Simple parametric and nonparametric models for excess and relative mortality

This paper studies two classes of hazard-rate-based models for the mortality in a group of individuals taking normal life expectancy into account. In a multiplicative hazard model, the estimate for the relative mortality generalises the standardised mortality ratio, and the adequacy of a model with constant relative mortality can be tested using a type of total time on test statistic. In an additive hazard model, continuous-time generalisations of a "corrected" survival curve and a "normal" survival curve are obtained, and the adequacy of a model with constant excess mortality can again be tested using a type of total time on test statistic. A model including both the multiplicative hazard model and the additive hazard model is briefly considered. The use of the models is illustrated on a set of data concerning survival after operation for malignant melanoma.     

Modeling the Impact of Adjustable Gastric Banding on Survival in Patients with Morbid Obesity

Objective: Morbid obesity is associated with premature death. Adjustable gastric banding may lead to substantial weight loss in patients with morbid obesity. Little is known about the impact of weight loss on survival after adjustable gastric banding. We therefore developed a mathematical model to estimate life expectancy in patients with a body mass index (BMI) ≥40 kg/m² undergoing bariatric surgery. Research Methods and Procedures: We developed a nonhomogeneous Markov chain consisting of five states: the absorbing state (“dead”) and the four recurrent states BMI ≥40 kg/m², BMI 36 to 39 kg/m², BMI 32 to 35 kg/m², and BMI 25 to 31 kg/m². Scenarios of weight loss and age‐ and sex‐dependent risk of death, as well as BMI‐dependent excess mortality were extracted from life tables and published literature. All patients entered the model through the state of BMI ≥40 kg/m². Results: In men aged either 18 or 65 years at the time of surgery, who moved from the state BMI ≥40 kg/m² to the next lower state of BMI 36 to 39 kg/m², life expectancy increased by 3 and 0.7 years, respectively. In women aged either 18 or 65 years at the time of surgery, who moved from the state BMI ≥40 kg/m² to the next lower state BMI 36 to 39 kg/m², life expectancy increased by 4.5 and 2.6 years, respectively. Weight loss to lower BMI strata resulted in further gains of life expectancy in both men and women. Discussion: Within the limitations of the modeling study, adjustable gastric banding in patients with morbid obesity may substantially increase life expectancy.     

Additive‐Multiplicative Regression Models for Spatio‐Temporal Epidemics

An extension of the stochastic susceptible–infectious–recovered (SIR) model is proposed in order to accommodate a regression context for modelling infectious disease data. The proposal is based on a multivariate counting process specified by conditional intensities, which contain an additive epidemic component and a multiplicative endemic component. This allows the analysis of endemic infectious diseases by quantifying risk factors for infection by external sources in addition to infective contacts. Inference can be performed by considering the full likelihood of the stochastic process with additional parameter restrictions to ensure non‐negative conditional intensities. Simulation from the model can be performed by Ogata's modified thinning algorithm. As an illustrative example, we analyse data provided by the Federal Research Centre for Virus Diseases of Animals, Wusterhausen, Germany, on the incidence of the classical swine fever virus in Germany during 1993–2004.     

Short‐term insurance versus long‐term bet‐hedging strategies as adaptations to variable environments

Understanding how organisms adapt to environmental variation is a key challenge of biology. Central to this are bet‐hedging strategies that maximize geometric mean fitness across generations, either by being conservative or diversifying phenotypes. Theoretical models have identified environmental variation across generations with multiplicative fitness effects as driving the evolution of bet‐hedging. However, behavioral ecology has revealed adaptive responses to additive fitness effects of environmental variation within lifetimes, either through insurance or risk‐sensitive strategies. Here, we explore whether the effects of adaptive insurance interact with the evolution of bet‐hedging by varying the position and skew of both arithmetic and geometric mean fitness functions. We find that insurance causes the optimal phenotype to shift from the peak to down the less steeply decreasing side of the fitness function, and that conservative bet‐hedging produces an additional shift on top of this, which decreases as adaptive phenotypic variation from diversifying bet‐hedging increases. When diversifying bet‐hedging is not an option, environmental canalization to reduce phenotypic variation is almost always favored, except where the tails of the fitness function are steeply convex and produce a novel risk‐sensitive increase in phenotypic variance akin to diversifying bet‐hedging. Importantly, using skewed fitness functions, we provide the first model that explicitly addresses how conservative and diversifying bet‐hedging strategies might coexist.     

Individual and Aggregate Years‐of‐life‐lost Associated With Overweight and Obesity

This study presents nationally representative estimates of individual and aggregate years‐of‐life‐lost (YLLs) associated with overweight and three categories of obesity separately by age, race, smoking status, and gender strata. Using proportional hazards analysis and data from the National Health Interview Survey (NHIS) Linked Mortality Files, we estimated life expectancies for each BMI strata and quantified YLLs by comparing differences between each strata and the normal BMI reference group. Our results provide further evidence that overweight and mild obesity are not associated with a reduction in life expectancy. However, higher BMI categories are associated with lower expected survival. In aggregate, excess BMI is responsible for ～95 million YLLs. White females account for more than two‐thirds of the aggregate YLLs. Unless something is done to reduce the rising prevalence of those with BMIs >35, or to mitigate the impact of obesity or its correlates on YLLs, expected life expectancy for US adults may decrease in the future.     

Dietary factors and cancer mortality among atomic-bomb survivors

Dietary factors such as fruit and vegetables are thought to reduce the risk of cancer incidence and mortality. We investigated the effect of a diet rich in fruit and vegetables against the long-term effects of radiation exposure on the risk of cancer. A cohort of 36,228 atomic-bomb survivors of Hiroshima and Nagasaki, for whom radiation dose estimates were currently available, had their diet assessed in 1980. They were followed for a period of 20 years for cancer mortality. The joint-effect of fruit and vegetables intake and radiation exposure on risk of cancer death was examined, in additive (sum of effects of diet alone and radiation alone) and multiplicative (product of effects of diet alone and radiation alone) models. In the additive model, a daily intake of fruit and vegetables significantly reduced the risk of cancer deaths by 13%, compared to an intake of once or less per week. Radiation exposure of 1 Sievert (Sv) increased significantly the risk of cancer death by 48-49%. The additive joint-effects showed a lower risk of cancer among those exposed to 1 Sv who had a diet rich in vegetables (49%-13%=36%) or fruit (48%-13%=35%). The multiplicative model gave similar results. The cancer risk reduction by vegetables in exposed persons went from 52% (effect of radiation alone) to 32% (product of effect of vegetables and radiation), and cancer risk reduction by fruit was 52% (radiation alone) to 34% (product of effect of fruit and radiation). There was no significant evidence to reject either the additive or the multiplicative model. A daily intake of fruit and vegetables was beneficial to the persons exposed to radiation in reducing their risks of cancer death.     

Estimating Attributable Life Expectancy Under the Proportional Mean Residual Life Model

In population-based health research, the so-called population attributable fraction is an important quantity that calculates the percentage of excess risk of morbidity and mortality associated with modifiable risk factors for a given population. While the concept of “risk” is usually measured by event probabilities, in practice it may be of a more direct interest to know the excess life expectancy associated with the modifiable risk factors instead, particularly when mortality is of the ultimate concern. In this paper, we thus propose to study a novel quantity, termed “attributable life expectancy,” to measure the population attributable fraction of life expectancy. We further develop a model-based approach for the attributable life expectancy under the Oakes–Dasu proportional mean residual life model, and establish its asymptotic properties for inferences. Numerical studies that include Monte-Carlo simulations and an actual analysis of the mortality associated with smoking cessation in an Asia Cohort Consortium are conducted to evaluate the performance of our proposed method.

     

Relationship of Serum γ‐Glutamyltransferase to Atherogenic Dyslipidemia and Glycemic Control in Type 2 Diabetes

We evaluated possible interactions between BMI and serum γ‐glutamyltransferase (GGT) concentration and their effects on the prevalence of poor glycemic control and common comorbidities of diabetes. We assessed whether the association of BMI with poor glycemic control, hypertension, atherogenic dyslipidemia (i.e., high triglycerides and/or low high‐density lipoprotein (HDL) cholesterol), hypercholesterolemia, and hyperuricemia differed according to serum GGT concentration in a cohort of 3,633 type 2 diabetic individuals. The associations of BMI with different outcome measures were significant, but the associations varied remarkably by GGT concentration. As GGT concentration increased, the association of BMI with atherogenic dyslipidemia and glycemic control strengthened (P = 0.01 and 0.004 for interactions, respectively); in contrast, the association of BMI with hypertension, hypercholesterolemia, and hyperuricemia did not change substantially across GGT quartiles. For example, within the lowest GGT quartile, BMI was not associated with atherogenic dyslipidemia or poor glycemic control, whereas in the highest GGT quartile, the prevalence rates ranged from 62.3 to 74.7% for dyslipidemia and from 75.3 to 83% for poor glycemic control. The results remained unchanged after adjustment for sex, age, alcohol consumption, diabetes duration, and diabetes treatment. In conclusion, our findings show that BMI was associated with atherogenic dyslipidemia and poor glycemic control only when serum GGT activity was in its high‐normal range. These findings suggest that obesity itself may not be a sufficient risk factor for atherogenic dyslipidemia or poor glycemic control in people with type 2 diabetes.     

Ergodicity-breaking reveals time optimal decision making in humans

Ergodicity describes an equivalence between the expectation value and the time average of observables. Applied to human behaviour, ergodic theories of decision-making reveal how individuals should tolerate risk in different environments. To optimize wealth over time, agents should adapt their utility function according to the dynamical setting they face. Linear utility is optimal for additive dynamics, whereas logarithmic utility is optimal for multiplicative dynamics. Whether humans approximate time optimal behavior across different dynamics is unknown. Here we compare the effects of additive versus multiplicative gamble dynamics on risky choice. We show that utility functions are modulated by gamble dynamics in ways not explained by prevailing decision theories. Instead, as predicted by time optimality, risk aversion increases under multiplicative dynamics, distributing close to the values that maximize the time average growth of in-game wealth. We suggest that our findings motivate a need for explicitly grounding theories of decision-making on ergodic considerations.     

The Lipid Accumulation Product and All‐cause Mortality in Patients at High Cardiovascular Risk: A PreCIS Database Study

The BMI is the most frequently used marker to evaluate obesity‐associated risks. An alternative continuous index of lipid over accumulation, the lipid accumulation product (LAP), has been proposed, which is computed from waist circumference (WC, cm) and fasting triglycerides (TGs) (mmol/l): (WC ? 65) × TG (men) and (WC ? 58) × TG (women). We evaluated LAP and BMI as predictors of mortality in a high‐risk cohort. Study population included 5,924 new consecutive patients seen between 1995 and 2006 at a preventive cardiology clinic. Fifty‐eight percent of patients were discordant for their LAP and BMI quartiles. Patients whose LAP quartile was greater than BMI quartile had higher mortality compared with those with LAP quartile was lower than BMI quartile (8.2 vs. 5.4% at 6 years, P = 0.007). After adjustment for age, gender, smoking, diabetes mellitus, blood pressure, low‐density lipoprotein‐cholesterol (LDL‐C) and high‐density lipoprotein‐cholesterol (HDL‐C), (ln)LAP was independently associated with mortality (hazard ratio (HR) = 1.46, P < 0.001). BMI was not associated with increased mortality (HR = 1.06, P = 0.39). Adding LAP to a model including traditional risk factors for atherosclerosis increased its predictive value (C statistic 0.762 vs. 0.750, P = 0.048). Adding BMI to the same model did not change its predictive value (0.749 vs. 0.750, P = 0.29). Subgroup analyses showed that LAP predicted mortality in the nondiabetic patients (adjusted HR for (ln)LAP 1.64, P < 0.001), but did not reach significance in the diabetic patients (HR = 1.21, P = 0.11). In conclusion, LAP and not BMI predicted mortality in nondiabetic patients at high risk for cardiovascular diseases. LAP may become a useful tool in clinical practice to stratify the risk of unfavorable outcome associated with obesity.     

Childhood Overweight Status Predicts Diabetes at Age 21 Years: A Follow‐up Study

We examined the prospective association of childhood BMI z‐score and BMI categories (normal or overweight) with young adult diabetes, controlling for early life, childhood, and adolescence factors. A subsample of 2,639 young adults from the Mater–University study of pregnancy (MUSP) and its outcomes, a prospective birth cohort who were born in Brisbane, Australia and for whom we had measured height and weight at 5 years and self‐reported diabetes at age 21 years. The risk of developing diabetes by age 21 years was greater among young adults who had greater BMI z‐score or were overweight at age 5 years than those who had normal BMI at age 5 years. Young adults who were overweight at age 5 years had an increased odds ratio of 2.60 (95% confidence interval (CI): 1.29, 5.22, in age‐ and sex‐adjusted model) of experiencing diabetes by age 21 years. Adjustment for potential confounders and mediators including intrauterine environmental factors, childhood dietary patterns, television watching, participation in sports and exercise, and current weight, did not substantively alter these associations. Overweight and increasing BMI z‐score at childhood is an independent predictor of young adult's type 1 and type 2 diabetes. Findings of this study suggest that childhood BMI may be central to the development and rising incidence of all diabetes.     

Effect of short-term low-intensity exercise on insulin sensitivity, insulin secretion, and glucose and lipid metabolism in non-obese Japanese type 2 diabetic patients.

The aim of the present study was to investigate the effects of short-term physical exercise that did not change body mass on insulin sensitivity, insulin secretion, and glucose and lipid metabolism in 39 non-obese Japanese type 2 diabetic patients. Insulin sensitivity and insulin secretion were estimated with homeostasis model assessment insulin resistance (HOMA-IR) and HOMA-B-cell function proposed by Matthews et al., respectively. All patients were hospitalized and were engaged in low-intensity exercise that consisted of walking and dumbbell exercise for successive 7 days. There were no changes in hospital diet and the dose of any medications used throughout the study. Fasting glucose, insulin, and lipids were measured before and after exercise.After exercise, serum triglyceride levels significantly decreased, but no significant changes were observed in total and HDL cholesterol concentrations. Fasting glucose, insulin, and HOMA-IR levels significantly decreased after exercise, but HOMA-B-cell function did not change during the study. There was no significant difference between BMI levels before and after exercise.From these results, it can be concluded that short-term (7 days) low-intensity physical exercise combined with hospital diet reduces serum triglycerides, insulin resistance, and fasting glucose levels without affecting BMI in non-obese Japanese type 2 diabetic patients.     

Analyses of two-way chronic studies

This paper proposes a method for analyzing tumor data from chronic studies when the experimental design includes combinations of two factors, for example, sex and dose. Both main effects and combined-effect (interaction) hypotheses are considered. A stratified log-rank statistic is presented for tests of no column or row (main) effects. The paper shows that when the numbers of animals in the cells are unequal and disproportional, the null distribution of the unstratified log-rank statistic does not have a chi-square distribution. Two simple models, additive and multiplicative, for representing the combined effect of row and column are considered under the proportional hazards model. A simple conservative statistic is proposed for testing the additivity of the row and column effects. A simulation experiment to examine the behavior of the null distribution of the combined-effect test statistic under the additive model and the power of the test against the multiplicative model is reported. The procedure is illustrated by analyzing mammary tumors induced by 7,12-dimethylbenz[a]anthracene (DMBA) in yellow and agouti F1 female mice from a laboratory experiment.     

Covariate Adjusted Correlation Analysis with Application to FMR1 Premutation Female Carrier Data

Summary .  Motivated by molecular data on female premutation carriers of the fragile X mental retardation 1 ( FMR1 ) gene, we present a new method of covariate adjusted correlation analysis to examine the association of messenger RNA (mRNA) and number of CGG repeat expansion in the  FMR1  gene. The association between the molecular variables in female carriers needs to adjust for activation ratio (ActRatio), a measure which accounts for the protective effects of one normal X chromosome in females carriers. However, there are inherent uncertainties in the exact effects of ActRatio on the molecular measures of interest. To account for these uncertainties, we develop a flexible adjustment that accommodates both additive and multiplicative effects of ActRatio nonparametrically. The proposed adjusted correlation uses local conditional correlations, which are local method of moments estimators, to estimate the Pearson correlation between two variables adjusted for a third observable covariate. The local method of moments estimators are averaged to arrive at the final covariate adjusted correlation estimator, which is shown to be consistent. We also develop a test to check the nonparametric joint additive and multiplicative adjustment form. Simulation studies illustrate the efficacy of the proposed method. (Application to  FMR1  premutation data on 165 female carriers indicates that the association between mRNA and CGG repeat after adjusting for ActRatio is stronger.) Finally, the results provide independent support for a specific jointly additive and multiplicative adjustment form for ActRatio previously proposed in the literature.     

The Role of Melanocortin‐1 Receptor Polymorphism in Skin Cancer Risk Phenotypes

We have examined melanocortin‐1 receptor (MC1R) variant allele frequencies in the general population and in a collection of adolescent dizygotic and monozygotic twins to determine statistical associations of pigmentation phenotypes with increased skin cancer risk. This included hair and skin color, freckling, mole count and sun exposed skin reflectance. Nine variants were studied and designated as either strong R (OR = 63; 95% CI 32–140) or weak r (OR = 5; 95% CI 3–11) red hair alleles. Penetrance of each MC1R variant allele was consistent with an allelic model where effects were multiplicative for red hair but additive for skin reflectance. To assess the interaction of the brown eye color gene BEY2/OCA2 on the phenotypic effects of variant MC1R alleles we imputed OCA2 genotype in the twin collection. A modifying effect of OCA2 on MC1R variant alleles was seen on constitutive skin color, freckling and mole count. In order to study the individual effects of these variants on pigmentation phenotype we have established a series of human primary melanocyte strains genotyped for the MC1R receptor. These include strains which are MC1R wild‐type consensus, variant heterozygotes, and homozygotes for strong R alleles Arg151Cys and Arg160Trp. Ultrastructural analysis demonstrated that only consensus strains contained stage III and IV melanosomes in their terminal dendrites whereas Arg151Cys and Arg160Trp homozygous strains contained only immature stage I and II melanosomes. Such genetic association studies combined with the functional analysis of MC1R variant alleles in melanocytic cells should provide a link in understanding the association between pigmentary phototypes and skin cancer risk.     

Additive and multiplicative models for the joint effect of two risk factors

Simple tests are given for consistency of the data with additive and with multiplicative effects of two risk factors on a binary outcome. A combination of the procedures will show whether data are consistent with neither, one or both of the models of no additive or no multiplicative interaction. Implications for the size of the study needed to detect differences between the models are also addressed. Because of the simple form of the test statistics, combination of evidence from different studies or strata is straightforward. Illustration of how the method could be extended to data from a 2xRxC table is also given.     

Choice of Scores in Trend Tests for Case‐Control Studies of Candidate‐Gene Associations

When applying the Cochran‐Armitage (CA) trend test for an association between a candidate allele and a disease in a case‐control study, a set of scores must be assigned to the genotypes. Sasieni (1997, Biometrics 53 , 1253–1261) suggested scores for the recessive, additive, and dominant models but did not examine their statistical properties. Using the criteria of minimizing the required sample size of the CA trend test to achieve prespecified type I and type II errors, we show that the scores given by Sasieni (1997) are optimal for the recessive and dominant models and locally optimal for the additive one. Moreover, the additive scores are shown to be locally optimal for the multiplicative model. The tests are applied to a real dataset.     

Diabetes mellitus y trastorno depresivo,un mal binomio

Type 2 diabetes and depressive disorder are 2 chronic diseases highly prevalent in developed countries and with a negative impact on quality of life and life expectancy. In recent years, both conditions have been shown to be strongly associated. Thus, diabetics have an increased risk of suffering depressive disorder, as well as impaired glucose homeostasis, if they experience depression. In diabetic patients, concurrent depression is associated to greater difficulties in disease management and metabolic control, increased risk of developing chronic complications, decreased quality of life, and higher healthcare expenses. As a result, the interest of diabetic scientific societies in this association has increased, and they recommend regular mood assessment in diabetic patients. However, the limited clinical experience available and the conflicting results reported to date make it difficult to draw conclusions.     

A genetic variant in LINGO2 contributes to the risk of gestational diabetes mellitus in a Chinese population

Genome-wide association studies (GWASs) showed that three single nucleotide polymorphisms (SNPs; rs10968576, rs1412239, and rs824248) in the leucine-rich repeat and Ig domain containing 2 (LINGO2) were associated with obesity or type 2 diabetes (T2D). We aimed to determine the influence of the LINGO2 variants on the gestational diabetes mellitus (GDM) risk. Thus, we performed a case–control study including 964 GDM cases and 1,021 controls to test the associations between the three LINGO2 variants (rs10968576, rs1412239, and rs824248) and susceptibility to GDM. Logistic regression analyses showed no significant association between LINGO2 variations (rs10968576 and rs1412239) and GDM susceptibility, but we observed that LINGO2 rs824248 A > T was significantly associated with an increased risk of GDM using the dominant model (TT/AT vs. AA: adjusted odds ratio [OR] = 1.26, 95% confidence interval [CI] = 1.05–1.51; p = 0.012) and the additive model (TT vs. AT vs. AA: adjusted OR = 1.16, 95% CI = 1.03–1.31; p = 0.016). In the additive model, a stronger risk effect of rs824248 was observed among obese women (prepregnancy body mass index [BMI] > 22 kg/m², adjusted OR = 1.34, 95% CI = 1.12–1.59) compared with that in lean women (prepregnancy BMI ≤ 22 kg/m², adjusted OR = 1.0², 95% CI = 0.86–1.21; p = 0.029 for heterogeneity test). Further interactive analyses also detected a significant multiplicative interaction between rs824248 and prepregnancy BMI for the risk of GDM (p = 0.041). These findings indicate that LINGO2 rs824248 may serve as a susceptibility marker for GDM in Chinese females.     

Association of TCF7L2 Gene Polymorphisms with T2DM in the Population of Hyderabad,India

We attempt to evaluate the nature of association of TCF7L2 gene variants with T2DM, for the first time in the population of Hyderabad, which is considered to be diabetic capital of India. It is a case-control study of the three SNPs of TCF7L2, rs7903146, rs12255372 and rs11196205, genotyped on Sequenom Massarray platform, in a sample of 758 patients and 621 controls. The risk allele frequency of the three SNPs was found to be significantly higher in the T2DM cases than controls, implicating susceptibility for diabetes (p<0.01). The greatest risk of developing the disease was conferred by rs7903146. Further, the logistic regression of genotypes of each SNP under log additive model, and the haplotypes constituted by at least one of the three risk alleles also show significantly greater risk of developing T2DM when compared to the wild type haplotype. Further, BMI and WHR emerge as significant covariates with confounding effects. The strong association of the TCF7L2 SNPs with T2DM is consistent with the findings among other Indian and Non-Indian populations, suggesting universal phenomena of its association across ethnic groups globally, both within and outside the Indian subcontinent, albeit the functional relevance of these SNPs needs yet to be established.