Measures of Stochastic Responses

2 Measures of stochastic responses. The primary measure of stochastic responses used in radiation protection and radiation risk assessment by ICRP and NCRP has been fatalities (i.e., fatal cancers and severe hereditary effects). Fatalities have been emphasized essentially because this was the only health-effect endpoint for which data generally were available, both for study populations 

Until recently, fatalities (especially latent cancer fatalities) was the only measure of stochastic response used in radiation protection and assessments of radiation risks in general terms (ICRP, 1977 NCRP, 1987a). No consideration was given to radiation-induced non-fatal stochastic responses or to the relative severity of different types of fatal responses (e.g., the expected length of life lost per fatality). 

In its current recommendations on radiation protection, ICRP (1991) developed a quantity called total detriment to describe stochastic responses (see also NCRP, 1993a). As summarized below, total detriment includes not only the probability of a fatal cancer or severe hereditary effect but also a contribution from nonfatal cancers and an additional adjustment that accounts for differences in expected length of life lost per fatal response in different organs or tissues. The term detriment, rather than response or risk, is used to describe this quantity because (1) the contribution from nonfatal cancers is not simply the probability of a nonfatal cancer, (2) severe hereditary responses are not experienced by exposed individuals but by their progeny, and (3) the adjustment for expected length of life lost per fatal response does not represent a probability of a fatality or incidence. 

ICRP (1991) has acknowledged that the modifications of the probability of a fatal response are necessarily judgmental and somewhat arbitrary, particularly the weight to be given to nonfatal cancers relative to fatal responses in assessing total detriment. Nonetheless, the following approach to assessing total detriment from radiation exposure for purposes of radiation protection was developed. 

In estimating the total detriment due to stochastic responses in any organ as described above, the probability coefficient for fatal cancers (F) or severe hereditary responses is based on data in humans and animals described in Section 3.2.2.2, and the lethality fraction (k) and relative length of life lost per fatal response (.II) are based on data on responses from all causes in various national populations. The values of F, k, and t/l for different organs, as well as the probability coefficient for severe hereditary responses, assumed by ICRP (1991) and the resulting estimates of total detriment, F((/T)(2 - k ), are summarized in Table 3.2. The two entries for Total in the last row represent the probability coefficient for 

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Second, the primary measure of stochastic response used in radiation protection and in most radiation risk assessments has been fatalities. In contrast, the measure of response for chemicals causing... 

The primary measure of stochastic responses for radionuclides used in radiation protection has been fatalities, whereas incidence is the universal measure of stochastic responses for hazardous chemicals. 

Incidence. In the first option, the common measure of stochastic response from exposure to radionuclides and hazardous chemicals would be incidence, without any modifications to account for such factors as differences in lethality fractions for responses in different organs or tissues or expected years of life lost per fatality. Such modifications are intended to represent differences in the severity of different stochastic responses. 

However, this option presents some difficulties for radionuclides, because studies of radiation effects in human populations have focused on cancer fatalities as the measure of response and probability coefficients for radiation-induced cancer incidence have not yet been developed by ICRP or NCRP for use in radiation protection. Probabilities of cancer incidence in the Japanese atomic-bomb survivors have been obtained in recent studies (see Section 3.2.3.2), but probability coefficients for cancer incidence appropriate for use in radiation protection would need to take into account available data on cancer incidence rates from all causes in human populations of concern, which may not be as reliable as data on cancer fatalities. Thus, in effect, if incidence were used as the measure of stochastic response for radionuclides, the most technically defensible database on radiation effects in human populations available at the present time (the data on fatalities in the Japanese atomic-bomb survivors) would be given less weight in classifying waste. 

ICRP s total detriment. In the third option, the common measure of stochastic response from exposure to radionuclides and... 

Incidence is the common measure of response for all substances that cause a deterministic effect, including radionuclides, used in routine health protection, and there is no evident reason to change this. As indicated by the discussions in the previous sections, arguments can be advanced in favor of using either incidence or fatalities as the common measure of stochastic response. Use of ICRP s total detriment appears to be disadvantageous, compared with either incidence or fatalities, and is not considered further. 

However, given the current state of knowledge and methods of dose-response assessment for substances that cause stochastic responses, there appear to be important technical and institutional impediments to the use of either incidence or fatalities exclusively. Data on radiation-induced cancer incidence and chemical-induced cancer fatalities for use at the low doses and dose rates relevant to health protection are not readily available, and current regulatory guidance calls for calculation of cancer incidence for hazardous chemicals. Since use of a common measure of response for all substances that cause stochastic responses may not be practical in the near term, both measures (fatalities for radionuclides and incidence for hazardous chemicals) could be used in the interest of expediency. The primary advantage of this approach is that the measures of stochastic response for radionuclides and hazardous chemicals would be based on the best available information from studies in humans and animals, and it would involve the fewest subjective modifying factors. This approach also would be the easiest to implement. 

Primary measure of stochastic response cancer fatalities for radionuclides but cancer incidence for hazardous chemicals that induce stochastic effects and... 

Given the different approaches to dose-response assessment and the different measures of response normally used for radionuclides and chemicals that cause stochastic effects, estimates of responses from exposure to the two types of substances clearly are not equivalent, and the correspondence of the estimated frequency of responses to the frequency that might actually be experienced differs substantially. Specifically, if the results of experiments indicating chemical-induced stochastic responses in animals are assumed to be indicative of stochastic responses in humans, estimates of responses for chemicals could be considerably more conservative (pessimistic) than estimates for radionuclides. This difference is primarily the result of... 

The sinc fiinction describes the best possible case, with often a much stronger frequency dependence of power output delivered at the probe-head. (It should be noted here that other excitation schemes are possible such as adiabatic passage [9] and stochastic excitation [fO] but these are only infrequently applied.) The excitation/recording of the NMR signal is further complicated as the pulse is then fed into the probe circuit which itself has a frequency response. As a result, a broad line will not only experience non-unifonn irradiation but also the intensity detected per spin at different frequency offsets will depend on this probe response, which depends on the quality factor (0. The quality factor is a measure of the sharpness of the resonance of the probe circuit and one definition is the resonance frequency/haltwidth of the resonance response of the circuit (also = a L/R where L is the inductance and R is the probe resistance). Flence, the width of the frequency response decreases as Q increases so that, typically, for a 2 of 100, the haltwidth of the frequency response at 100 MFIz is about 1 MFIz. Flence, direct FT-piilse observation of broad spectral lines becomes impractical with pulse teclmiques for linewidths greater than 200 kFIz. For a great majority of... 

A single experiment consists of the measurement of each of the m response variables for a given set of values of the n independent variables. For each experiment, the measured output vector which can be viewed as a random variable is comprised of the deterministic part calculated by the model (Equation 2.1) and the stochastic part represented by the error term, i.e.,... 

The risk index for any hazardous substance in Equation 1.1 or 1.2 (see Section 1.5.1) is calculated based on assumed exposure scenarios for hypothetical inadvertent intruders at near-surface waste disposal sites and a specified negligible risk or dose in the case of exempt waste or acceptable (barely tolerable) risk or dose in the case of low-hazard waste. Calculation of the risk index also requires consideration of the appropriate measure of risk (health-effect endpoint), especially for carcinogens, and the appropriate approaches to estimating the probability of a stochastic response per unit dose for carcinogens and the thresholds for deterministic responses for noncarcinogens. Given a calculated risk index for each hazardous substance in a particular waste, the waste then would be classified using Equation 1.3. 

UCL takes into account measurement uncertainty in the study used to estimate the dose-response relationship, such as the statistical uncertainty in the number of tumors at each administered dose, but it does not take into account other uncertainties, such as the relevance of animal data to humans. It is important to emphasize that UCL gives an indication of how well the model fits the data at the high doses where data are available, but it does not indicate how well the model reflects the true response at low doses. The reason for this is that the bounding procedure used is highly conservative. Use of UCL has become a routine practice in dose-response assessments for chemicals that cause stochastic effects even though a best estimate (MLE) also is available (Crump, 1996 Crump et al., 1976). Occasionally, EPA will use MLE of the dose-response relationship obtained from the model if human epidemiologic data, rather than animal data, are used to estimate risks at low doses. MLEs have been used nearly universally in estimating stochastic responses due to radiation exposure. 

This option does not appear to be advantageous for either radionuclides or chemicals that cause stochastic responses. In radiation protection, total detriment is used mainly to develop the tissue weighting factors in the effective dose (see Section 3.2.2.3.3), but ICRP and NCRP have continued to emphasize fatal responses as the primary health effect of concern in radiation protection and radiation risk assessments. Since total detriment is based on an assumption that fatalities are the primary health effect of concern, the same difficulties described in the previous section would occur if this measure of response were used for chemicals that induce stochastic responses. Other disadvantages of using total detriment include that detriment is not a health-effect endpoint experienced by an exposed individual and the approach to weighting nonfatal responses in relation to fatalities is somewhat arbitrary. Furthermore, total detriment is not as simple and straightforward to understand as either incidence or fatalities. 

The use of MLEs of probability coefficients for radionuclides but UCLs for chemicals that induce stochastic responses is the most important issue that would need to be resolved to achieve a consistent approach to estimating risks for the purpose of waste classification. For some chemicals, the difference between MLE and UCL can be a factor of 100 or more. The difference between using fatalities or incidence as the measure of response is unlikely to be important. Use of the linearized, multistage model to extrapolate the dose-response relationship for chemicals that induce stochastic effects, as recommended by NCRP, should be reasonably consistent with estimates of the dose-response relationship for radionuclides, and this model has been used widely in estimating probability coefficients in chemical risk assessments. The difference in the number of organs or tissues that are taken into account, although it cannot be reconciled at the present time, should be unimportant. 

Approaches to Estimating Dose-Response Relationships for Substances That Cause Deterministic Responses. Most of the factors that must be considered in developing reasonably consistent approaches to estimating risk for radionuclides and chemicals that induce stochastic responses discussed in the previous section do not apply to substances that induce deterministic responses. For purposes of health protection, incidence generally is the appropriate measure of response for substances that cause deterministic responses. Furthermore, an accounting of deterministic responses... 

The most common way to deal with the problem of stochastic drift is to modulate the exposure of the analyte to the sensor and to synchronously detect the sensor response. When the analyte is off (i.e., the sensor is zeroed ), the sensor signal can be recorded as the baseline value. Drift-corrected signals can be obtained by subtracting the baseline signal from that recorded when the analyte is on. If the frequency of the on/off modulation is much higher than the frequency of the baseline drift, then this scheme results in dramatically improved stability in the measured data. An implicit requirement in this measurement strategy is that the response kinetics of the sensitive film/analyte combination be sufficiently fast to allow on/off modulation at the desired frequency. 

This part provides a conceptual understanding of stochastic, bias, and fitting errors m frequency-domain measurements. A major advantage of frequency-domain measurements is that real and imaginary parts of the response must be internally consistent. The expression of this consistency takes different forms that are known collectively as the Kramers-Kronig relations. The Kramers-Kronig relations and their application to spectroscopy measurements are described. Measurement models, used to assess the error structure, are described and compared with process models used to extract physical properties. 

Most work on the development of dynamic process models has been empirical this work is usually referred to as process identification. As mentioned earlier, two classes of empirical identification techniques are available one uses deterministic (step, pulse, etc.) functions, the other stochastic (random) identification functions. With either technique, the process is perturbed and the resulting variations of the response are measured. The relationship between the perturbing variable and the response is expressed as a transfer function. This function is the process model. Empirical identification of process models by the deterministic method has been reported by various workers [55-58]. A drawback of this method is the difficulty in obtaining a measurable response while restricting the process to a linear response (small perturbation). If the perturbation is large, the process response will be nonlinear and the representations of the process with a linear process model will be inaccurate. 

A first-order stochastic finite element method for reliability analysis of complex structures is described. The method is based on the first-order reliability approach and is applicable to any limit-state criterion that is prescribed in terms of random variables. Measures of reliability sensitivity with respect to any set of parameters are easily computed. The main effort for finite element implementation is in computing the gradient of response variables in terms of basic load, material property or geometry variables. Such an implementation for linear elastic structures under static loads is described. Two alternate methods of random field discretization are investigated and their respective... 

Summary Quasistationary and nonstationary random vibrations of elasto-plastic structures are treated using a time-invariant linear elastic system with effectively updated loading. Stochastic response measures of the plastic drift process are given in nondimensional form. Design charts are presented for the case of a Kanai-Taiimi re-... 

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