mean BMIs in 2014 for men ranged from 21·4 kg/m(2) in central Africa and south Asia to 29·2 kg/m(2) (28·6-29·8) in Polynesia and Micronesia; for women the range was from 21·8 kg/m(2) (21·4-22·3) in south Asia to 32·2 kg/m(2) (31·5-32·8) in Polynesia and Micronesia. Over these four decades, age-standardised global prevalence of underweight decreased from 13·8% (10·5-17·4) to 8·8% (7·4-10·3) in men and from 14·6% (11·6-17·9) to 9·7% (8·3-11·1) in women. South Asia had the highest prevalence of underweight in 2014, 23·4% (17·8-29·2) in men and 24·0% (18·9-29·3) in women. Age-standardised prevalence of obesity increased from 3·2% (2·4-4·1) in 1975 to 10·8% (9·7-12·0) in 2014 in men, and from 6·4% (5·1-7·8) to 14·9% (13·6-16·1) in women. 2·3% (2·0-2·7) of the world's men and 5·0% (4·4-5·6) of women were severely obese (ie, have BMI ≥35 kg/m(2)). Globally, prevalence of morbid obesity was 0·64% (0·46-0·86) in men and 1·6% (1·3-1·9) in women. INTERPRETATION: If post-2000 trends continue, the probability of meeting the global obesity target is virtually zero. Rather, if these trends continue, by 2025, global obesity prevalence will reach 18% in men and surpass 21% in women; severe obesity will surpass 6% in men and 9% in women. Nonetheless, underweight remains prevalent in the world's poorest regions, especially in south Asia. FUNDING: Wellcome Trust, Grand Challenges Canada.