Random Error Components Research Articles

Modeling airport choice for a multi-airport area using a random parameter logit model

Recent years have seen a growing demand for air transport which has led to an increase in the number of airports providing a significant number of flights in Spain and throughout the rest of Europe. Choosing which airport to use depends on the competition between the airlines operating from them and how accessible they are to the residents in the surrounding areas. This research introduces an efficient design based on D-error using a stated preferences survey to study user behaviour when choosing between competing airports. The data is modelled using a Multinomial Logit Model and a Random Parameter Error Component Logit (RPECL), a discrete choice model which allows us to study user preferences taking into account their varying systemic and random tastes, as well as find specific correlations which may exist between similar alternatives. This meant the authors were also able to calculate the direct and cross elasticities to examine the weight of the different variables involved in making the choice of airport. The results showed, for a study case in Spain (Bilbao and Seve Ballesteros - Santander airports), that increased access time to the furthest airport caused an important fall in demand (choice) for that airport. It was also shown that access fees had a lower elasticity than the flight cost and that the fewer the transfers required to reach the final destination increased the probability of choosing an airport. Therefore, in order for smaller airports to compete with larger airports they need to invest more in reducing the cost of flights, attracting more low-cost companies and offering more direct complementary destinations than those provided by larger airports.

Pairwise fitting of piecewise mixed models for the joint modeling of multivariate longitudinal outcomes, in a randomized crossover trial.

Many statistical models have been proposed in the literature for the analysis of longitudinal data. One may propose to model two or more correlated longitudinal processes simultaneously, with a goal of understanding their association over time. Joint modeling is then required to carefully study the association structure among the outcomes as well as drawing joint inferences about the different outcomes. In this study, we sought to model the associations among six nutrition outcomes while circumventing the computational challenge posed by their clustered and high-dimensional nature. We analyzed data from a 2 2 randomized crossover trial conducted in Kenya, to compare the effect of high-dose and low-dose iodine in household salt on systolic blood pressure (SBP) and diastolic blood pressure (DBP) in women of reproductive age and their household matching pair of school-aged children. Two additional outcomes, namely, urinary iodine concentration (UIC) in women and children were measured repeatedly to monitor the amount of iodine excreted through urine. We extended the model proposed by Mwangi etal. (2021, Communications in Statistics: Case Studies, Data Analysis and Applications, 7(3), 413-431) allowing flexible piecewise joint models for six outcomes to depend on separate random effects, which are themselves correlated. This entailed fitting 15 bivariate general linear mixed models and deriving inference for the joint model using pseudo-likelihood theory. We analyzed the outcomes separately and jointly using piecewise linear mixed-effects (PLME) model and further validated the results using current state-of-the-art Jones and Kenward methodology (JKME model) used for analyzing randomized crossover trials. The results indicate that high-dose iodine in salt significantly reduced blood pressure (BP) compared to low-dose iodine in salt. Estimates for the random effects and residual error components showed that SBP and DBP had strong positive correlation, with effect of the random slope indicating that significantly related outcomes are strongly associated in their evolution. There was a moderately strong inverse relationship between evolutions of UIC and BP both in women and children. These findings confirmed the original hypothesis that high-dose iodine salt has significant lowering effect on BP. We further sought to evaluate the performance of our proposed PLME model against the widely used JKME model, within the multivariate joint modeling framework through a simulation study mimicking a crossover design. From our findings, the multivariate joint PLME model performed exceptionally well both in estimation of random-effects matrix (G) and Hessian matrix (H), allowing satisfactory model convergence during estimation. It allowed a more complex fit to the data with both random intercepts and slopes effects compared to the multivariate joint JKME model that allowed for random intercepts only. When a hierarchical viewpoint is adopted, in the sense that outcomes are specified conditionally upon random effects, the variance-covariance matrix of the random effects must be positive definite. In some cases, additional random effects could explain much variability in the data, thus improving precision in estimation of the estimands (effect size) parameters. The key highlight in this evaluation shows that multivariate joint JKME model is a powerful tool especially while fitting mixed models with random intercepts only, in crossover design settings. Addition of random slopes may lead to model complexities in most cases, resulting in unsatisfactory model convergence during estimation. To circumvent convergence pitfalls, extention of JKME model to PLME model allows a more flexible fit to the data (generated from crossover design settings), especially in the multivariate joint modelingframework.

Comparative estimation of a random error component of automatic well level gauges based on processing measurements of earth-tidal level of groundwater

Relevance. Introduction of autonomous digital level gauges allows significantly expanding the range of tasks solved in various fields of geology and ecology, by increasing the frequency of measurements and applying mathematical processing methods to avoid distortions of different nature. The expansion of the field of application of downhole level meters makes it a topical issue to choose a particular type of device to ensure the required measurement accuracy. Aim. To consider the approaches to comparative estimation of random error of several types of automatic level gauges based on their recording of earth-tidal variations of groundwater level. Methods. Methods of compensating the influence of variations in atmospheric pressure on groundwater levels; methods of calculating tidal level variations; methods of correlation and frequency analysis of the calculated and experimental data. Results. The authors have carried out a comparative assessment of the accuracy in readings of several digital level gauges, installed in one well, by comparing the measured values of earth-tidal variations of the groundwater level with the calculated ones. Based on the experimental data, tidal variations of the groundwater level were obtained by eliminating distortions from variations in atmospheric pressure and then filtering with the moving mean. From correlation and amplitude-frequency analysis of the calculated and experimental data, indicators were determined for making a comparative assessment of a random component of the error of the tested level gauges. Conclusions. The approach suggested allows choosing independent digital level gauges with a minimum random error component using the totality of calculated parameters. The most promising way to eliminate the distorting effects of tidal variation of groundwater level is the method based on the cutter frequency filtering of the level signal measured by the level gauge.

Sensorimotor adaptation in virtual reality: Do instructions and body representation influence aftereffects?

Perturbations in virtual reality (VR) lead to sensorimotor adaptation during exposure, but also to aftereffects once the perturbation is no longer present. An experiment was conducted to investigate the impact of different task instructions and body representation on the magnitude and the persistence of these aftereffects. Participants completed the paradigm of sensorimotor adaptation in VR. They were assigned to one of three groups: control group, misinformation group or arrow group. The misinformation group and the arrow group were each compared to the control group to examine the effects of instruction and body representation. The misinformation group was given the incorrect instruction that in addition to the perturbation, a random error component was also built into the movement. The arrow group was presented a virtual arrow instead of a virtual hand. It was hypothesised that both would lead to a lower magnitude and persistence of the aftereffect because the object identity between hand and virtual representation would be reduced, and errors would be more strongly attributed to external causes. Misinformation led to lower persistence, while the arrow group showed no significant differences compared to the control group. The results suggest that information about the accuracy of the VR system can influence the aftereffects, which should be considered when developing VR instructions. No effects of body representation were found. One possible explanation is that the manipulated difference between abstract and realistic body representation was too small in terms of object identity.

Evaluation and analysis of systematic and random error components of airflow velocity measurements by anemometers

Evaluation and analysis of systematic and random error components of airflow velocity measurements by anemometers

ESMGFZ EAM Products for EOP Prediction: Toward the Quantification of Time Variable EAM Forecast Errors

Abstract Since more than 10 years, the Earth system modeling group at GFZ (ESMGFZ) provides effective angular momentum (EAM) functions for Earth orientation parameter assessment on a routinely daily basis. In addition to EAM of the individual Earth’s subsystems atmosphere, ocean, and hydrology, the global mass balance is calculated as barystatic sea level variation by solving explicitly the sea-level equation. ESMGFZ provides also 6-day forecasts for all of these EAM products. EAM forecasts are naturally degraded by forecast errors that typically grow with increasing forecast length, but they also show recurring patterns with occasionally higher errors at very short forecast horizons. To characterize such errors which are not randomly distributed in time, we divided the errors into a systematic and a stochastic contribution. In an earlier study, we were able to detect and remove the large systematic fraction occurring in the atmospheric angular momentum (AAM) wind term forecast errors with a cascading forward neural network model, thereby reducing the total forecast error by about 50%. In contrast, we were not able to remove the random error component assed in this study. Nevertheless, we show that machine learning methods are able to predict quasi-daily variations in time variable EAM forecasts error levels. We plan to provide these forecast error estimates along with the deterministic EAM forecast products for subsequent use in, for example, EOP Kalman filter prediction schemes.

Role of Public Debt in Indian States in the Post-Reform Era

The substantial amount of existing literature investigating the debt–growth association for high-income countries shows that debt has a negative impact on economic growth or the existence of an inverted U-shaped relationship between these two variables on some occasions. Given the lack of literature involving developing economies in this space, our study entirely focuses on a developing country like India. The study examines the empirical relationship between public debt (internal) and state gross domestic product (SGDP) for India in the post-reform era. The panel data extend from the year 2000 till 2020. Our random error component model findings indicate a positive and significant impact of debt in enhancing the Indian SGDPs for the above-mentioned period. Results are also confirmed by using an alternative estimation technique, namely, fixed effect. Next, we address the issue of endogeneity by employing generalized method of moments. Our results continue to remain robust. Finally, the inclusion of other control variables does not alter our findings. JEL Codes: H63, H54, O50, C51

Revealing systematic errors in hole drilling measurements through a calibration bench: the case of zero-depth data

An accurate estimation of the measurement error in the hole drilling method is needed to choose an appropriate level of regularization and to perform a sensitivity analysis on the stress results. The latest release of ASTM E837 standard for the hole drilling method includes a procedure aimed at estimatingthe standard deviation of the random error component on strain measurements, proposed by Schajer. Nevertheless, strain measurements are also affected to some extent by systematic errors which are not included in the estimation and need to be compensated. For example, an error in the rosette gage factor orin the identification of the zero-depth datum systematically affects all strain measurements in a strongly correlated fashion. This paper describes a calibration bench, designed to superimpose a reference bending stress distribution on a given specimen while simultaneously performing a hole drilling measurement.Since the reference solution is known a priori and shares the measurement instrumentation, the hole geometry and the stepping process with the actual residual stress distribution, the bench provides the user with a direct validation of the obtained accuracy. In addition, strategies aimed at compensating systematicerrors can be tested on the reference solution and then applied on the residual stress evaluation. The imperfect hole geometry and drilling alignment are proven to cause a significant underestimation of stresses near the surface, as they lead to an incorrect identification of the zero-depth datum. It is shown that this effect can be corrected through the proposed calibration bench.

СРАВНИТЕЛЬНАЯ ОЦЕНКА МЕТОДОВ УСРЕДНЕНИЙ ДЛЯ ФИЛЬТРАЦИИ ИЗМЕРИТЕЛЬНЫХ СИГНАЛОВ

To improve the quality of manufactured products, it is necessary to improve all technologicalprocesses, which requires increasing the accuracy of the entire measuring path as a whole.For this it is necessary to carefully analyze systematic, random and fluctuating errors in the measurementchannel and take all measures to reduce them. Digital filtering or averaging of intermediatemeasurements (observations) according to certain rules is a radical means of improving theaccuracy of measurements performed. The aim of this work is to compare the quality of suppressionof near-real noise interference using the eight most well-known averaging methods. A model of the measurement path and a general block diagram for modeling the measurement process on acomputer under the influence of random interference are proposed for eight averaging algorithms.As a criterion for evaluating the quality of averaging methods, the ratios of absolute error variancesand mean square deviations before the computing device and after applying the specified averagingalgorithm are taken. Based on the simulation results, the following conclusions are made. 1. All averagingalgorithms provide suppression of random error components of complex interference to thelevel of 40–60 dB. Three algorithms are the best: arithmetic mean AR, a-truncated mean AU5 and atenderizedmean AB5, which provide for the suppression of 5 % of anomalous results. With an increasein the number of observations, the suppression coefficients increase proportionally. 2. Thesampling time must be a multiple of the duration of the 50 Hz AC mains period (20 ms). The optimalnumber of observations (measurements) is 100–128; with 128 measurements, the division operationis reduced to a simple shift, and the averaging result can be obtained in 1–2 μs. 3. When experimentallyapplying the AR averaging method for filtering a highly noisy measurement signal in a communicationline with a length of 800 m, a decrease in the spread of ADC output codes was observedfrom ± 3.5 % to ± 0.1 % after filtering (AR, 64 measurements in 40 ms).

Discrete choice models with multiplicative stochasticity in choice environment variables: Application to accommodating perception errors in driver behaviour models

This paper presents a mixed multinomial logit-based discrete choice modelling framework to accommodate decision-makers’ errors in perceiving choice environment variables that do not vary across choice alternatives. An analysis is undertaken to evaluate two different ways of specifying errors in the choice environment variables in discrete choice models – (a) the additive specification and (b) the multiplicative specification. Between these two approaches, the multiplicative error specification is consistent with psychophysical theories of human perception of physical quantities in that the variability in perception tends to be greater for quantities of greater magnitude. Further, it is shown that models with an additive error specification run into parameter (un)identifiability problems if the analyst attempts to accommodate errors in several variables. In contrast, models with multiplicative errors in variables allow separate identification of stochasticity in as many variables as needed, as long as those variables have a significant influence on the choice outcome.The usefulness of the proposed framework with multiplicative errors is demonstrated through simulation experiments and an empirical application for analysing driver behaviour while considering drivers’ errors in perceiving traffic environment variables. The empirical analysis is carried out using space-time trajectories of vehicles from a heterogeneous, disorderly (HD) traffic stream in Chennai, India. Results suggest that the proposed model, with power lognormal distributed multiplicative errors in traffic environment variables, outperformed the typically used mixed logit models with random coefficients (uncorrelated and correlated) or error components. Further, allowing for perception errors in traffic environment variables was found to be more important than allowing unobserved heterogeneity in the drivers’ sensitivity to those variables. In addition, the empirical model offers interesting insights into the extent of variability due to perception errors in different traffic environment variables.

Evaluation of the random error of the methods of accelerated determination of the endurance limit

The article considers a task related to the general approach to determining the random error in determining the endurance limit by accelerated methods. Based on the conducted analysis, it was shown that in the calculation of the accuracy of accelerated methods for determining the endurance limit, it is necessary to separately determine the systematic and random components of the total error. It was also proposed to determine the random error of accelerated methods for determining the endurance limit using a general statistical approach. At the same time, it is proposed to find the accuracy of the assessment of the endurance limit itself, depending on the specific test scheme of one or another accelerated method.

Assessment of the error budget for stratospheric ozone profiles retrieved from OMPS limb scatter measurements

Abstract. This study presents an error budget assessment for the ozone profiles retrieved at the University of Bremen through limb observations of the Ozone Mapper and Profiler Suite – Limb Profiler Suomi National Polar-orbiting Partnership (OMPS-LP SNPP) satellite instrument. The error characteristics are presented in a form that aims at being compliant with the recommendations and the standardizing effort of the Towards Unified Error Reporting (TUNER) project. Besides the retrieval noise, contributions from retrieval parameters are extensively discussed and quantified by using synthetic retrievals performed with the SCIATRAN radiative transfer model. For this investigation, a representative set of OMPS-LP measurements is selected to provide a reliable estimation of the uncertainties as a function of latitude and season. Errors originating from model approximations and spectroscopic data are also taken into account and found to be non-negligible. The choice of the ozone cross section is found to be relevant, as expected. Overall, we classify the estimated errors as random or systematic and investigate correlations between errors from different sources. After summing up the relevant error components, we present an estimate of the total random uncertainty on the retrieved ozone profiles, which is found to be in the 5 %–30 % range in the lower stratosphere, 3 %–5 % in the middle stratosphere, and 5 %–7 % at upper altitudes. The systematic uncertainty is mainly due to cloud contamination and model errors in the lower stratosphere and due to the retrieval bias at higher altitudes. The corresponding total bias exceeds 5 % only above 50 km and below 20 km. After computing the estimate of the overall random and systematic error components, we also provide an ex-post assessment of the uncertainties using self-collocated OMPS-LP observations and collocated Microwave Limb Sounder (MLS) data in a χ2 fashion.

Quantitative Study of the T-AVIM-Based Simulated IMU Error in Polar Regions.

For solving the problem of polar performance of the inertial navigation system (INS) at mid-low latitudes, the simulation test system constructed by the “attitude and velocity invariant method of trajectory transfer rule based on the transverse coordinate system (T-AVIM)” of the Earth sphere model is used. The test system structure, especially the IMU conversion formula from mid-low latitudes to polar region simulation test, is introduced, and it is proved that the IMU conversion error can be equivalently superimposed on the bias error of the polar simulated IMU. According to the marine estimation formula for the effect of the reference error on the IMU conversion error, the specific influence of the constant error component and the random error component of the reference system on the simulated IMU is analyzed. The calculation method of the simulated IMU error is given with examples and intuitively explained, and the correctness of the theory is verified through simulation experiments.

Towards mid-position based Stereotactic Body Radiation Therapy using online magnetic resonance imaging guidance for central lung tumours.

Background and purpose: Central lung tumours can be treated by magnetic resonance (MR)-guided radiotherapy. Complications might be reduced by decreasing the Planning Target Volume (PTV) using mid-position (midP)-based planning instead of Internal Target Volume (ITV)-based planning. In this study, we aimed to verify a method to automatically derive patient-specific PTV margins for midP-based planning, and show dosimetric robustness of midP-based planning for a 1.5T MR-linac.Materials and methods: Central(n = 12) and peripheral(n = 4) central lung tumour cases who received 8x7.5 Gy were included. A midP-image was reconstructed from ten phases of the 4D-Computed Tomography using deformable image registration. The Gross Tumor Volume (GTV) was delineated on the midP-image and the PTV margin was automatically calculated based on van Herk’s margin recipe, treating the standard deviation of all Deformation Vector Fields, within the GTV, as random error component. Dosimetric robustness of midP-based planning for MR-linac using automatically derived margins was verified by 4D dose-accumulation. MidP-based plans were compared to ITV-based plans. Automatically derived margins were verified with manually derived margins.Results: The mean D95% target coverage in GTV + 2 mm was 59.9 Gy and 62.0 Gy for midP- and ITV-based central lung plans, respectively. The mean lung dose was significantly lower for midP-based treatment plans (difference:-0.3 Gy; ). Automatically derived margins agreed within one millimeter with manually derived margins.Conclusions: This retrospective study indicates that mid-position-based treatment plans for central lung Stereotactic Body Radiation Therapy yield lower OAR doses compared to ITV-based treatment plans on the MR-linac. Patient-specific GTV-to-PTV margins can be derived automatically and result in clinically acceptable target coverage.

Идентификация квадратичного ядра уравнения Вольтерра для моделирования нелинейных динамических систем

In the last two decades, integral models have been used to describe the dynamics of stationary nonlinear systems in which the terms of the Volterra series are the kernels. The most commonly used are the linear term (the impulse transition function depends on one variable) and the quadratic term (depending on two variables). An active experiment in which a special combination of rectangular pulses is fed to the input of the system is carried out to select two of its components in the output signal of the identified system - the output of the linear "subsystem" and the output of the "quadratic" subsystem. After isolating the output of the "quadratic" subsystem, the identification of the quadratic term of the Volterra series is reduced to solving a two-dimensional integral equation of the first kind. In the literature, inversion formulas are given in which the quadratic kernel function is obtained as a result of arithmetic operations with second-order derivatives of the output signal. Differentiation of functions is an incorrectly posed problem, when small errors in the assignment of a function (measurement noise) cause large errors in derivatives (especially in second-order derivatives). The paper proposes the use of smoothing cubic splines for stable calculation of derivatives. To calculate the mixed second-order derivative, a spline with two variables is built - a smoothing bicubic spline. The main problem that arises in practice when processing the data of a real experiment is the selection of a smoothing parameter, on the value of which a smoothing error of noisy data depends. As a rule, the value of the variance of the measurement noise is unknown in the experiment. Therefore, in this work, it is proposed to use an algorithm based on the L-curve method to select the smoothing parameter in the constructed splines (especially in the bicubic one), which does not require setting the variance of the measurement noise. The proposed identification algorithm has a high computational efficiency. The performed computational experiment showed a small methodical error (about 1%) and good resistance to noise in measurements of the output signals of the identified system. To reduce the random component of the identification error, it is proposed to use post-processing with a local-spatial compound filter.

Improving the ESA CCI daily soil moisture time series with physically-based land surface model datasets using a Fourier time-filtering method

Abstract Models have historically been the source of global soil moisture (SM) analyses and estimates of land-atmosphere coupling, even though they are usually calibrated and validated only locally. Satellite-based analyses have grown in fidelity and duration, offering an independent observationally-based alternative. However, satellite-retrieved SM time series include random and periodic errors that degrade estimates of land-atmosphere coupling, including correlations with other variables. This study proposes a mathematical approach to adjust daily time series of the European Space Agency (ESA) Climate Change Initiative (CCI) satellite SM product using information from physical-based land surface model (LSM) datasets using a Fourier transform time-filtering method to match the temporal power spectra locally to the LSMs, which tend to agree well with in situ observations. When the original and time-filtered SM products are evaluated against ground-based SM measurements over the conterminous U.S., Europe, and Australia, results show the filtered SM has significantly improved subseasonal variability. The skill of the time-filtered SM is increased in temporal correlation by ∼0.05 over all analysis domains without introducing spurious regional patterns, affirming the stochastic nature of noise in satellite estimates, and skill improvement is found for nearly all land cover classes, especially savannas and grassland. Autocorrelation-based soil moisture memory (SMM), and the derived random component of soil moisture error (SME) are used to investigate the improvement of SM features. Time filtering reduces the random noise from the satellite-based SM product that is not explainable by physically-based SM dynamics; SME is usually diminished and the increased SMM is generally statistically significant.

Large Scale Hotel Resource Retrieval Algorithm Based on Characteristic Threshold Extraction

At present, the hotel resource retrieval algorithm has the problem of low retrieval efficiency, low accuracy, low security and high energy consumption, and this study proposes a large scale hotel resource retrieval algorithm based on characteristic threshold extraction. In the large-scale hotel resource data, the mass sequence is decomposed into periodic component, trend component, random error component and burst component. Different components are extracted, the singular point detection is realized by the extraction results, and the abnormal data in the hotel resource data are obtained. Based on the attribute of hotel resource data, the data similarity is processed with variable window, the total similarity of data is obtained, and the abnormal detection of redundant resource data is realized. The abnormal data detection results and redundant data detection results are substituted into the space-time filter, and the data processing is completed. The retrieval problem is identified, and the data processing results are replaced in the hotel resource retrieval based on the characteristic threshold extraction to achieve the normalization of data source and rule knowledge. The characteristic threshold and retrieval strategy are determined, and data fusion reasoning is carried out. After repeated iteration, effective solutions are obtained. The effective solution is fused to get the best retrieval result. Experimental results showed that the algorithm has higher retrieval accuracy, efficiency and security coefficient, and the average search energy consumption is 56n J/bit.

Performance evaluation, error decomposition and Tree-based Machine Learning error correction of GPM IMERG and TRMM 3B42 products in the Three Gorges Reservoir Area

Satellite precipitation products (SPPs) have excellent development prospects in hydrometeorology research for their high spatial-temporal resolution. Understanding the performance of SPPs is essential before their application in estimating multiple processes. This paper evaluated the accuracy and error composition of GPM IMERG Final-run V06 and TRMM 3B42V7 in the Three Gorges Reservoir Area (TGRA) based on the China Gauge-based Daily Precipitation Analysis dataset (CGDPA) during 2001–2019. Afterwards, the precipitation correction by merging satellite and gauge observation precipitation was conducted with three Tree-based Machine Learning models, Decision Tree (DT), Adaptive Boosting Decision Trees (Adaboost), and Random Forest (RF). The results show that: (1) Two SPPs can well reflect the spatial pattern and in-year variation of precipitation in the TGRA. However, they are limited in estimating precipitation amount for seriously underestimated the light rain or overestimated torrential rain. Under the influence of climate and variety terrains, the SPPs accuracy in the middle-elevation relief mountains of downstream is significantly higher than that in the low-elevation relief mountains of upstream. Moreover, that on the monthly and annual scales are higher than on the daily scale. Comparing two SPPs, the area proportions of IMERG-F better than 3B42V7 are 64.0%, 86.0%, and 81.6% on daily, monthly and annual scales, respectively. (2) Both the systematic error components of two SPPs raise with the increase of precipitation amount, and the error spatial pattern of 3B42V7 is more affected by precipitation. The random error component of light rain and daily precipitation is higher than other grades and scales. Despite this, the random error component decreases significantly when daily precipitation is accumulated. (3) The three primary factors affecting error correction of SPPs are precipitation amount, longitude, and DEM in TGRA. Among the three Tree-based methods, the RF showed the best error correction effect, and it can significantly improve the monthly and annual precipitation accuracy and better reproduce probability density function (PDF). Cumulative precipitation can reduce the random error component of daily precipitation and have high correction accuracy when cumulative time exceeds 5-days.

Analytical setup margin for spinal stereotactic body radiotherapy based on measured errors

BackgroundNo consensus currently exists about the correct margin size to use for spinal SBRT. Margins have been proposed to account for various errors individually, but not with all errors combined to result in a single margin value. The purpose of this work was to determine a setup margin for five-fraction spinal SBRT based on known errors during radiotherapy to achieve at least 90% coverage of the clinical target volume with the prescription dose for at least 90% of patients and not exceed a 30 Gy point dose or 23 Gy to 10% of the spinal cord subvolume.MethodsThe random and systematic error components of intrafraction motion, residual setup error, and end-to-end system accuracy were measured. The patient’s surface displacement was measured to quantify intrafraction motion, the residual setup error was quantified by re-registering accepted daily cone beam computed tomography setup images, and the displacement between measured and planned dose profiles in a phantom quantified the end-to-end system accuracy. These errors and parameters were used to identify the minimum acceptable margin size. The margin recommendation was validated by assessing dose delivery across 140 simulated patient plans suffering from various random shifts representative of the measured errors.ResultsThe errors were quantified in three dimensions and the analytical margin generated was 2.4 mm. With this margin applied in the superior/inferior direction only, at least 90% of the CTV was covered with the prescription dose for 96% of the 140 patients simulated with minimal negative effect on the spinal cord dose levels.ConclusionsThe findings of this work support that a 2.4 mm margin applied in the superior/inferior direction can achieve at least 90% coverage of the CTV for at least 90% of dual-arc volumetric modulated arc therapy spinal SBRT patients in the presence of errors when immobilized with vacuum bags.

Optimal trimming proportion in regression analysis for non-normal distributions

ABSTRACT Regression analysis is a widely used modelling tool in business decision making. However, proper application of this methodology requires that certain assumptions, associated with the model, be satisfied. The assumption we focus on is the normality of the response variable, which is directly related to the assumption of normality of the error component. In a variety of fields in business, such as finance, marketing, information systems, operations, and healthcare, the selected dependent variable does not inherently have a normal distribution. In the regression context, where the model parameters and independent variables are assumed to be constant, the distribution of the random error component thus influences the distribution of the dependent variable. Here, we study the impact of symmetric and asymmetric error distributions on the performance of the estimated model parameters. To create robust estimates, through a process of trimming the response variable, we study the effectiveness of the trimmed estimators with respect to the ordinary least squares estimator (OLS) via a simulation procedure. Accordingly, to minimise the ratio of the mean squared error of the trimmed estimator to that of the OLS, a recommendation is developed for the optimal trimming proportion.