Analysis of a Hormesis Effect in the Leukemia-Caused Mortality Among Atomic Bomb Survivors

Yakovlev and Polig (1996) developed a mechanistically motivated stochastic model of radiation carcinogenesis allowing for cell death. The key feature of the model is that it allows for radiation-induced cell killing to compete with the process of tumor promotion. This model describes and explains a wide range of experimental findings documented in the radiobiological literature, including the inverse dose-rate effect and radiation hormesis. The model has successfully been applied to various sets of experimental and epidemiological data to gain quantitative insight into the processes of tumorigenesis induced by radiation and chemical carcinogens. In this paper, we discuss the most recent application of the Yakovlev-Polig model to the analysis of epidemiological data on the mortality caused by radiation-induced leukemia (all types) among the atomic bomb survivors (Hiroshima and Nagasaki). Nonparametric estimates of the hazard function for leukemia latency time were obtained for three different dose groups identified in the Hiroshima cohort. The behavior of these estimates suggests the presence of the hormesis-type effect in relation to leukemia-caused mortality. A parsimonious version of the mechanistic model yields parametric estimates that are in good agreement with their nonparametric counterparts. Using the parametric model, we corroborated the presence of a moderate hormesis effect in the Hiroshima data. However, we have been unable to uncover the same effect with the Nagasaki cohort of the atomic bomb survivors.     

Dead or gone? Bayesian inference on mortality for the dispersing sex

Estimates of age‐specific mortality are regularly used in ecology, evolution, and conservation research. However, estimating mortality of the dispersing sex, in species where one sex undergoes natal dispersal, is difficult. This is because it is often unclear whether members of the dispersing sex that disappear from monitored areas have died or dispersed. Here, we develop an extension of a multievent model that imputes dispersal state (i.e., died or dispersed) for uncertain records of the dispersing sex as a latent state and estimates age‐specific mortality and dispersal parameters in a Bayesian hierarchical framework. To check the performance of our model, we first conduct a simulation study. We then apply our model to a long‐term data set of African lions. Using these data, we further study how well our model estimates mortality of the dispersing sex by incrementally reducing the level of uncertainty in the records of male lions. We achieve this by taking advantage of an expert's indication on the likely fate of each missing male (i.e., likely died or dispersed). We find that our model produces accurate mortality estimates for simulated data of varying sample sizes and proportions of uncertain male records. From the empirical study, we learned that our model provides similar mortality estimates for different levels of uncertainty in records. However, a sensitivity of the mortality estimates to varying uncertainty is, as can be expected, detectable. We conclude that our model provides a solution to the challenge of estimating mortality of the dispersing sex in species with data deficiency due to natal dispersal. Given the utility of sex‐specific mortality estimates in biological and conservation research, and the virtual ubiquity of sex‐biased dispersal, our model will be useful to a wide variety of applications.     

A model for analyzing insect stage-frequency data when mortality varies with time

A model is developed for the analysis of insect stage-frequency data which may be applied to populations with age-dependent mortality. The analysis of stage-frequency data is divided into two steps. In the first step, the number of different mortality rates and their values are estimated. The second step provides estimates of developmental rates and variances for each developmental stage and in addition provides estimates of the number of recruits to each stage. The model may be used both in analysis and prediction of insect stage frequencies. Hence, in addition to estimating developmental and mortality rates from stage-frequency data, it may also be used as a simulation model for an insect population. The model is applied to two populations of Hemileuca oliviaeCockerell , a lepidopterous pest of New Mexico grasslands. The model identifies, in the two populations, different mortality rates that are related to plant productivity.     

The adequacy of aging techniques in vertebrates for rapid estimation of population mortality rates from age distributions

As a key parameter in population dynamics, mortality rates are frequently estimated using mark–recapture data, which requires extensive, long‐term data sets. As a potential rapid alternative, we can measure variables correlated to age, allowing the compilation of population age distributions, from which mortality rates can be derived. However, most studies employing such techniques have ignored their inherent inaccuracy and have thereby failed to provide reliable mortality estimates. In this study, we present a general statistical model linking birth rate, mortality rate, and population age distributions. We next assessed the reliability and data needs (i.e., sample size) for estimating mortality rate of eight different aging techniques. The results revealed that for half of the aging techniques, correlations with age varied considerably, translating into highly variable accuracies when used to estimate mortality rate from age distributions. Telomere length is generally not sufficiently correlated to age to provide reliable mortality rate estimates. DNA methylation, signal‐joint T‐cell recombination excision circle (sjTREC), and racemization are generally more promising techniques to ultimately estimate mortality rate, if a sufficiently high sample size is available. Otolith ring counts, otolithometry, and age‐length keys in fish, and skeletochronology in reptiles, mammals, and amphibians, outperformed all other aging techniques and generated relatively accurate mortality rate estimation with a sample size that can be feasibly obtained. Provided the method chosen is minimizing and estimating the error in age estimation, it is possible to accurately estimate mortality rates from age distributions. The method therewith has the potential to estimate a critical, population dynamic parameter to inform conservation efforts within a limited time frame as opposed to mark–recapture analyses.     

Extrapolation of the relative risk of radiogenic neoplasms across mouse strains and to man

We have examined two interrelated questions: is the susceptibility for radiogenic cancer related to the natural incidence, and are the responses of cancer induction by radiation described better by an absolute or a relative risk model. Also, we have examined whether it is possible to extrapolate relative risk estimates across species, from mice to humans. The answers to these questions were obtained from determinations of risk estimates for nine neoplasms in female and male C3Hf/Bd and C57BL/6 Bd mice and from data obtained from previous experiments with female BALB/c Bd and RFM mice. The mice were exposed to 137Cs gamma rays at 0.4 Gy/min to doses of 0, 0.5, 1.0, or 2.0 Gy. When tumors that were considered the cause of death were examined, both the control and induced mortality rates for the various tumors varied considerably among sexes and strains. The results suggest that in general susceptibility is determined by the control incidence. The relative risk model was significantly superior in five of the tumor types: lung, breast, liver, ovary, and adrenal. Both models appeared to fit myeloid leukemia and Harderian gland tumors, and neither provided good fits for thymic lymphoma and reticulum cell sarcoma. When risk estimates of radiation-induced tumors in humans and mice were compared, it was found that the relative risk estimates for lung, breast, and leukemia were not significantly different between humans and mice. In the case of liver tumors, mice had a higher risk than humans. These results indicate that the relative risk model is the appropriate approach for risk estimation for a number of tumors. The apparent concordance of relative risk estimates between humans and mice for the small number of cancers examined encourages us to undertake further studies.     

Estimating predation rates in experimental systems: scale-dependent effects of aggregative behaviour

We studied the effect of arena size on estimates of prey mortality rate in predation experiments. In a laboratory experiment involving two of the dominating benthic species in the northern Baltic Sea, the predacious isopod Saduria entomon , and its main prey, the amphipod Monoporeia affinis , the prey mortality rate increased with container radius. The densities of both predator and prey close to the wall increased with container size. We hypothesised that this scale-dependent coaggregation of predator and prey caused the mortality rates to increase with arena size. We tested the hypothesis with the help of a simple model, by calculating the expected number of prey eaten in containers of different size from experimental data on the distributions of predator and prey within the arenas. A significant relationship between expected and observed numbers eaten supported our hypothesis. As the aggregative response was most pronounced in large arenas, this leads to the counterintuitive conclusion that large containers produced more biased estimates of morality rates than small containers.
To further study the effects of coaggregation we explored a general simulation model where both predator and prey preferred the habitat close to the arena wall. The model predicted a humpshaped relationship between encounter rate and arena size. This suggests that when predators and prey show a scale-dependent tendency to aggregate along arena walls, the most accurate estimates of predation rates may be obtained with very small or very large arenas.     

Identification of insulin receptor systems: assessing the impact of model selection and measurement error on precision of parameter estimates using Monte Carlo study

An extensive Monte Carlo study has been carried out in order to study the effect of measurement error on the precision of parameter estimates of an insulin binding system. Hypothetical radioimmunoassay experiments were generated for insulin binding to erythrocytes. The design of experiments followed strictly the protocol of real experiments. Randomly generated error was added to the synthetic data. The standard technique, a weighted non-linear regression analysis, was employed to re-estimate parameters of a model of two receptor sites and a model of negative co-operativity. As the original parameter values were known, the differences between original and estimated values was studied for (a) measurement error in the range from 0-17%, (b) random initial estimates and (c) error-free non-specific binding. In addition, analytical estimates of parameter precision were compared with the true between-experiment variation of parameter estimates. At the measurement error of 12%, a one site model is recommended to estimate the high affinity population of the two sites model. Plausible results can be expected in 90% of experiments, the between-experiment variation being approximately 30%. The model of two receptor sites gives approximately two thirds of plausible results. The high affinity population can be estimated with the between-experiment variation of 40%, the low affinity population is virtually unidentifiable with the between-experiment variation of approximately 100% and parameter estimates biased to higher values. Only half of the results obtained from the model of negative co-operativity are plausible, the variation in parameter estimates ranges from 90-150% and estimates are biased to higher values. At the level of 12% measurement error, random initial estimates do not significantly affect the estimation process, provided initial estimates are selected from a feasible range. At the same measurement error, the error-free non-specific binding does not improve the results, indicating that the mean of six replicates may be taken as a reliable estimate of non-specific binding. The analytical estimates of the coefficient of variation systematically underestimates the true between-experiments coefficient of variation, the difference has been found to be about 50%.     

New models for evaluation of radiation-induced lifetime cancer risk and its uncertainty employed in the UNSCEAR 2006 report

Generalized relative and absolute risk models are fitted to the latest Japanese atomic bomb survivor solid cancer and leukemia mortality data (through 2000), with the latest (DS02) dosimetry, by classical (regression calibration) and Bayesian techniques, taking account of errors in dose estimates and other uncertainties. Linear-quadratic and linear-quadratic-exponential models are fitted and used to assess risks for contemporary populations of China, Japan, Puerto Rico, the U.S. and the UK. Many of these models are the same as or very similar to models used in the UNSCEAR 2006 report. For a test dose of 0.1 Sv, the solid cancer mortality for a UK population using the generalized linear-quadratic relative risk model is estimated as 5.4% Sv(-1) [90% Bayesian credible interval (BCI) 3.1, 8.0]. At 0.1 Sv, leukemia mortality for a UK population using the generalized linear-quadratic relative risk model is estimated as 0.50% Sv(-1) (90% BCI 0.11, 0.97). Risk estimates varied little between populations; at 0.1 Sv the central estimates ranged from 3.7 to 5.4% Sv(-1) for solid cancers and from 0.4 to 0.6% Sv(-1) for leukemia. Analyses using regression calibration techniques yield central estimates of risk very similar to those for the Bayesian approach. The central estimates of population risk were similar for the generalized absolute risk model and the relative risk model. Linear-quadratic-exponential models predict lower risks (at least at low test doses) and appear to fit as well, although for other (theoretical) reasons we favor the simpler linear-quadratic models.     

The Distribution of Mutation Effects on Viability in Drosophila Melanogaster

Parameters of continuous distributions of effects and rates of spontaneous mutation for relative viability in Drosophila are estimated by maximum likelihood from data of two published experiments on accumulation of mutations on protected second chromosomes. A model of equal mutant effects gives a poor fit to the data of the two experiments; higher likelihoods are obtained with leptokurtic distributions or for models in which there is more than one class of mutation effect. Minimum estimates of mutation rates (events per generation) at polygenes affecting viability on chromosome 2 are 0.14 and 0.068, but estimates are strongly confounded with other parameters in the model. Separate information on rates of molecular divergence between Drosophila species and from rates of movement of transposable elements is used to infer the overall genomic mutation rate in Drosophila, and the viability data are analyzed with mutation rate as a known parameter. If, for example, a mutation rate for chromosome 2 of 0.4 is assumed, maximum likelihood estimates of mean mutant effect on relative viability are 0.4% and 1%, but the majority of mutations have very much smaller effects than these values as distributions are highly leptokurtic. The methodology is applied to estimate viability effects of single P element insertional mutations. The mean effect per insertion is found to be higher, and their distribution is found to be less leptokurtic than for spontaneous mutations. The equilibrium genetic variance of viability predicted by a mutation-selection balance model with parameters estimated from the mutation accumulation experiments is similar to laboratory estimates of genetic variance of viability from natural populations of Drosophila.     

A measurement error model for time-series studies of air pollution and mortality

One barrier to interpreting the observational evidence concerning the adverse health effects of air pollution for public policy purposes is the measurement error inherent in estimates of exposure based on ambient pollutant monitors. Exposure assessment studies have shown that data from monitors at central sites may not adequately represent personal exposure. Thus, the exposure error resulting from using centrally measured data as a surrogate for personal exposure can potentially lead to a bias in estimates of the health effects of air pollution. This paper develops a multi-stage Poisson regression model for evaluating the effects of exposure measurement error on estimates of effects of particulate air pollution on mortality in time-series studies. To implement the model, we have used five validation data sets on personal exposure to PM10. Our goal is to combine data on the associations between ambient concentrations of particulate matter and mortality for a specific location, with the validation data on the association between ambient and personal concentrations of particulate matter at the locations where data have been collected. We use these data in a model to estimate the relative risk of mortality associated with estimated personal-exposure concentrations and make a comparison with the risk of mortality estimated with measurements of ambient concentration alone. We apply this method to data comprising daily mortality counts, ambient concentrations of PM10measured at a central site, and temperature for Baltimore, Maryland from 1987 to 1994. We have selected our home city of Baltimore to illustrate the method; the measurement error correction model is general and can be applied to other appropriate locations.Our approach uses a combination of: (1) a generalized additive model with log link and Poisson error for the mortality-personal-exposure association; (2) a multi-stage linear model to estimate the variability across the five validation data sets in the personal-ambient-exposure association; (3) data augmentation methods to address the uncertainty resulting from the missing personal exposure time series in Baltimore. In the Poisson regression model, we account for smooth seasonal and annual trends in mortality using smoothing splines. Taking into account the heterogeneity across locations in the personal-ambient-exposure relationship, we quantify the degree to which the exposure measurement error biases the results toward the null hypothesis of no effect, and estimate the loss of precision in the estimated health effects due to indirectly estimating personal exposures from ambient measurements.     

Kinetic Cell-Cycle Analysis of a Cultured Mammalian Cell Population

The parameters of the cell cycle are analyzed in terms of the stochastic theory of cell proliferation for a murine mastocytoma line. The cells were grown in suspension culture under steady-state conditions in a chemostat. Initial estimates of the parameters from synchronous growth indicate that agreement of the data with the model is obtained only if the model is modified to include an initial proliferating fraction of less than 100%, and a cell loss continuing throughout the course of the experiment. The analysis verifies that the modified theory adequately describes the data, and that similar parameters are obtained from both desynchronization and percent labeled mitosis experiments. The average cycle time from 10 desynchronization experiments was 8.24 ± 0.52 h with a cellular standard deviation of 1.28 ± 0.18. The combined parameter obtained by dividing the cellular standard deviation by the cycle time is shown to be a useful measure of biological variability well defined over many different experiments. The rate constant for cell loss is about 0.009 which gives an 8% cell loss per cycle. The cell loss is sufficient to account for the apparent deficit in initially proliferating cells. The initial distribution of the synchronous cells is qualitatively examined and is found to be peaked late in G₁ or early in S.     

World whale stocks

The history of whaling is very largely one of repeated over-exploitation of the various whale stocks which became available through discovery or technological advance. Modern whaling has similarly caused considerable reductions in the numbers of some species in the major whaling grounds. Stock assessment methods are based on catch and effort statistics, biological information including age and reproductive status, marking and sightings records. Catch effort data have to be used with caution, because of changes in species preference, shifts in the whaling grounds and national fleet variations. With allowance made for these factors, cumulative catches adjusted for recruitment can be used to estimate the initial stock number. Changes in stock density after known catches also lead to abundance estimates. Logarithmic regression of age composition data are used to find the total mortality rates. The natural mortality can be estimated from early season catches in a fishery or pre-fishery year classes caught more recently; fishing mortality is found by subtraction, which again leads to abundance estimates. Mathematical approaches incorporating recruitment estimates from actual age composition data and theoretical population models have been employed. Additional estimates come from mark release-recapture experiments and direct sightings counts from whaling vessels and research ships. The latter are the only means of estimating the protected species. The yields which the various stocks can sustain are calculated from direct observations and theoretical considerations of the changes in recruitment, largely due to increased pregnancy rates and the lower ages at sexual maturity which occur in exploited stocks. The results of all the available analyses have been compared and combined to produce the population estimates and yields tabulated. The object of whale management is to bring all stocks to the levels providing the maximum or optimum sustainable yields. These are defined in terms of numbers at the moment, but may be expressed as biomass in the future.     

An administrative claims model for profiling hospital 30-day mortality rates for pneumonia patients

Background

Outcome measures for patients hospitalized with pneumonia may complement process measures in characterizing quality of care. We sought to develop and validate a hierarchical regression model using Medicare claims data that produces hospital-level, risk-standardized 30-day mortality rates useful for public reporting for patients hospitalized with pneumonia.

Methodology/Principal Findings

Retrospective study of fee-for-service Medicare beneficiaries age 66 years and older with a principal discharge diagnosis of pneumonia. Candidate risk-adjustment variables included patient demographics, administrative diagnosis codes from the index hospitalization, and all inpatient and outpatient encounters from the year before admission. The model derivation cohort included 224,608 pneumonia cases admitted to 4,664 hospitals in 2000, and validation cohorts included cases from each of years 1998–2003. We compared model-derived state-level standardized mortality estimates with medical record-derived state-level standardized mortality estimates using data from the Medicare National Pneumonia Project on 50,858 patients hospitalized from 1998–2001. The final model included 31 variables and had an area under the Receiver Operating Characteristic curve of 0.72. In each administrative claims validation cohort, model fit was similar to the derivation cohort. The distribution of standardized mortality rates among hospitals ranged from 13.0% to 23.7%, with 25^th, 50^th, and 75^th percentiles of 16.5%, 17.4%, and 18.3%, respectively. Comparing model-derived risk-standardized state mortality rates with medical record-derived estimates, the correlation coefficient was 0.86 (Standard Error = 0.032).

Conclusions/Significance

An administrative claims-based model for profiling hospitals for pneumonia mortality performs consistently over several years and produces hospital estimates close to those using a medical record model.     

Modeling Cell and Matrix Anisotropy in Fibroblast Populated Collagen Vessels

Microstructurally based models for bio-artificial tissues are needed to predict in vivo mechanical behavior and to validate assumptions for models of biologic tissues. We develop a microstructural model, based on on Zahalak et al. (2000) [Biophys 79(5):2369–2381], to describe matrix and tissue anisotropy observed in recent biaxial tests of fibroblast populated collagen vessels (FPCVs) with different cell orientations (Wagenseil et al. in Ann Biomed Eng 32(5):720–731 2004). The model includes pseudo-elastic cell behavior and pseudo-elastic, non-linear matrix behavior with recruitment of initially buckled collagen fibers. We obtained estimates of collagen matrix parameters from measurements of FPCVs treated with 2× 10⁻⁶ M Cytochalasin D and used these estimates to determine cell parameters in FPCVs activated with 5% fetal calf serum. The estimated stiffness of individual fibroblasts was 41–1,165 kPa. Parameter estimates for both cell and matrix were influenced by the non-linearity of the biaxial test data, making it difficult to obtain unique parameter values for some experiments. Additional microstructural measurements of the collagen matrix may help to more precisely determine the relative contributions of cells and matrix.     

Oxidative DNA damage background estimated by a system model of base excision repair

Human DNA can be damaged by natural metabolism through free radical production. It has been suggested that the equilibrium between innate damage and cellular DNA repair results in an oxidative DNA damage background that potentially contributes to disease and aging. Efforts to quantitatively characterize the human oxidative DNA damage background level, based on measuring 8-oxoguanine lesions as a biomarker, have led to estimates that vary over three to four orders of magnitude, depending on the method of measurement. We applied a previously developed and validated quantitative pathway model of human DNA base excision repair, integrating experimentally determined endogenous damage rates and model parameters from multiple sources. Our estimates of at most 100 8-oxoguanine lesions per cell are consistent with the low end of data from biochemical and cell biology experiments, a result robust to model limitations and parameter variation. Our findings show the power of quantitative system modeling to interpret composite experimental data and make biologically and physiologically relevant predictions for complex human DNA repair pathway mechanisms and capacity.     

A model for the relationship between wing fray and chronological and ovarian ages in tsetse (Glossina spp)

Age-dependent mortality changes in haematophagous insects are difficult to measure but are important determinants of population dynamics and vectorial capacity. A Markov process was used to model age-dependent changes in wing fray in tsetse (Glossina spp), calibrated using published mark–recapture data for male G. m. morsitans in Tanzania. The model was applied to female G. m. morsitans, captured in Zimbabwe using a vehicle-mounted electric net and subjected to ovarian dissection and wing fray analysis. Rates of fray increased significantly with age in males but not females, where the rate was constant for ovarian categories 0–3. A jump in mean fray between ovarian categories 3 and 4 + 4n is consistent with the latter category including flies that have ovulated 4, 8, 12, 16 times and so on. The magnitude of the jump could, theoretically, facilitate improved mortality estimates. In practice, although knowledge of fly mortality was required for modelling wing fray, mortality estimates derived from ovarian dissection data are independent of patterns and rates of change in wing fray. Significantly better fits to ovarian age data resulted when age-specific mortality was modelled as the sum of two exponentials, with high mortality in young and old flies, than when mortality was constant at 2.3% per day.     

Comparison of analytical and inverse finite element approaches to estimate cell viscoelastic properties by micropipette aspiration

The viscoelastic properties of cells are important in predicting cell deformation under mechanical loading and may reflect cell phenotype or pathological transition. Previous studies have demonstrated that viscoelastic parameters estimated by finite element (FE) analyses of micropipette aspiration (MA) data differ from those estimated by the analytical half-space model. However, it is unclear whether these differences are statistically significant, as previous studies have been based on average cell properties or parametric analyses that do not reflect the inherent experimental and biological variability of real experimental data. To determine whether cell material parameters estimated by the half-space model are significantly different from those predicted by the FE method, we implemented an inverse FE method to estimate the viscoelastic parameters of a population of primary porcine aortic valve interstitial cells tested by MA. We found that inherent differences between the analytical and inverse FE estimation methods resulted in statistically significant differences in individual cell properties. However, in cases with small pipette to cell radius ratios and short loading periods, model-dependent differences were masked by experimental and cell-to-cell variability. Analytical models that account for finite cell-size and loading rate further relaxed the experimental conditions for which accurate cell material parameter estimates could be obtained. These data provide practical guidelines for analysis of MA data that account for the wide range of conditions encountered in typical experiments.     

A negative binomial model for sampling mosquitoes in a malaria survey

Sampling models are investigated for counts of mosquitoes from a malaria field survey conducted by the World Health Organization in Nigeria. The data can be described by a negative binomial model for two-way classified counted data, where the cell means are constrained to satisfy row-by-column independence and the parameter k is constant across rows. An algorithm, based on iterative proportional fitting, is devised for finding maximum likelihood estimates. Sampling properties of the estimates and likelihood-ratio statistics for the small sample sizes of the data are investigated by Monte Carlo experiments. The WHO reported an observation that the relative efficiencies of four trapping methods vary over time. Out of eight villages in the survey area, this observation is found to be true in only the one village that is near a swamp.     

A life-like virtual cell membrane using discrete automata

A framework is presented that captures the discrete and probabilistic nature of molecular transport and reaction kinetics found in a living cell as well as formally representing the spatial distribution of these phenomena. This particle or agent-based approach is computationally robust and complements established methods. Namely it provides a higher level of spatial resolution than formulations based on ordinary differential equations (ODE) while offering significant advantages in computational efficiency over molecular dynamics (MD). Using this framework, a model cell membrane has been constructed with discrete particle agents that respond to local component interactions that resemble flocking or herding behavioural cues in animals. Results from simulation experiments are presented where this model cell exhibits many of the characteristic behaviours associated with its biological counterpart such as lateral diffusion, response to osmotic pressure gradients, membrane growth and cell division. Lateral diffusion rates and estimates for the membrane modulus of elasticity derived from these simple experiments fall well within a biologically relevant range of values. More importantly, these estimates were obtained by applying a simple qualitative tuning of the model membrane. Membrane growth was simulated by injecting precursor molecules into the proto-cell at different rates and produced a variety of morphologies ranging from a single large cell to a cluster of cells. The computational scalability of this methodology has been tested and results from benchmarking experiments indicate that real-time simulation of a complete bacterial cell will be possible within 10 years.