Standardized tumor rates for chronic bioassays

If crude experimental proportions of animals with tumors from chronic bioassays for carcinogenicity are used for low-dose extrapolation in a risk analysis, different dose-specific patterns of mortality due to competing risks can bias the results. In order to adjust tumor rates for differential mortality across dose groups, Farmer, Kodell, and Gaylor (1982, Risk Analysis 2, 27-34) recommended using nonparametric estimates of probability distributions of times to onset of tumors, with competing causes of death removed, when performing a risk analysis. This paper extends the approach of Farmer et al. by proposing a method for adjusting tumor rates to reflect lifetime or near-lifetime tumor incidences that would be obtained if all dose groups experienced the control mortality rate from causes other than the tumor of interest. Thus, natural mortality due to competing risks is explicitly included, rather than removed. The proposed standardized tumor rates are calculated as a summation of adjusted age-specific probabilities of dying with a tumor during the course of an animal bioassay for carcinogenicity plus the probability of being alive with a tumor at the terminal sacrifice.     

Studies of radon-exposed miner cohorts using a biologically based model: comparison of current Czech and French data with historic data from China and Colorado

Cosmic radiation is an occupational risk factor for commercial aircrews. In this large European cohort study (ESCAPE) its association with cancer mortality was investigated on the basis of individual effective dose estimates for 19,184 male pilots. Mean annual doses were in the range of 2–5 mSv and cumulative lifetime doses did not exceed 80 mSv. All-cause and all-cancer mortality was low for all exposure categories. A significant negative risk trend for all-cause mortality was seen with increasing dose. Neither external and internal comparisons nor nested case-control analyses showed any substantially increased risks for cancer mortality due to ionizing radiation. However, the number of deaths for specific types of cancer was low and the confidence intervals of the risk estimates were rather wide. Difficulties in interpreting mortality risk estimates for time-dependent exposures are discussed.Abbreviations CI confidence interval - CLL chronic lymphatic leukemia - RRC radiation-related cancers - NRRC non-radiation-related cancers - RR relative risk - SMR standardized mortality ratio     

Only Simpson Diversity can be Estimated Accurately from Microbial Community Fingerprints

Lalande et al. (Microb. Ecol. 66(3):647–658, 2013) introduced a promising approach to quantify microbial diversity from fingerprinting profiles. Their analysis is based on extrapolating the abundance of the phylotypes detectable in a fingerprint towards the rare phylotypes of the community. By considering a set of reconstructed communities, Lalande et al. obtained a range of estimates for phylotype richness, Shannon diversity and Simpson diversity. They reported narrow ranges indicating accurate estimation, especially for Shannon and Simpson diversities. Here, we show that a much larger set of reconstructed communities than the one considered by Lalande et al. is consistent with the fingerprint. We find that the estimates for phylotype richness and Shannon diversity vary over orders of magnitude, but that the estimates for Simpson diversity are restricted to a narrow range (around 10 %). We conclude that only Simpson diversity can be estimated accurately from fingerprints.     

Estimating the under-five mortality rate using a bayesian hierarchical time series model

Background

Millennium Development Goal 4 calls for a reduction in the under-five mortality rate by two-thirds between 1990 and 2015, which corresponds to an annual rate of decline of 4.4%. The United Nations Inter-Agency Group for Child Mortality Estimation estimates under-five mortality in every country to measure progress. For the majority of countries, the estimates within a country are based on the assumption of a piece-wise constant rate of decline.

Methods and Findings

This paper proposes an alternative method to estimate under-five mortality, such that the underlying rate of change is allowed to vary smoothly over time using a time series model. Information about the average rate of decline and changes therein is exchanged between countries using a Bayesian hierarchical model. Cross-validation exercises suggest that the proposed model provides credible bounds for the under-five mortality rate that are reasonably well calibrated during the observation period. The alternative estimates suggest smoother trends in under-five mortality and give new insights into changes in the rate of decline within countries.

Conclusions

The proposed model offers an alternative modeling approach for obtaining estimates of under-five mortality which removes the restriction of a piece-wise linear rate of decline and introduces hierarchy to exchange information between countries. The newly proposed estimates of the rate of decline in under-5 mortality and the uncertainty assessments would help to monitor progress towards Millennium Development Goal 4.     

Darting Primates: Steps Toward Procedural and Reporting Standards

Darting, a common method of capturing wild primates, poses risks to the individuals that must be appropriately minimized. A recent article in the International Journal of Primatology by Cunningham et al. (International Journal of Primatology, 36(5), 894–915, 2015) presented a literature review of the reporting of darting procedures in primatology and anonymously surveyed primatologists on darting methods and their effects, to report general trends in the field. We quantitatively reexamined 29 articles described by the authors as having information on fatalities and/or injuries. We think that the various body masses of primates (1 kg–150 kg), along with their locations and habitat types, and the degree of experience of the darting team, should be considered when estimating mortality and injury rates, and thus preclude the computation of an average mortality value across taxa. Nevertheless, we computed an average (mean) for comparison with the previous analyses. Our mean estimated mortality rate was 2.5% and the mean estimated injury risk was 1.5% (N = 21 articles). Thus, our estimated mortality rate is smaller than the combined mortality and injury rate of 5% reported by Cunningham et al. (International Journal of Primatology, 36(5), 894–915, 2015) and smaller than the mortality rates of medium-sized terrestrial mammals they used for comparison. Our study strongly suggests the critical need for more data to be analyzed in a standardized fashion.     

Soil ingestion estimates for use in site evaluations based on the best tracer method

This paper develops a novel methodology, the Best Tracer method (BTM), that substantially overcomes the principal limitations (intertracer inconsistencies, and poor precision of recovery) of estimating soil ingestion by specific soil‐based tracers in massbalance studies. The BTM incorporates a biological and statistical framework that improves precision of recovery of tracer estimates, markedly reducing input‐output misalignment error resulting from a lack of correspondence between food tracer input and fecal tracer output.

This method is then used to re‐estimate the soil ingestion distribution of previously published soil ingestion estimates from two children studies (Calabrese et al. 1989; Davis et al., 1990) and one adult study (Calabrese et al., 1990). Revised estimates of soil ingestion are provided for each study. In addition, the results from the two children's studies are combined to form a single estimate of the soil ingestion distribution. These collective findings result in more reliable quantitative estimates of soil ingestion than trace element specific estimates, as well as providing improved understanding of current published soil ingestion studies, and improved methods that will enhance the design and interpretation of future soil ingestion studies.

With respect to children, the data indicate that the Calabrese et al. (1989) study provides the most reliable estimates of soil ingestion based on the estimated precision of recovery. However, estimates for the combined data of the Calabrese et al. (1989) and Davis et al. (1990) studies include all available children's data from mass balance studies, and thus provide more robust estimates. The collective data suggest that the median child in these studies ingested 30–40 mg/day of soil, while the upper 95% estimate is approximately 200 mg/day. Current data are insufficient to distinguish the children's soil ingestion distribution from that of adults. The revised and improved estimates of soil ingestion for children and adults have important implications for contaminant exposure estimates used in site evaluation risk assessment procedures.     

Risk coefficient for gamma-rays with regard to solid cancer

A previous investigation has uncoupled the solid cancer risk coefficient for neutrons from the low dose estimates of the relative biological effectiveness (RBE) of neutrons and the photon risk coefficient, and has related it to two more tangible quantities, the excess relative risk (ERR1) due to an intermediate reference dose D1 = 1 Gy of gamma-rays and the RBE of neutrons, R1, against this reference dose. With tentatively assumed RBE values between 20 and 50 and in terms of organ-averaged doses--rather than the usually invoked colon doses--the neutron risk factor was seen to be in general agreement with the current risk estimate of the International Commission on Radiation Protection (ICRP). The present assessment of the risk coefficient for gamma-rays incorporates--in terms of the unchanged A-bomb dosimetry system, DS86--this treatment of the neutrons, but is otherwise largely analogous to the evaluation of the A-bomb data for the ICRP report and for the recent report of the United Nations Scientific Committee on the effects of ionizing radiation, UNSCEAR. The resulting central estimate of the lifetime attributable risk (LAR) for solid cancer mortality is 0.043/Gy for a working population (ages 25-65), and is nearly the same whether the age at exposure or the attained age model is used for risk projection. For a population of all ages 0.042/Gy is obtained with the attained age model and 0.068/Gy with the age at exposure model. The values do not include a dose and dose rate effectiveness factor (DDREF), and they are only half as large as the new UNSCEAR estimates of 0.082/Gy (attained age model and all ages) and 0.13/Gy (age at exposure model and all ages). The difference is only partly due to the more explicit treatment of the neutrons. It reflects also the fact that UNSCEAR has converted ERR into LAR in a way that differs from the ICRP procedure, and that it has summed the overall risk coefficient for solid tumor mortality and incidence from separate estimates for eight solid tumor categories, whereas the present study employs a combined computation for all solid tumors and uses the ICRP procedure for the conversion of ERR into LAR. The appendix gives results for the solid cancer incidence data.     

The effect of diagnostic misclassification on non-cancer and cancer mortality dose response in A-bomb survivors.

We used the EM algorithm in the context of a joint Poisson regression analysis of cancer and non-cancer mortality in the Radiation Effects Research Foundation (RERF) Life Span Study (LSS) to assess whether the observed increased risk of non-cancer death due to radiation exposure (Shimizu et al., RERF Technical Report 02-91, 1991) can be attributed solely to misclassification of cancer as non-cancer on death certificates. We show that greater levels of dose-independent misclassification than are indicated by a series of autopsies conducted on a subset of LSS members would be required to explain the non-cancer dose response, but that a relatively small amount of dose-dependence in the misclassification of cancer would explain the result. The adjustment for misclassification also results in higher risk estimates for cancer mortality. We review applications of similar statistical methods in other contexts and discuss extensions of the methods to more than two causes of death.     

The Increase in Animal Mortality Risk following Exposure to Sparsely Ionizing Radiation Is Not Linear Quadratic with Dose

Introduction

The US government regulates allowable radiation exposures relying, in large part, on the seventh report from the committee to estimate the Biological Effect of Ionizing Radiation (BEIR VII), which estimated that most contemporary exposures- protracted or low-dose, carry 1.5 fold less risk of carcinogenesis and mortality per Gy than acute exposures of atomic bomb survivors. This correction is known as the dose and dose rate effectiveness factor for the life span study of atomic bomb survivors (DDREF_LSS). It was calculated by applying a linear-quadratic dose response model to data from Japanese atomic bomb survivors and a limited number of animal studies.

Methods and Results

We argue that the linear-quadratic model does not provide appropriate support to estimate the risk of contemporary exposures. In this work, we re-estimated DDREF_LSS using 15 animal studies that were not included in BEIR VII’s original analysis. Acute exposure data led to a DDREF_LSS estimate from 0.9 to 3.0. By contrast, data that included both acute and protracted exposures led to a DDREF_LSS estimate from 4.8 to infinity. These two estimates are significantly different, violating the assumptions of the linear-quadratic model, which predicts that DDREF_LSS values calculated in either way should be the same.

Conclusions

Therefore, we propose that future estimates of the risk of protracted exposures should be based on direct comparisons of data from acute and protracted exposures, rather than from extrapolations from a linear-quadratic model. The risk of low dose exposures may be extrapolated from these protracted estimates, though we encourage ongoing debate as to whether this is the most valid approach. We also encourage efforts to enlarge the datasets used to estimate the risk of protracted exposures by including both human and animal data, carcinogenesis outcomes, a wider range of exposures, and by making more radiobiology data publicly accessible. We believe that these steps will contribute to better estimates of the risks of contemporary radiation exposures.     

Confidence intervals for population growth rate of organisms with two-stage life histories

Although life histories can be modelled with great generality using projection matrices, for organisms with life histories that can be accurately described by a simplified set of parameters, e.g. when adult fecundity and mortality are independent of age, more accurate estimates of life table parameters and of population growth rate and its standard error can be readily obtained. Here an analytic method for calculating approximate confidence intervals for population growth rate is given for two-stage life histories that can be described by four variables representing age at first breeding, fecundity per unit time, and juvenile and adult survivorships per unit time. The method is applied to experimental data on Capitella sp. I obtained by Hansen et al., and quite good agreement is found between the analytic and bootstrap estimates of the standard error of Λ. The analytic estimates were a little conservative, probably because of the way the action of mortality was modelled. Alternative life-history models are briefly discussed, and the desirability of formulating life-history models so that the variables involved are independent of each other is stressed. Analytic estimates of Λ may be biassed if an inappropriate model is chosen or if variables are not independent and the correlations between them are not measured. To allow for these possibilities, where necessary a conservative approach should be taken to significance testing using the analytic method.     

The log multinomial regression model for nominal outcomes with more than two attributes

An estimate of the risk or prevalence ratio, adjusted for confounders, can be obtained from a log binomial model (binomial errors, log link) fitted to binary outcome data. We propose a modification of the log binomial model to obtain relative risk estimates for nominal outcomes with more than two attributes (the "log multinomial model"). Extensive data simulations were undertaken to compare the performance of the log multinomial model with that of an expanded data multinomial logistic regression method based on the approach proposed by Schouten et al. (1993) for binary data, and with that of separate fits of a Poisson regression model based on the approach proposed by Zou (2004) and Carter, Lipsitz and Tilley (2005) for binary data. Log multinomial regression resulted in "inadmissable" solutions (out-of-bounds probabilities) exceeding 50% in some data settings. Coefficient estimates by the alternative methods produced out-of-bounds probabilities for the log multinomial model in up to 27% of samples to which a log multinomial model had been successfully fitted. The log multinomial coefficient estimates generally had lesser relative bias and mean squared error than the alternative methods. The practical utility of the log multinomial regression model was demonstrated with a real data example. The log multinomial model offers a practical solution to the problem of obtaining adjusted estimates of the risk ratio in the multinomial setting, but must be used with some care and attention to detail.     

Experimental derivation of relative biological effectiveness of A-bomb neutrons in Hiroshima and Nagasaki and implications for risk assessment

Epidemiological data on the health effects of A-bomb radiation in Hiroshima and Nagasaki provide the framework for setting limits for radiation risk and radiological protection. However, uncertainty remains in the equivalent dose, because it is generally believed that direct derivation of the relative biological effectiveness (RBE) of neutrons from the epidemiological data on the survivors is difficult. To solve this problem, an alternative approach has been taken. The RBE of polyenergetic neutrons was determined for chromosome aberration formation in human lymphocytes irradiated in vitro, compared with published data for tumor induction in experimental animals, and validated using epidemiological data from A-bomb survivors. The RBE of fission neutrons was dependent on dose but was independent of the energy spectrum. The same RBE regimen was observed for lymphocyte chromosome aberrations and tumors in mice and rats. Used as a weighting factor for A-bomb survivors, this RBE system was superior in eliminating the city difference in chromosome aberration frequencies and cancer mortality. The revision of the equivalent dose of A-bomb radiation using DS02 weighted by this RBE system reduces the cancer risk by a factor of 0.7 compared with the current estimates using DS86, with neutrons weighted by a constant RBE of 10.     

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.     

Bayesian Updating of Model-Based Risk Estimates Using Imperfect Public Health Surveillance Data

Model-based estimation of the human health risks resulting from exposure to environmental contaminants can be an important tool for structuring public health policy. Due to uncertainties in the modeling process, the outcomes of these assessments are usually probabilistic representations of a range of possible risks. In some cases, health surveillance data are available for the assessment population over all or a subset of the risk projection period and this additional information can be used to augment the model-based estimates. We use a Bayesian approach to update model-based estimates of health risks based on available health outcome data. Updated uncertainty distributions for risk estimates are derived using Monte Carlo sampling, which allows flexibility to model realistic situations including measurement error in the observable outcomes. We illustrate the approach by using imperfect public health surveillance data on lung cancer deaths to update model-based lung cancer mortality risk estimates in a population exposed to ionizing radiation from a uranium processing facility.     

Hierarchical Modeling for Estimating Relative Risks of Rare Genetic Variants: Properties of the Pseudo‐Likelihood Method

Summary Many major genes have been identified that strongly influence the risk of cancer. However, there are typically many different mutations that can occur in the gene, each of which may or may not confer increased risk. It is critical to identify which specific mutations are harmful, and which ones are harmless, so that individuals who learn from genetic testing that they have a mutation can be appropriately counseled. This is a challenging task, since new mutations are continually being identified, and there is typically relatively little evidence available about each individual mutation. In an earlier article, we employed hierarchical modeling ( Capanu et al., 2008 , Statistics in Medicine 27 , 1973–1992) using the pseudo‐likelihood and Gibbs sampling methods to estimate the relative risks of individual rare variants using data from a case–control study and showed that one can draw strength from the aggregating power of hierarchical models to distinguish the variants that contribute to cancer risk. However, further research is needed to validate the application of asymptotic methods to such sparse data. In this article, we use simulations to study in detail the properties of the pseudo‐likelihood method for this purpose. We also explore two alternative approaches: pseudo‐likelihood with correction for the variance component estimate as proposed by Lin and Breslow (1996, Journal of the American Statistical Association 91 , 1007–1016) and a hybrid pseudo‐likelihood approach with Bayesian estimation of the variance component. We investigate the validity of these hierarchical modeling techniques by looking at the bias and coverage properties of the estimators as well as at the efficiency of the hierarchical modeling estimates relative to that of the maximum likelihood estimates. The results indicate that the estimates of the relative risks of very sparse variants have small bias, and that the estimated 95% confidence intervals are typically anti‐conservative, though the actual coverage rates are generally above 90%. The widths of the confidence intervals narrow as the residual variance in the second‐stage model is reduced. The results also show that the hierarchical modeling estimates have shorter confidence intervals relative to estimates obtained from conventional logistic regression, and that these relative improvements increase as the variants become more rare.     

Modeling and E-M estimation of haplotype-specific relative risks from genotype data for a case-control study of unrelated individuals

The US National Cancer Institute has recently sponsored the formation of a Cohort Consortium (http://2002.cancer.gov/scpgenes.htm) to facilitate the pooling of data on very large numbers of people, concerning the effects of genes and environment on cancer incidence. One likely goal of these efforts will be generate a large population-based case-control series for which a number of candidate genes will be investigated using SNP haplotype as well as genotype analysis. The goal of this paper is to outline the issues involved in choosing a method of estimating haplotype-specific risk estimates for such data that is technically appropriate and yet attractive to epidemiologists who are already comfortable with odds ratios and logistic regression. Our interest is to develop and evaluate extensions of methods, based on haplotype imputation, that have been recently described (Schaid et al., Am J Hum Genet, 2002, and Zaykin et al., Hum Hered, 2002) as providing score tests of the null hypothesis of no effect of SNP haplotypes upon risk, which may be used for more complex tasks, such as providing confidence intervals, and tests of equivalence of haplotype-specific risks in two or more separate populations. In order to do so we (1) develop a cohort approach towards odds ratio analysis by expanding the E-M algorithm to provide maximum likelihood estimates of haplotype-specific odds ratios as well as genotype frequencies; (2) show how to correct the cohort approach, to give essentially unbiased estimates for population-based or nested case-control studies by incorporating the probability of selection as a case or control into the likelihood, based on a simplified model of case and control selection, and (3) finally, in an example data set (CYP17 and breast cancer, from the Multiethnic Cohort Study) we compare likelihood-based confidence interval estimates from the two methods with each other, and with the use of the single-imputation approach of Zaykin et al. applied under both null and alternative hypotheses. We conclude that so long as haplotypes are well predicted by SNP genotypes (we use the Rh2 criteria of Stram et al. [1]) the differences between the three methods are very small and in particular that the single imputation method may be expected to work extremely well.     

On analyzing circadian rhythms data using nonlinear mixed models with harmonic terms

Wang, Ke, and Brown (2003, Biometrics59, 804-812) developed a smoothing-based approach for modeling circadian rhythms with random effects. Their approach is flexible in that fixed and random covariates can affect both the amplitude and phase shift of a nonparametrically smoothed periodic function. In motivating their approach, Wang et al. stated that a simple sinusoidal function is too restrictive. In addition, they stated that "although adding harmonics can improve the fit, it is difficult to decide how many harmonics to include in the model, and the results are difficult to interpret." We disagree with the notion that harmonic models cannot be a useful tool in modeling longitudinal circadian rhythm data. In this note, we show how nonlinear mixed models with harmonic terms allow for a simple and flexible alternative to Wang et al.'s approach. We show how to choose the number of harmonics using penalized likelihood to flexibly model circadian rhythms and to estimate the effect of covariates on the rhythms. We fit harmonic models to the cortisol circadian rhythm data presented by Wang et al. to illustrate our approach. Furthermore, we evaluate the properties of our procedure with a small simulation study. The proposed parametric approach provides an alternative to Wang et al.'s semiparametric approach and has the added advantage of being easy to implement in most statistical software packages.     

On estimating the polyclonal fraction in lineage-marker studies of tumor origin

Insight into the biology of tumor formation is provided by studies which demonstrate through the use of cell-lineage markers that some tumors have a polyclonal origin. Novelli et al. (1996) proposed to use the proportion of heterotypic tumors among the tumors that are either heterotypic or pure and of the minority marker type as a lower bound on the marginal fraction of polyclonal tumors. Generally, Novelli's ratio does not provide a valid lower bound for the marginal polyclonal fraction, as we demonstrate by analyzing relevant conditional probabilities. Estimation of the polyclonal fraction requires modeling assumptions on the distribution of the number of involved clones. Using three elementary models, we develop maximum likelihood estimation of the polyclonal fraction. We establish robustness of our estimates to misspecification of the clone-marking process, though the estimates are sensitive to assumptions about polyclonal mechanisms. On data from several published studies, our estimates of the polyclonal fraction are substantially smaller than Novelli's ratio.     

Clinical and epidemiological analysis of possibility of acute myocardial infarction development in personnel of radiation dangerous plants

According to the data of cohort and to the "case-control" studies, dynamics of an acute myocardial infarction (AMI) morbidity during the period 1998-2002 and role of radiation factor in AMI development among personnel of radiation dangerous plants (by the example of Siberian Group of Chemical Enterprises (SGCE) exposed to a long-term impact of ionizing radiation in the range of "low" doses) were being carried out. It was determined that in personnel of the main production (working in contact with IR sources) the gradient increase of AMI morbidity was registered during the study period. Personnel of the main production in comparison to personnel of support production (correlating age, sex and examination level) have statistically significant increase of standardized relative risk coefficients of AMI development. When evaluating standardized relative risk coefficient depending on the cumulative dose of external y-radiation, it was impossible to determine the reliance between the rate of increase of radiation dose and standardized relative risk coefficient. According to logistic regression, was determined that individual features of dose load formation are of great significance in AMI development for the personnel of the main production. Absolute values of standardized regression coefficients peculiar to the values characterizing technogenic impact, exceed correspondent values for "traditional" risk factors to be the components of the regression equation, two-three times as much. The combination of these factors allowed to prognosticate AMI development in 94.3% cases. Obtained data made possible to conclude that in pathogenesis of acute coronary diseases ionizing radiation acts as a factor that aggravate negative influence of "traditional" risk factors of cardio-vascular diseases through pleiotropic effects.