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A two-stage interval-stochastic programming model for waste management under uncertainty.

This study introduces a two-stage interval-stochastic programming (TISP) model for the planning of solid-waste management systems under uncertainty. The model is derived by incorporating the concept of two-stage stochastic programming within an interval-parameter optimization framework. The approach has the advantage that policy determined by the authorities, and uncertain information expressed as intervals and probability distributions, can be effectively communicated into the optimization processes and resulting solutions. In the modeling formulation, penalties are imposed when policies expressed as allowable waste-loading levels are violated. In its solution algorithm, the TISP model is converted into two deterministic submodels, which correspond to the lower and upper bounds for the desired objective-function value. Interval solutions, which are stable in the given decision space with associated levels of system-failure risk, can then be obtained by solving the two submodels sequentially. Two special characteristics of the proposed approach make it unique compared with other optimization techniques that deal with uncertainties. First, the TISP model provides a linkage to predefined policies determined by authorities that have to be respected when a modeling effort is undertaken; second, it furnishes the reflection of uncertainties presented as both probabilities and intervals. The developed model is applied to a hypothetical case study of regional solid-waste management. The results indicate that reasonable solutions have been generated. They provide desired waste-flow patterns with minimized system costs and maximized system feasibility. The solutions present as stable interval solutions with different risk levels in violating the waste-loading criterion and can be used for generating decision alternatives.

Environment↗

Third birth intentions and uncertainty in Canada.

Using data from the 1995 Canadian General Society Survey (GSS-95), we study the intention to have a third child among a sample of women and men who have already had two children (N = 505). Our results show that 15 per cent of the respondents intend to have a third child. Nearly 20 per cent of the respondents are uncertain about their fertility intentions. We found that the same factors that predict intentions also predict uncertainty, and that the effects of these predictors are remarkably similar. In particular, intentions and uncertainty generally decline with age, but increase with regular church attendance, remarriage, and being Catholic. Unlike earlier studies, we found that the sex of previous children has virtually no impact on third-birth intentions or uncertainty.

Adolescent↗

Quantifying uncertainty: calculating interval estimates using quality control results.

EPA's Great Lakes National Program Office (GLNPO) is leading one of the most extensive studies of a lake ecosystem ever undertaken. The Lake Michigan Mass Balance Study (LMMB Study) is a coordinated effort among state, federal, and academic scientists to monitor tributary and atmospheric pollutant loads, develop source inventories of toxic substances, and evaluate the fate and effects of these pollutants in Lake Michigan. A key objective of the LMMB Study is to construct a mass balance model for several important contaminants in the environment: PCBs, atrazine, mercury, and trans-nonachlor. The mathematical mass balance models will provide a state-of-the-art tool for evaluating management scenarios and options for control of toxics in Lake Michigan. At the outset of the LMMB Study, managers recognized that the data gathered and the model developed from the study would be used extensively by data users responsible for making environmental, economic, and policy decisions. Environmental measurements are never true values and always contain some level of uncertainty. Decision makers, therefore, must recognize and be sufficiently comfortable with the uncertainty associated with data on which their decisions are based. The quality of data gathered in the LMMB was defined, controlled, and assessed through a variety of quality assurance (QA) activities, including QA program planning, development of QA project plans, implementation of a QA workgroup, training, data verification, and implementation of a standardized data reporting format. As part of this QA program, GLNPO has been developing quantitative assessments that define data quality at the data set level. GLNPO also is developing approaches to derive estimated concentration ranges (interval estimates) for specific field sample results (single study results) based on uncertainty. The interval estimates must be used with consideration to their derivation and the types of variability that are and are not included in the interval.

Confidence Intervals↗

Uncertainty analysis of the estimated ingestion rates used to derive the methylmercury reference dose.

The U.S. EPA's Reference Dose (RfD) for methylmercury (MeHg) uses a simple one-compartment toxicokinetic model to estimate ingestion doses in mg/kg-day from measured concentrations of mercury in hair. The model includes a number of input variables for which point estimates are made. Uncertainty in the inputs is addressed by the use of a 3-fold uncertainty factor. There are, however, published ranges for each variable which are used to develop distributions for each of the inputs. Monte Carlo output of the model is generated. The 90% confidence interval spans a 3-fold to 5-fold range of ingestion doses for any given concentration of mercury in hair. The hair:blood mercury concentration ratio contributes most to the variance of the output. The results indicate that the uncertainty factor of three is appropriate.

Dose-Response Relationship, Drug↗

Uncertainties in dosemeter intercomparison techniques.

The results of 180 intercomparisons of field dosemeters with an NPL secondary-standard exposure meter (type 2560, with a type 2561 chamber) have been analyzed in order to study variations in readings when ionization chambers are interchanged during the comparison process. It is suggested that the percentage standard error of the mean of the combined series of chamber intercomparisons be used to set a target uncertainty (0.3%), action level (0.5%) and limit of acceptability (1.0%). The target uncertainty is consistent with IAEA estimates of uncertainty for this part of the calibration chain. It is shown that if the calibration procedure is repeated, the percentage difference between the geometric means calculated from each calibration (i.e. a single interchange of chambers) may be as high as +/- 1%. This reinforces the need for at least one repetition of the intercomparison procedure.

Biophysical Phenomena↗

An adaptive control algorithm for optimization of intensity modulated radiotherapy considering uncertainties in beam profiles, patient set-up and internal organ motion.

A new general beam optimization algorithm for inverse treatment planning is presented. It utilizes a new formulation of the probability to achieve complication-free tumour control. The new formulation explicitly describes the dependence of the treatment outcome on the incident fluence distribution, the patient geometry, the radiobiological properties of the patient and the fractionation schedule. In order to account for both measured and non-measured positioning uncertainties, the algorithm is based on a combination of dynamic and stochastic optimization techniques. Because of the difficulty in measuring all aspects of the intra- and interfractional variations in the patient geometry, such as internal organ displacements and deformations, these uncertainties are primarily accounted for in the treatment planning process by intensity modulation using stochastic optimization. The information about the deviations from the nominal fluence profiles and the nominal position of the patient relative to the beam that is obtained by portal imaging during treatment delivery, is used in a feedback loop to automatically adjust the profiles and the location of the patient for all subsequent treatments. Based on the treatment delivered in previous fractions, the algorithm furnishes optimal corrections for the remaining dose delivery both with regard to the fluence profile and its position relative to the patient. By dynamically refining the beam configuration from fraction to fraction, the algorithm generates an optimal sequence of treatments that very effectively reduces the influence of systematic and random set-up uncertainties to minimize and almost eliminate their overall effect on the treatment. Computer simulations have shown that the present algorithm leads to a significant increase in the probability of uncomplicated tumour control compared with the simple classical approach of adding fixed set-up margins to the internal target volume.

Algorithms↗

The effect of statistical uncertainty on inverse treatment planning based on Monte Carlo dose calculation.

The effect of the statistical uncertainty, or noise, in inverse treatment planning for intensity modulated radiotherapy (IMRT) based on Monte Carlo dose calculation was studied. Sets of Monte Carlo beamlets were calculated to give uncertainties at Dmax ranging from 0.2% to 4% for a lung tumour plan. The weights of these beamlets were optimized using a previously described procedure based on a simulated annealing optimization algorithm. Several different objective functions were used. It was determined that the use of Monte Carlo dose calculation in inverse treatment planning introduces two errors in the calculated plan. In addition to the statistical error due to the statistical uncertainty of the Monte Carlo calculation, a noise convergence error also appears. For the statistical error it was determined that apparently successfully optimized plans with a noisy dose calculation (3% 1sigma at Dmax), which satisfied the required uniformity of the dose within the tumour, showed as much as 7% underdose when recalculated with a noise-free dose calculation. The statistical error is larger towards the tumour and is only weakly dependent on the choice of objective function. The noise convergence error appears because the optimum weights are determined using a noisy calculation, which is different from the optimum weights determined for a noise-free calculation. Unlike the statistical error, the noise convergence error is generally larger outside the tumour, is case dependent and strongly depends on the required objectives.

Algorithms↗

Design of adaptive treatment margins for non-negligible measurement uncertainty: application to ultrasound-guided prostate radiation therapy.

Daily imaging during the course of a fractionated radiotherapy treatment has the potential for frequent intervention and therefore effective adaptation of the treatment to the individual patient. The treatment information gained from such images can be analysed and updated daily to obtain a set of patient individualized parameters. However, in many situations, the uncertainty with which these parameters are estimated cannot be neglected. In this work this methodology is applied to the adaptive estimation of setup errors, the derivation of a daily optimal pre-treatment correction strategy, and the daily update of the treatment margins after application of these corrections. For this purpose a dataset of 19 prostate cancer patients was analysed retrospectively. The position of the prostate was measured daily with an optically guided 3D ultrasound localization system. The measurement uncertainty of this system is approximately 2 mm. The algorithm finds the most likely position of the target maximizing an a posteriori probability given the set of measurements. These estimates are used for the optimal corrections applied to the target volume. The results show that the application of the optimal correction strategy allows a reduction in the treatment margins in a systematic way with increasing progression of the treatment. This is not the case using corrections based only on the measured values that do not take the measurement uncertainty into account.

Algorithms↗

Treatment simulation approaches for the estimation of the distributions of treatment quality parameters generated by geometrical uncertainties.

Geometric uncertainties arise during treatment planning and treatment and mean that dose-dependent parameters such as EUD are random variables with a patient specific probability distribution. Treatment planning with highly conformal treatment techniques such as intensity modulated radiation therapy requires new evaluation tools which allow us to estimate this influence of geometrical uncertainties on the probable treatment dose for a planned dose distribution. Monte Carlo simulations of treatment courses with recalculation of the dose according to the daily geometric errors are a gold standard for such an evaluation. Distribution histograms which show the relative frequency of a treatment quality parameter in the treatment simulations can be used to evaluate the potential risks and chances of a planned dose distribution. As treatment simulations with dose recalculation are very time consuming for sufficient statistical accuracy, it is proposed to do treatment simulations in the dose parameter space where the result is mainly determined by the systematic and random component of the geometrical uncertainties. Comparison of the parameter space simulation method with the gold standard for prostate cases and a head and neck case shows good agreement as long as the number of fractions is high enough and the influence of tissue inhomogeneities and surface curvature on the dose is small.

Body Burden↗

Effect of statistical uncertainties on Monte Carlo treatment planning.

This paper reviews the effect of statistical uncertainties on radiotherapy treatment planning using Monte Carlo simulations. We discuss issues related to the statistical analysis of Monte Carlo dose calculations for realistic clinical beams using various variance reduction or time saving techniques. We discuss the effect of statistical uncertainties on dose prescription and monitor unit calculation for conventional treatment and intensity-modulated radiotherapy (IMRT) based on Monte Carlo simulations. We show the effect of statistical uncertainties on beamlet dose calculation and plan optimization for IMRT and other advanced treatment techniques such as modulated electron radiotherapy (MERT). We provide practical guidelines for the clinical implementation of Monte Carlo treatment planning and show realistic examples of Monte Carlo based IMRT and MERT plans.

Computer Simulation↗

Bias and uncertainty in heart rate variability spectral indices due to the finite ECG sampling frequency.

Spectral analysis of the heart rate variability is becoming a usual tool as a marker of the autonomic nervous system. The final output of the spectral analysis is a set of indices that are always estimators due to technical limitations. In this work, the bias and the uncertainty in the VLF, LF, HF and LF/HF indices due to the finite sampling frequency of the ECG are analysed. The results indicate that for low sampling frequency (125 Hz), the bias and uncertainty in the HF and LF/HF indices can blur the results of the analysis, especially if the RR time series has low variability. The HF index is overestimated and, accordingly, the LF/HF index is underestimated. Then, results from RR time series with low sampling frequency must be used with care. The uncertainty of the spectral indices is proportional to the inverse of the sampling frequency and the bias is proportional to the inverse of the square sampling frequency.

Electrocardiography↗

Allowing for uncertainty in economic evaluations: qualitative sensitivity analysis.

Sensitivity analysis allows analysts to explore the impact of uncertainty on their findings. It is an important part of any economic evaluation, and a lack of analysis is evidence of a poor quality study. Sensitivity analysis helps the analyst evaluate the reliability of conclusions for the context of the evaluation and can also facilitate consideration of the generalizability of results to other settings. The variety of one and multi-way sensitivity analyses offer simple and complementary approaches to evaluating the impact of uncertainty on the results and conclusions of economic evaluations. The paper begins with a brief discussion of the types of uncertainty that can arise in economic evaluation, and follows with suggestions of how to plan a justified sensitivity analysis. A number of specific techniques are worked through with examples, followed by a discussion of when it is best to use them. The main weakness associated with sensitivity analysis is the control that the analyst retains over three parts of the process: the choice of which variables to vary and which to treat as known or fixed; the amount of variation around the base value of the parameter that is considered clinically meaningful or policy-relevant; and the determination of what constitutes a sensitive or robust finding. It is therefore essential that the approach of the analyst is clear and justified. It is likely that the future will see further developments in the approaches and training of statistical analysis. But in the meantime, an increase in the number of evaluators undertaking a wider range of sensitivity analysis would improve the quality of evidence for, and outcomes of, decision-making.

Costs and Cost Analysis↗

Brief report: illness uncertainty and dispositional self-focus in adolescents and young adults with childhood-onset asthma.

OBJECTIVE: To investigate differences in self-focused attention between college students with childhood-onset asthma and a group of healthy controls and to determine whether self-focused attention mediates the relationship between illness uncertainty and psychological distress among individuals with asthma. METHODS: Forty-two adolescent and young adult participants with childhood-onset asthma and 40 age- and gender-matched healthy participants completed measures of self-focused attention, perceived illness uncertainty, psychological distress, and health status. RESULTS: Adolescents and young adults with childhood-onset asthma evidenced an increased tendency to engage in private self-focus compared to age- and gender-matched peers without a chronic illness history. Self-focused attention also mediated the relationship between perceived illness uncertainty and psychological distress among those with asthma. CONCLUSIONS: The need for self-monitoring in asthma management may result in an increased propensity to self-focus, which may result in heightened levels of psychological distress.

Adolescent↗

Uncertainties on the committed equivalent dose to the thyroid as a function of age for different iodine isotopes.

This study compares uncertainties of equivalent doses after internal contamination by 125I, 129I or 131I. Uncertainties were calculated using reported distributions of physiological parameters and Monte Carlo simulation. In adults, uncertainties increase from 131I to 125I and 129I with 1% of the population receiving 3.9, 4.0 and 7.2 times the median dose for the respective isotopes. In newborns, these values were 7.5, 12.3 and 19.0 for 131I, 125I and 129I respectively. The ratio of the beta dose delivered to the epithelium versus a homogeneous distributed dose was estimated for different iodine concentrations in colloid, epithelium and interstitium. In adults, for 131I, about 40% of the beta dose was delivered to the epithelial cells, whereas this fraction varied depending on the concentration for 125I and 129I, i.e. 20-30% at a relative epithelial concentration of 20% and 7-14% at a concentration of 3%. Small variations were observed depending on age.

Absorption↗

A survey on uncertainty in bioassay measurements carried out within the OMINEX project.

One of the topics covered by the OMINEX (Optimisation of Monitoring for Internal Exposure) project was to look at the bioassay measurements performed in the European laboratories. Questionnaires on bioassay measurements by alpha spectrometry or inductively coupled plasma-mass spectrometry (ICP-MS) were sent to European laboratories. The main objective was to collect information on analytical procedures and on the uncertainties associated with bioassay results. Alpha spectrometry is the technique most often used for the determination of alpha emitters, such as actinides in biological samples. ICP-MS is not used much as yet for routine measurements of actinides in biological samples, but is very sensitive for measurements of long-lived radionuclides. The different parameters influencing the uncertainties on the results and the minimum detectable amount have been investigated. Optimum conditions for achieving low result uncertainties and high sensitivity are given for alpha spectrometry and ICP-MS.

Alpha Particles↗

Uncertainty analysis in the task of individual monitoring data.

Assessment of internal doses is an essential component of individual monitoring programmes for workers and consists of two stages: individual monitoring measurements and interpretation of the monitoring data in terms of annual intake and/or annual internal dose. The overall uncertainty in assessed dose is a combination of the uncertainties in these stages. An algorithm and a computer code were developed for estimating the uncertainty in the assessment of internal dose in the task of individual monitoring data interpretation. Two main influencing factors are analysed in this paper: the unknown time of the exposure and variability of bioassay measurements. The aim of this analysis is to show that the algorithm is applicable in designing an individual monitoring programme for workers so as to guarantee that the individual dose calculated from individual monitoring measurements does not exceed a required limit with a certain confidence probability.

Algorithms↗

Uncertainties in thyroid dose reconstruction after Chernobyl.

The most significant impact of the Chernobyl accident of 26 April 1986 is the increased incidence of thyroid cancer among Belarusians, Russians and Ukrainians who were exposed as children to radioiodines in fallout resulting from atmospheric releases. The US National Cancer Institute (NCI), in cooperation with the ministries of health of Belarus and Ukraine, is involved in epidemiological studies of thyroid diseases related to the accident. Individual thyroid doses, as well as uncertainties, have been estimated for the members of the cohort studies (approximately 13,000 Ukrainians and 12,000 Belarusians). The cohort subjects, who were selected from the large group of children whose thyroids were monitored for gamma radiation within a few weeks of the accident, provided personal information on their residence history and dietary habits during interviews. Thyroid dose estimates range from 1 mGy to more than 20 Gy. The uncertainties are found to be approximately log-normally distributed, with geometric standard deviations ranging from 1.6 to 5.0. The medians of the geometric standard deviations are 1.7 for the Ukrainian subjects and 2.1 for the Belarusian subjects. The major sources of uncertainty in the thyroid dose estimates are found to be those related to the thyroid mass of the subject and to the estimation of the thyroidal content of 131I at the time of thyroid monitoring.

Adolescent↗

Calibration and evaluation of uncertainty in the measurement of environmental electromagnetic fields.

After a brief description of the reference systems for the calibration of the electromagnetic field meters set up at IEN and the Ivrea Department of ARPA, the procedures for the evaluation of the measurement uncertainty are discussed, with reference to the problem of identifying and quantifying the different uncertainty components. which are due both to the field meter characteristics and to the measurement procedure and conditions. The problem of how to compare a measurement result, which consists of the measurement value and its associated uncertainty, with a limit fixed by the standards is also faced.

Calibration↗