Nonidentifiability of competing risks

Frequently one is interested in examining the survival experience of a set of individuals exposed to k risks. If W is the time of failure for the individual and J is the indicator variable for cause of death, then the competing risk framework assumes that W = min X_i and J = j if X_j is the minimum, where the X_i's are the survival lifetimes when only risk R_i is operating on the population. To examine the underlying structure of the survival experience one has to know the joint distribution of the $\text{X}{}_{\mathrm{i}}\text{(F}{}_{\mathrm{<mtext>x</mtext>}}\text{)}$. It is shown here that if only W and J are observed, the joint distribution of the $\text{X}{}_{\mathrm{i}}\text{(F}{}_{\mathrm{<mtext>x</mtext>}}\text{)}$ is nonidentifiable.     

Determination of 99Tc, 63Ni and 121m+126Sn in the marine environment

Four artificially produced radionuclides (${}^{99}\text{Tc, t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 2·15 × 10}{}^5\text{y;}{}^{63}\text{Ni, t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 93 y}$ and ${}^{\mathrm{121m+126}}\text{Sn, t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 55·5 y}$) have been analyzed in sediments and organisms from the marine environment. The samples were obtained from the vicinities of nuclear energy facilities, at sites of nuclear weapon tests and at sites remote from both of these locales. The activities of these nuclides per unit dry weight are remarkably similar at the first two of the above areas but are usually detectable only with difficulty, if at all, in the third area. Techniques for sample treatment and measurement are given.     

Uptake and loss of technetium-95m in the crab Pachygrapsus marmoratus

The uptake and loss kinetics of ^95mTc in seawater have been investigated in the crab Pachygrapsus marmoratus. Both the uptake and loss kinetics can be represented as the sum of two exponential functions, one short-term ($\text{tb}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 16}\text{d}$) and one long-term ($\text{tb}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 63}\text{d}$), $\text{tb}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ being the biological half-time. The predicted steady state concentration factor was estimated to be about 18.No significant linear correlation between Tc uptake rate and animal weight was found during the accumulation phase. At the end of this phase, 77% of the Tc was found to be distributed in the digestive system and particularly in the hepatopancreas (56%); this organ also appeared to lose the radionuclide most quickly. During the loss phase, 90% of the incorporated radioactivity was eliminated in about three months. Therefore P. marmoratus does not appear to be a good bioindicator of Tc in the marine environment nor an important pathway for Tc contamination along marine food chains.     

Experimental studies on the bioaccumulation of plutonium from sea water and a deep-sea sediment by clams and polychaetes

The bioavailability of ²³⁷Pu in the (III + IV) and (V + VI) oxidation states from sea water and a NE Atlantic deep-sea sediment has been studied for clams (Venerupis decussata) and polychaete worms (Hermione hystrix). After 22 days' exposure in sea water transfer factors (TF) had not reached equilibrium, and were 74 ± 5 and 61 ± 1 for clams and 370 ± 10 and 275 ± 11 for polychaetes, for Pu (III + IV) and Pu (V + VI) respectively. Depuration rates after sea water exposure followed a single exponential form ($\text{T}{}_{\mathrm{<mtext>b</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{= 50}\text{days}$) for clams, and for polychaetes at least a two component from with $\text{T}{}_{\mathrm{<mtext>b</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{= 1·3}\text{days}$ and 54 days. TF values for ²³⁷Pu bioaccumulation from sediments were very low, 6 × 10^?3 and 5 × 10^?2 for clams and polychaetes, respectively, after 20 days' exposure.Plotonium appears to be about 50% more bioavailable to the same species than americium as measured by laboratory experiments using a similar deep-sea sediment. Depuration experiments with clams after 40 days' exposure to labelled sediment indicated loss followed a single exponential form with a $\text{T}{}_{\mathrm{<mtext>b</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{= 24}\text{days}$. Significant differences in the behaviour of Pu introduced into the uptake and loss experiments in different oxidation states were not observed in general.     

Air-to-vegetation transfer rates of natural submicron aerosols

Submicron aerosol deposition to outdoor vegetation was evaluated by measuring vegetation and air concentrations of ²¹²Pb, ²¹⁴Pb, and ⁷Be attached to atmospheric aerosols. A biomass-normalized deposition velocity (V_D), with units of m³ kg^?1 s^?1, was used to compare species and isotopes with respect to air-to-vegetation transfer rates. For ²¹²Pb ($\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 10·64 h}$), higher night-time air concebtrations dominate deposition, while for ²¹⁴Pb ($\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 26·8}\text{min}$), deposition measurements over shorter time periods relative to changing atmospheric conditions were possible. Calculated V_D values were usually higher for ²¹⁴Pb, possibly reflecting wind-enhanced deposition during the afternoon period of sampling. Evergreen species, including pines, were not appreciably different from deciduous species. Most striking was the narrow range of results (factor of 6 for 34 ²¹²Pb measurements of 20 species). Beryllium-7 ($\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 53·3 d}$) was used to evaluate time-integrated deposition by sampling vegetation in California near the end of dry summers. Similar deposition rates were found for this isotope. The results of the study indicated that naturally radioactive atmospheric aerosols can be used to understand the dynamics of submicron aerosol deposition to ecosystems.     

Threshold and dose response estimation using the “filter model”

The “filter model” has been developed to explain the biologic effects of radiation and chemicals. We have examined nearly 300 sets of dose response data, of which 50 are presented here. Responses (induced by radiation and chemicals) which have been examined include in vitro survival studies on animal and plant tissues, induction of cellular aberrations and time to tumor or death. Similar data from in vivo studies has also been examined. All of the data appear to fit the model R = a lnD + b(lnD)² + c, where R is the response, a and b are parameters fitted by regression to a particular set of data, and c is the response at zero (or lowest) dose. By writing this model in exponential form, it can be seen that the response R results from multistage filtering (by net amounts a and b) of the initial dose, D. The threshold is obtained from this model as the point, $\text{D}\text{?}{}_{\mathrm{T}}$, at which the second derivative becomes zero. This is given by $\text{D}\text{?}{}_{\mathrm{T}}\text{=}\text{exp}\text{(1 ?}\text{a}\text{2b}\text{)}$ when a and b are oppositelt signed.     

Statistical assessment of subsampling procedures

As shown by the examples in this paper, the concentrations in subsamples are not necessarily independently and normally distributed despite vigorous grinding and mixing of the original sample. Studies of the statistical properties of subsample concentrations should test for deviations from independence and normality and, if deviations are found, should model the observed distribution. The tests include an analysis of variance to check for less variation among nearby subsamples than among widely spaced subsamples, as well as the computation of the probability plot correlation coefficient to check for nonnormality. These tests are illustrated with ${}^{239}\text{Pu}\text{+}{}^{240}\text{Pu}$ measurements on subsamples prepared for use as standard reference materials. These materials are used in quality assurance for environmental radioactivity measurements. The material consisting of Human Liver (SRM 4352) exhibits dependence, which may be due to inadequate mixing or to later handling that caused segregation. The material consisting of Human Lung (SRM 4351) and the material consisting of soil from Rocky Flats (SRM 4353) exhibit nonnormality due to the particulate nature of some plutonium-bearing fractions of the material. The lung measurements are modeled with the gamma distribution. The soil measurements are modeled with a combination of the normal distribution and a distribution that models the occurrence of outliers. The use of these models to describe the subsamples involves assessment of the contribution of the measurement error.     

Krypton-85 in the atmosphere 1950–1977: a data review

For over 20 years the radioactive noble gas ⁸⁵Kr, the product of nuclear industry, has been released to the environment mainly from nuclear fuel reprocessing plants. Owing to its relatively long half-life $\text{T(}\text{1}\text{2}\text{= 10.76}\text{y}\text{)}$ and the absence of other appreciable sinks, a cumulative buildup of ⁸⁵Kr in the atmosphere is observed. The mean ⁸⁵Kr surface air activity in the northern hemisphere has increased from about 20 dpm/mmol Kr in 1950 to about 750 dpm/mmol Kr in 1977. In recent years, a substantial slow-down of the ⁸⁵Kr emission rate to the atmosphere has been observed. The published data indicate rather good mixing of ⁸⁵Kr in the northern hemisphere, but a gradient is observed in the southern hemisphere due to the fact that all nuclear fuel reprocessing plants are situated in the northern hemisphere and due to poor mixing of the atmosphere in the meridional direction.This paper summarizes nearly all of the data on ⁸⁵Kr activity in the atmosphere published up to the middle of 1978. The spatio-temporal distribution of ⁸⁵Kr atmospheric activity is discussed. Some forecasts of future ⁸⁵Kr concentration in the atmosphere and its possible ecological consequences are also presented.     

137Cs in marine samples from the Brazilian southeastern coastal region

The present work presents the results of ¹³⁷Cs concentration in seawater, fish and sediments samples collect in 11 sampling points, crossing the Brazilian Southeastern coastal region, from Vitória (ES) to Santos (SP), on a routine basis from 1997 to 2002. This monitoring program was carried out by the Instituto de Radioproteção e Dosimetria (IRD/CNEN/MCT), in cooperation with the Instituto de Estudos do Mar Almirante Paulo Moreira (IEAPM/Brazilian Navy), aiming at determining artificial radionuclides in marine samples. Additionally to the ¹³⁷Cs results, ⁹⁰Sr concentrations in fish samples from 1998 to 2002 are also reported.The ¹³⁷Cs in seawater follows a lognormal distribution, with a geometric mean of 1.8 Bq m^-3 and a geometric standard deviation of 1.4 (n=54), decay corrected to June/2002. For ¹³⁷Cs levels in fish samples a geometric mean of 0.19 Bq kg⁻¹ and a geometric standard deviation of 2.9 (n=39), decay corrected to June/2002, with a range of 0.03 to 1.7 Bq kg⁻¹, were obtained. Based on the ¹³⁷Cs mean concentration in fish as well as in seawater, a transfer factor of 1 × 10² was calculated, which is quite in agreement with the recommended value found in the Safety Report Serie 19.     

Indoor radon levels in Greek schools

Radon and gamma dose rate measurements were performed in 512 schools in 8 of the 13 regions of Greece. The distribution of radon concentration was well described by a lognormal distribution. Most (86%) of the radon concentrations were between 60 and 250 Bq m⁻³ with a most probable value of 135 Bq m⁻³. The arithmetic and geometric means of the radon concentration are 149 Bq m⁻³ and 126 Bq m⁻³ respectively. The maximum measured radon gas concentration was 958 Bq m⁻³. As expected, no correlation between radon gas concentration and indoor gamma dose rate was observed. However, if only mean values for each region are considered, a linear correlation between radon gas concentration and gamma dose rate is apparent. Despite the fact that the results of radon concentration in schools cannot be applied directly for the estimation of radon concentration in homes, the results of the present survey indicate that it is desirable to perform an extended survey of indoor radon in homes for at least one region in Northern Greece.     

Total fluoride in Guangdong soil profiles, China: spatial distribution and vertical variation

A total of 260 soil profiles were reported to investigate the fluoride distribution and vertical variation in Guangdong province. The soil fluoride contents followed an approximately lognormal distribution. Although the soil fluoride geometric mean concentration of 407 mg/kg is lower than that of China, its content varied from 87 to 2860 mg/kg. An upper baseline concentration of 688 mg/kg was estimated for surface soils. In A-, B-, and C-horizon soil fluoride spatial distribution presented similar patterns that high fluoride concentration mainly located in limestone, purple shale, and sandshale areas, indicated that soil fluoride spatial distribution was primarily dependent on the regional bedrock properties rather than anthropogenic inputs. From A- to C- horizon soil fluoride geometric mean concentration had an increasing tendency of 407, 448, and 465 mg/kg. This vertical variation was the result of the intensive eluviation under the subtropical hydrothermal condition, and had closely related with soil properties, such as lower organic matters and clay content variations. Moreover, the soil degradation and erosion was also an important pathway of soil fluoride movement, as a result the soil fluoride exported into surface and groundwaters would reach about 4.1x10(4) t year-1 in the study area.     

Variation among chlorine concentration ratios for native and agronomic plants

Variation among plant/soil concentration ratios (CRs) for important radionuclides requires attention because it is a major source of uncertainty in nuclear environmental safety assessments. For agronomic plants, variation among plant species is easy to deal with because there are relatively few species. In natural settings, there are vastly more species and the question becomes how to develop representative statistical distributions of CRs. Chlorine (Cl) is a good element with which to address this problem, because ³⁶Cl is a key radionuclide in nuclear waste disposal and yet stable Cl is easily measured in the environment. We measured CRs (dry weight basis) for Cl among edible parts of agronomic plants at one site, and found a geometric mean (GM) of 10, a geometric standard deviation (GSD) of 1.9 and a range of 5–66. When the GM was weighted by the relative contributions of the various plants to the human diet, it rose to 16. Among native plants at five sites, each site representative of a specific environment, the GMs were 4.0–13 and the GSDs were 2.9–6.2. The CRs for individual species ranged from 0.8 to 170. However, when weighted by relative contributions of the plants to selected animal diets, the GMs were as high as 50. The conclusions are that: the variation in CR for agronomic plants is a subset of the variation among native or all plants, variation among species (the GSD) can be sixfold, and variation among species is large enough that typical diets of specific animals could expose them to several-fold higher amounts of Cl (or ³⁶Cl) than expected from generic CR values.     

Cesium isotope ratios as indicators of nuclear power plant operations

There are multiple paths by which radioactive cesium can reach the effluent from reactor operations. The radioactive ¹³⁵Cs/¹³⁷Cs ratios are controlled by these paths. In an effort to better understand the origin of this radiation, these ¹³⁵Cs/¹³⁷Cs ratios in effluents from three power reactor sites have been measured in offsite samples. These ratios are different from global fallout by up to six fold and as such cannot have a significant component from this source. A cesium ratio for a sample collected outside of the plant boundary provides integration over the operating life of the reactor. A sample collected inside the plant at any given time can be much different from this lifetime ratio. The measured cesium ratios vary significantly for the three reactors and indicate that the multiple paths have widely varying levels of contributions. There are too many ways these isotopes can fractionate to be useful for quantitative evaluations of operating parameters in an offsite sample, although it may be possible to obtain limited qualitative information for an onsite sample.     

Concentration ratios for small mammals collected from the exposed sediments of a 137Cs contaminated reservoir

(137)Cs concentration ratios were computed for small mammals collected from the dried sediments of a partially drained, contaminated reservoir. Soil (137)Cs activity concentrations were heterogeneous on small and large spatial scales and had a geometric mean of 253 (range 23-2110) Bq/kg dry weight. Mean (137)Cs activity concentrations in composite cotton rat Sigmodon hispidus and cotton mouse Peromyscus gossypinus samples averaged 2480 (range 556-6670) and 471 (range 96-1000) Bq/kg whole body dry weight, respectively. About 50% of the variance in cotton rat tissue (137)Cs activity was explained by variation in soil (137)Cs activity. Soil-to-animal dry weight concentration ratios averaged 6.0 for cotton rats and 1.2 for cotton mice and were generally similar to (137)Cs concentration ratios for herbivorous, homeothermic animals from other contaminated ecosystems. In the RESRAD-BIOTA dose model, the default wet-weight concentration ratio for (137)Cs in terrestrial animals is 110 resulting in an estimate of internal and external radiation doses to terrestrial biota that is 44 times more than the dose calculated with the actual measured wet-weight concentration ratio for cotton rats (1.6). These results show that site-specific concentration ratios can significantly affect the estimation of dose.