Electron Beam Measurements Employing Electron Montecarlo Algorithm on TrueBeam STx® and Clinac iX® Linear Accelerators

Electron beam measurement comparison between TrueBeam STx® and Clinac iX® established. Data evaluation of eMC-calculated and measured for TrueBeam STx® performed. Dosimetric parameters measured including depth dose curves for each applicator, percentage depth dose (PDDs) curves without applicator, the profile in-air for a large field size 40×40 cm2, and the Absolute Dose (cGy/MU) for each applicator using a large water phantom (PTW, Freiburg, Germany), employing Roos and Markus plane-parallel ionization chambers. The data were examined for five electron beams of Varian’s TrueBeam STx® and Clinac iX® machines. A comparison between measurement PDDs and calculated by the Eclipse electron Monte Carlo (eMC) algorithm was performed to validate Truebeam STx® commissioning. The measured data indicated that electron beam PDDs from the TrueBeam STx® machine are well matched to those from Clinac iX® machine. The quality index R50 for applicator 15×15 cm2 was in the tolerance intervals. However, Surface dose (Ds) increases with increasing energy for both accelerators. Comparisons between the measured and eMC-calculated values revealed that the R100, R90, R80, and R50 values mostly agree within 5 mm. Measured and calculated bremsstrahlung tail Rp correlates well statistically. Ds agrees mostly within 2%. Electron beams were successfully validated for TrueBeam STx®, a good agreement between modeled and measured data was observed.

Teaching: confidence, prediction and tolerance intervals in scientific practice: a tutorial on binary variables

Background One of the emerging themes in epidemiology is the use of interval estimates. Currently, three interval estimates for confidence (CI), prediction (PI), and tolerance (TI) are at a researcher's disposal and are accessible within the open access framework in R. These three types of statistical intervals serve different purposes. Confidence intervals are designed to describe a parameter with some uncertainty due to sampling errors. Prediction intervals aim to predict future observation(s), including some uncertainty present in the actual and future samples. Tolerance intervals are constructed to capture a specified proportion of a population with a defined confidence. It is well known that interval estimates support a greater knowledge gain than point estimates. Thus, a good understanding and the use of CI, PI, and TI underlie good statistical practice. While CIs are taught in introductory statistical classes, PIs and TIs are less familiar. Results In this paper, we provide a concise tutorial on two-sided CI, PI and TI for binary variables. This hands-on tutorial is based on our teaching materials. It contains an overview of the meaning and applicability from both a classical and a Bayesian perspective. Based on a worked-out example from veterinary medicine, we provide guidance and code that can be directly applied in R. Conclusions This tutorial can be used by others for teaching, either in a class or for self-instruction of students and senior researchers.

Tolerance intervals in statistical software and robustness under model misspecification

A tolerance interval is a statistical interval that covers at least 100ρ% of the population of interest with a 100(1−α)% confidence, where ρ and α are pre-specified values in (0, 1). In many scientific fields, such as pharmaceutical sciences, manufacturing processes, clinical sciences, and environmental sciences, tolerance intervals are used for statistical inference and quality control. Despite the usefulness of tolerance intervals, the procedures to compute tolerance intervals are not commonly implemented in statistical software packages. This paper aims to provide a comparative study of the computational procedures for tolerance intervals in some commonly used statistical software packages including JMP, Minitab, NCSS, Python, R, and SAS. On the other hand, we also investigate the effect of misspecifying the underlying probability model on the performance of tolerance intervals. We study the performance of tolerance intervals when the assumed distribution is the same as the true underlying distribution and when the assumed distribution is different from the true distribution via a Monte Carlo simulation study. We also propose a robust model selection approach to obtain tolerance intervals that are relatively insensitive to the model misspecification. We show that the proposed robust model selection approach performs well when the underlying distribution is unknown but candidate distributions are available.

Coverage Intervals

Since coverage intervals are widely used expressions of measurement uncertainty, this contribution reviews coverage intervals as defned in the Guide to the Expression of Uncertainty in Measurement (GUM), and compares them against the principal types of probabilistic intervals that are commonly used in applied statistics and in measurement science. Although formally identical to conventional confdence intervals for means, the GUM interprets coverage intervals more as if they were Bayesian credible intervals, or tolerance intervals. We focus, in particular, on a common misunderstanding about the intervals derived from the results of the Monte Carlo method of the GUM Supplement 1 (GUM-S1), and offer a novel interpretation for these intervals that we believe will foster realistic expectations about what they can deliver, and how and when they can be useful in practice

Assessment of OTT Pluvio2 Rain Intensity Measurements

This study investigates the OTT Pluvio2 weighing precipitation gauge’s random and systematic error components as well as stabilization of the measurements on time varying rainfall intensities (RI) under laboratory conditions. A highly precise programmable peristaltic pump that provided both constant and time varying RI was utilized in the experiments. Abrupt, gradual step, and cyclic step changes in the RI values were evaluated. RI readings were taken in real-time (RT) at different time resolution (6-60s) for the RI range of 6-70mm/h. Our analysis indicates that the lower threshold for the OTT Pluvio2’s real-time RI measurements should be redefined as 7mm/h at a one-minute resolution. Tolerance intervals containing 95% of the repeated measurements with probability 0.95 are given. It is shown that the measurement variances are unequal over the range of RI and the measurement repeatability is not uniform. A statistically significant negative bias was observed for the RI values of 7 and 8mm/h, while there was not a statistically significant linearity problem. Through the use of statistical control limits, it is shown that means of the RI measurements stabilized on the actual RI value. A detailed investigation on RT bucket weight measurements revealed a time delay in bucket weight measurements, which causes notable errors in reported RI measurements under dynamic rainfall conditions. To demonstrate the potentiality of large errors in Pluvio2’s real-time RI measurements, a set of equations was developed that faithfully reproduced the Pluvio2’s internal (hidden) algorithm, and results from dynamic laboratory and in-situ rainfall scenarios were simulated. The results of this investigation show the necessity of modifying the present Pluvio2 RI algorithm to enhance its performance and show the possibility of post-processing the existing Pluvio2 RI datasets for improved measurement accuracies.