A Model for Antagonistic Pleiotropic Gene Action for Mortality and Advanced Age

Association or linkage studies involving control and long-lived populations provide information on genes that influence longevity. However, the relationship between allele-specific differences in survival and the genetic structure of aging cohorts remains unclear. We model a heterogeneous cohort comprising several genotypes differing in age-specific mortality. In its most general form, without any specific assumption regarding the shape of mortality curves, the model permits derivation of a fundamental property underlying abrupt age-related changes in the composition of a cohort. The model is applied to sex-specific survival curves taken from period life tables, and Gompertz-Makeham mortality coefficients are calculated for the French population. Then, adjustments are performed under Gompertz-Makeham mortality functions for three genotypes composing a heterogeneous cohort, under the constraint of fitting the resultant mortality to the real French population mortality obtained from life tables. Multimodal curves and divergence after the 8th decade appear as recurrent features of the frequency trajectories. Finally, a fit to data previously obtained at the angiotensin-converting-enzyme locus is realized, explaining what had seemed to be paradoxical results-namely, that the frequency of a genotype known as a cardiovascular risk factor was increased in centenarians. Our results help explain the well-documented departure from Gompertz-Makeham mortality kinetics at older ages. The implications of our model are discussed in the context of known genetic effects on human longevity and age-related pathologies. Since antagonistic pleiotropy between early and late survival emerges as a general rule, extrapolating the effects measured for a gene in a particular age class to other ages could be misleading.     

The propagation of uncertainty in human mortality processes operating in stochastic environments

This paper presents a model describing how the uncertainty due to influential exogenous processes combines with stochasticity intrinsic to physiological aging processes and propagates through time to generate uncertainty about the future physiological state of the population. Variance expressions are derived for (a) the future values of the physiological variables under the assumption that external factors evolve under a linear stochastic diffusion process, and (b) the cohort survival functions and cohort life expectancies which reflect the uncertainty in the future values of the physiological variables. The model implies that a major component of uncertainty in forecasts of the physiological characteristics of a closed cohort is due to differential rates of survival associated with different realizations of the external process. This suggests that the limits to forecasting may be different in physiological systems subject to systematic mortality than in physical systems such as weather where the concepts of closed cohorts and of mortality selection have no simple analog.     

Exact Maximum Likelihood Estimates of Cox's Regression Parameters Based on Categorized Factorial Data

This paper describes how Cox's Proportional Hazards model may be used to analyze dichotomized factorial data obtained from a right-censored epidemiological study where time to response is of interest. Exact maximum likelihood estimates of the relative mortality rates are obtained for any number of prognostic factors, as well as their joint asymptotic sampling distribution. These rates represent excess mortality due to the various levels of the prognostic factors. The results are used to discuss the effect of the factors on the survival probability distribution of a cohort of industrial workers who have been exposed to a carcinogen. Kaplan-Meier estimates of the survival function of the internal control population are used to determine the expected number of deaths in the study population. This method differs from the usual lite-table procedure. Asymptotic tests are proposed for some simultaneous and conditional statistical hypotheses.     

Demographic window to aging in the wild: constructing life tables and estimating survival functions from marked individuals of unknown age

Summary We address the problem of establishing a survival schedule for wild populations. A demographic key identity is established, leading to a method whereby age-specific survival and mortality can be deduced from a marked cohort life table established for individuals that are randomly sampled at unknown age and marked, with subsequent recording of time-to-death. This identity permits the construction of life tables from data where the birth date of subjects is unknown. An analogous key identity is established for the continuous case in which the survival schedule of the wild population is related to the density of the survival distribution in the marked cohort. These identities are explored for both life tables and continuous lifetime data. For the continuous case, they are implemented with statistical methods using non-parametric density estimation methods to obtain flexible estimates for the unknown survival distribution of the wild population. The analytical model provided here serves as a starting point to develop more complex models for residual demography, i.e. models for estimating survival of wild populations in which age-at-entry is unknown and using remaining information in randomly encountered individuals. This is a first step towards a broad new concept of 'expressed demographic information content of marked or captured individuals'.     

Survival and aging in the wild via residual demography

Information about the age distribution and survival of wild populations is of much interest in ecology and biodemography, but is hard to obtain. Established schemes such as capture-recapture often are not feasible. In the proposed residual demography paradigm, individuals are randomly sampled from the wild population at unknown ages and the resulting captive cohort is reared out in the laboratory until death. Under some basic assumptions one obtains a demographic convolution equation that involves the unknown age distribution of the wild population, the observed survival function of the captive cohort, and the observed survival function of a reference cohort that is independently raised in the laboratory from birth. We adopt a statistical penalized least squares method for the deconvolution of this equation, aiming at extracting the age distribution of the wild population under suitable constraints. Under stationarity of the population, the age density is proportional to the survival function of the wild population and can thus be inferred. Several extensions are discussed. Residual demography is demonstrated for data on fruit flies Bactrocera oleae.     

SMR analysis of historical follow-up studies with missing death certificates

The evaluation of epidemiological follow-up studies is frequently based on a comparison of the number O of deaths observed in the cohort from a specified cause with the expected number E calculated from person years in the cohort and mortality rates from a reference population. The ratio SMR = 100 x O/E is called the standardized mortality ratio (SMR). While person years can easily be calculated from the cohort and reference rates are generally available from the national statistical offices or the World Health Organization (WHO), problems can arise with the accessibility of the causes of death of the deceased study participants. However, the information that a person has died may be available, e.g., from population registers. In this paper, a statistical model for this situation is developed to derive a maximum likelihood (ML) estimator for the true (but unknown) number O* of deaths from a specified cause, which uses the known number O of deaths from this cause and the proportion p of all known causes of death among all decreased participants. It is shown that the standardized mortality ratio SMR* based on this estimated number is just SMR* = SMR/p. Easily computable confidence limits can be obtained by dividing the usual confidence limits of the SMR by the opposite limit of the proportion p. However, the confidence level alpha has to be adjusted appropriately.     

Bayesian Testing of Relative Mortality,with Application to Occupational Cohort Studies

An important issue in epidemiology, often exploratory, is to compare the mortality of a certain cohort, exposed to some dangerous conditions, to that of a reference population. The main statistical tool to study relative mortality has long been the subject-years method. We propose a Bayesian version of the subject-years method, particularly suited to analyse the mortality of small cohorts. In particular, we employ the Bayes factor in order to test whether the mortality of a cohort exceeds that of a reference population. The methodology is applied to an occupational epidemiology study. The results are compared to those obtained from the classical one-sided tests on the same data.     

Stochastic dynamic population model for northern corn rootworm (Coleoptera: Chrysomelidae).

A stochastic dynamic population model for the complete life cycle of northern corn rootworm, Diabrotica barberi Smith & Lawrence, is described. Adult population dynamics from emergence to oviposition are based on a published single-season model for which temperature-dependent development and age-dependent advancement determine adult population dynamics and oviposition. Randomly generated daily temperatures make this model component stochastic. Stochastic hatch is 50+/-8%. A stochastic nonlinear density-dependent larval survival model is estimated using field data from artificial infestation experiments. A regional model of corn phenology is estimated to incorporate the effect of dispersal on adult mortality. Random daily weather is generated using parameters for Brookings, SD. Model performance is evaluated with deterministic simulations, which show that the population converges to zero unless adult mortality is reduced by the availability of corn pollen from the regional model of corn phenology. Stochastic model performance is evaluated with stochastic daily weather, egg hatch, and larval survival in various combinations. Sensitivity analysis is conducted to evaluate model responsiveness to each parameter. Model results are generally consistent with published data.     

Theory and applications of a computationally efficient cohort simulation model of human reproduction

Ease of implementation and computational efficiency are two necessary criteria if a simulation system is to be run repeatedly. Described in this paper is a cohort simulation model, based on the theory of terminating renewal processes, which satisfies these two criteria. There are two versions of the model. In one version, waiting times till pregnancy and times spent in the postpartum sterile state, as well as parity progression ratios reflecting hypothetical birth intentions, are taken into account. Unlike simulation systems described in earlier papers, pregnancy wastage is not accommodated in this version of the model. A second version is a model of birth intervals in which parity progression ratios and distributions of waiting times among live births, both of which may reflect pregnancy wastage when based on birth history data, serve as computer input. Female mortality, expressed as a survival function, and a distribution of age at marriage in a cohort are essential parts of both versions of the system. High efficiency in computing the many required convolutions has been obtained by use of a fast Fourier transform algorithm. After an overview of computer software design is given, the computer input for twelve simulation runs is described. These twelve runs are designed to test the impact of various combinations of levels of mortality, age of marriage, and fertility on population growth. One of the interesting substantive conclusions stemming from the simulation runs was that in populations of low mortality and fertility, late age at marriage, as observed in some historical populations, can be a significant factor in increasing the population doubling time.     

Culling Versus Density Effects in Management of a Deer Population

Abstract: Wildlife managers often manipulate hunting regulations to control deer populations. However, few empirical studies have examined the level of hunting effort (hunter-days) required to limit population growth and demographic effects through harvesting of females. Moreover, the relative importance of density effects on population growth has not been quantified. We reconstructed a sika deer [Cervus nippon] population over a period of 12 years (1990–2001) using age- and sex-specific harvest data. Using cohort analysis, we analyzed population dynamics, focusing on 1) the relationship between hunting effort and hunting-induced mortality rate, 2) relative contributions of hunting mortality and recruitment of yearlings to annual changes in population growth rate, and 3) annual variation in recruitment rate. Population size increased until 1998 and declined thereafter. The population growth rate changed more in response to annual changes in recruitment rate than hunting mortality rate. Temporal variation in recruitment rate was not controlled by birth rate alone; direct density dependence, intensities of hunting mortality for fawns, and for females (≥2 yr of age), which accounted for the fawn survival rate, were required as factors to explain temporal variation. Density effects on the recruitment rate were not strong enough to regulate the population within the study period; high hunting mortality, with intensive female harvesting, was necessary to prevent population growth. Hunting effort was a good predictor of the hunting mortality rate, and female harvest had a negative effect on the recruitment rate through fawn survival. We suggest that >3,500 hunter-days and prioritization of female harvesting are required to prevent increases in this deer population.     

Density dependence in an island population of silvereyes

The population of silvereyes Zosterops lateralis chlorocephalus , on Heron Island, Great Barrier Reef has been monitored accurately since 1965. Between 1979 and 1993, the breeding success of all birds was determined by monitoring nests. The population fluctuated between 225 and 483 individuals. Four cyclones led to substantial mortality. As this data set is long-term, has little observation error, and is from an effectively closed population, it provides an unusual opportunity to examine density dependence in reproduction or mortality. Using a stochastic logistic model, we found clear evidence of density dependence in adult population size. Logistic regression suggested that fledgling survival decreased with the numbers of birds attempting to breed. There was also some suggestion that adult survival might be density dependent. The fitted stochastic logistic model predicts negligible risks of extinction for this population, in contrast to the predictions of a published population viability analysis. Whilst our statistical model including density dependence may provide better predictions of the "usual" behaviour of a population than a population viability analysis, we suggest that caution should be exercised when statistically fitted models are used to predict the behaviour of the population at extremes, such as near extinction.     

Genetic association analysis of human longevity in cohort studies of elderly subjects: an example of the PON1 gene in the Danish 1905 birth cohort

Although the case-control or the cross-sectional design has been popular in genetic association studies of human longevity, such a design is prone to false positive results due to sampling bias and a potential secular trend in gene-environment interactions. To avoid these problems, the cohort or follow-up study design has been recommended. With the observed individual survival information, the Cox regression model has been used for single-locus data analysis. In this article, we present a novel survival analysis model that combines population survival with individual genotype and phenotype information in assessing the genetic association with human longevity in cohort studies. By monitoring the changes in the observed genotype frequencies over the follow-up period in a birth cohort, we are able to assess the effects of the genotypes and/or haplotypes on individual survival. With the estimated parameters, genotype- and/or haplotype-specific survival and hazard functions can be calculated without any parametric assumption on the survival distribution. In addition, our model estimates haplotype frequencies in a birth cohort over the follow-up time, which is not observable in the multilocus genotype data. A computer simulation study was conducted to specifically assess the performance and power of our haplotype-based approach for given risk and frequency parameters under different sample sizes. Application of our method to paraoxonase 1 genotype data detected a haplotype that significantly reduces carriers' hazard of death and thus reveals and stresses the important role of genetic variation in maintaining human survival at advanced ages.     

Survival and Cause-Specific Mortality of Mature Male White-Tailed Deer

ABSTRACT Understanding sources of male deer mortality is a prerequisite to a successful management program, especially in Texas, USA, where white-tailed deer (Odocoileus virginianus) are the most economically important game species. South Texas, USA, is one of the few areas where males reach older age classes (> 4.5 yr), in part because of intense population management. Therefore, we obtained survival rates and causes of mortality of 48 mature male deer in south Texas, USA, over 2 years. We calculated Kaplan—Meier survival estimates during 2 study years modified for a staggered-entry design and annual survival rates for one cohort of deer from 1998 to 2004 using recapture and radiotelemetry data. We documented 21 mortalities (16 harvest and 5 nonhunting mortalities). Average annual survival of the known-aged 1998 cohort was 82% with 52% of surviving to 6.5 years of age. Survival in study year 2 (0.497 ± 0.069) was less than in study year 1 (0.781 ± 0.073; P = 0.0047), largely because males had finally reached harvestable age (> 6.5 yr old). All but one non-harvest mortality occurred during the rut or postrut periods. It appears that a large percentage of males can reach mature age classes under intense population management, making them available for harvest when at peak antler size. This allows for increased economic returns on intensively managed white-tailed deer populations.     

A new mathematical model of the dynamics of an age cohort population

A new generalized conception of an organism is given. Based on this conception, a new mathematical model of ontogenesis of an individual and the survival of the age cohort of population was proposed. By using real data on the dynamics of the survival of the age cohort of population, the model enables one to determine the parameters characterizing the relationship man-environment in the context of survival and calculate the dynamics (from birth to death) of the model variables of the state of the organism.     

Population dynamics of the white wax scale, Ceroplastes destructor (Hemiptera: Coccidae), on citrus in South Africa, with implications for biological control

The population dynamics of the white wax scale, Ceroplastes destructor Newstead, was studied intensively in four easy-peel citrus orchards in the Western Cape Province of South Africa over three consecutive years (1997-1999). Key factor analysis was used to determine and quantify the contribution of individual mortality factors to the total generation mortality. Key stage mortality, determined from a cohort life table, was in the third instar and pre-ovipositing female stages. Mortality of C. destructor was caused primarily by parasitoids, predators and miscellaneous factors. Parasitoids and miscellaneous factors acted as density-dependent regulatory agents during the pre-ovipositional and first instar stages respectively. This has implications for biological control of C. destructor. Some of the mortality factors acted either randomly with no reference to the population densities or in an inverse density-dependent manner during the egg-crawler, second or third instar stages.     

Long-Term Mortality in Patients Diagnosed with Meningococcal Disease: A Danish Nationwide Cohort Study

Background

In contrast to the case fatality rate of patients diagnosed with meningococcal disease (MD) the long-term mortality in these patients is poorly documented.

Methodology/Principal Findings

We performed a nationwide, population-based cohort study including all Danish patients diagnosed with MD from 1977 through 2006 and alive one year after diagnosis. Data was retrieved from the Danish National Hospital Register, the Danish Civil Registration System and the Danish Register of Causes of Death. For each patient four age- and gender-matched individuals were identified from the population cohort. The siblings of the MD patients and of the individuals from the population cohort were identified. We constructed Kaplan-Meier survival curves and used Cox regression analysis, cumulative incidence function and subdistribution hazard regression to estimate mortality rate ratios (MRR) and analyze causes of death. We identified 4,909 MD patients, 19,636 individuals from the population cohort, 8,126 siblings of MD patients and 31,140 siblings of the individuals from the population cohort. The overall MRR for MD patients was 1.27 (95% confidence interval (CI), 1.12–1.45), adjusted MRR, 1.21 (95% CI, 1.06–1.37). MD was associated with increased risk of death due to nervous system diseases (MRR 3.57 (95% CI, 1.82–7.00). No increased mortality due to infections, neoplasms or cardiovascular diseases was observed. The MRR for siblings of MD patients compared with siblings of the individuals from the population cohort was 1.17 (95% CI, 0.92–1.48).

Conclusions

Patients surviving the acute phase of MD have increased long-term mortality, but the excess risk of death is small and stems mainly from nervous system diseases.     

Convergence of body mass with aging: The longitudinal interrelationship of health, weight, and survival

There has been ongoing debate about the health risks associated with increased body weight among the elderly population. One issue has not been investigated thoroughly is that body weight changes over time, as both the reasons and results of, the development of chronic diseases and functional disabilities. Structural models have the ability to unravel the complicated simultaneous relationship between body weight, disability, and mortality along the aging process. Using longitudinal data from the Medicare Current Beneficiary Survey from 1992 to 2001, we constructed a structural model to estimate the longitudinal dynamic relationship between weight, chronic diseases, functional status, and mortality among the aging population. A simulation of an age cohort from 65 to 100 was conducted to show the changes in weight and health outcomes among the cohorts with different baseline weight based on the parameters estimated by the model. The elderly with normal weight at age 65 experience higher life expectancy and lower disability rates than the same age cohorts in other weight categories. The interesting prediction of our model is that the average body size of an elderly cohort will converge to the normal weight range through a process of survival, senescence, and behavioral adjustment.     

Overhydration,Cardiac Function and Survival in Hemodialysis Patients

Background and objectives

Chronic subclinical volume overload occurs very frequently and may be ubiquitous in hemodialysis (HD) patients receiving the standard thrice-weekly treatment. It is directly associated with hypertension, increased arterial stiffness, left ventricular hipertrophy, heart failure, and eventually, higher mortality and morbidity. We aimed to assess for the first time if the relationship between bioimpedance assessed overhydration and survival is maintained when adjustments for echocardiographic parameters are considered.

Design, setting, participants and measurements

A prospective cohort trial was conducted to investigate the impact of overhydration on all cause mortality and cardiovascular events (CVE), by using a previously reported cut-off value for overhydration and also investigating a new cut-off value derived from our analysis of this specific cohort. The body composition of 221 HD patients from a single center was assessed at baseline using bioimpedance. In 157 patients supplemental echocardiography was performed (echocardiography subgroup). Comparative survival analysis was performed using two cut-off points for relative fluid overload (RFO): 15% and 17.4% (a value determined by statistical analysis to have the best predictive value for mortality in our cohort).

Results

In the entire study population, patients considered overhydrated (using both cut-offs) had a significant increased risk for all-cause mortality in both univariate (HR = 2.12, 95%CI = 1.30–3.47 for RFO>15% and HR = 2.86, 95%CI = 1.72–4.78 for RFO>17.4%, respectively) and multivariate (HR = 1.87, 95%CI = 1.12–3.13 for RFO>15% and HR = 2.72, 95%CI = 1.60–4.63 for RFO>17.4%, respectively) Cox survival analysis. In the echocardiography subgroup, only the 17.4% cut-off remained associated with the outcome after adjustment for different echocardiographic parameters in the multivariate survival analysis. The number of CVE was significantly higher in overhydrated patients in both univariate (HR = 2.46, 95%CI = 1.56–3.87 for RFO >15% and HR = 3.67, 95%CI = 2.29–5.89 for RFO >17.4%) and multivariate (HR = 2.31, 95%CI = 1.42–3.77 for RFO >15% and HR = 4.17, 95%CI = 2.48–7.02 for RFO >17.4%) Cox regression analysis.

Conclusions

The study shows that the hydration status is associated with the mortality risk in a HD population, independently of cardiac morphology and function. We also describe and propose a new cut-off for RFO, in order to better define the relationship between overhydration and mortality risk. Further studies are needed to properly validate this new cut-off in other HD populations.     

Long-term mortality in patients with tuberculous meningitis: a Danish nationwide cohort study

Background

With high short-term mortality and substantial excess morbidity among survivors, tuberculous meningitis (TBM) is the most severe manifestation of extra-pulmonary tuberculosis (TB). The objective of this study was to assess the long-term mortality and causes of death in a TBM patient population compared to the background population.

Methods

A nationwide cohort study was conducted enrolling patients notified with TBM in Denmark from 1972–2008 and alive one year after TBM diagnosis. Data was extracted from national registries. From the background population we identified a control cohort of individuals matched on gender and date of birth. Kaplan-Meier survival curves and Cox regression analysis were used to estimate mortality rate ratios (MRR) and analyse causes of death.

Findings

A total of 55 TBM patients and 550 individuals from the background population were included in the study. Eighteen patients (32.7%) and 107 population controls (19.5%) died during the observation period. The overall MRR was 1.79 (95%CI: 1.09–2.95) for TBM patients compared to the population control cohort. TBM patients in the age group 31–60 years at time of diagnosis had the highest relative risk of death (MRR 2.68; 95%CI 1.34–5.34). The TBM patients had a higher risk of death due to infectious disease, but not from other causes of death.

Conclusion

Adult TBM patients have an almost two-fold increased long-term mortality and the excess mortality stems from infectious disease related causes of death.