Photon Beam Treatment Planning: Part II
Eric Ford in Primer on Radiation Oncology Physics, 2020
The expansion of CTV (or ITV) to PTV is intended to account for variability in targeting of the beam relative to the patient, and one can evaluate what is the appropriate expansion, or “margin.” A rational basis for margins requires an understanding of uncertainty in patient setup variability. This is illustrated in Figure 13.1.3 which shows the two types of variability in setup: (1) random errors (denoted by the symbol, σ). This is the variability of the targeting in the patient from day-to-day around an ideal position, indicated by the “+” in the figure. The symbol σ is the standard deviation (spread) of a Gaussian probability distribution. (2) Systematic error (denoted by the symbol, Σ). This is the overall offset of the average position averaged over all days compared to an ideal position, indicated by the “+” in the figure. Note that a systematic error effects every treatment in the same direction and so has a larger impact than random errors.
Introduction
Gueorguieva Ralitza in Statistical Methods in Psychiatry and Related Fields, 2017
Variability of observations around the mean from a simple random sample is described by the variance or standard deviation of the observations (see Section 1.7). The sample standard deviation is often preferable as it provides a measure of variability that is evaluated in the same units as the mean. In repeated measures situations with longitudinal data, often the variability of the response at one particular time point differs from the variability at another, in which case it makes sense to estimate separate variances in order to assess data spread at individual time points. However, in some situations it may be reasonable to assume that the variances on all repeated occasions are the same. In this case, a better statistical estimate of the common variance can be obtained by pooling information from all occasions. Examples of both scenarios are considered in Chapter 2.
Retinal image enhancement and analysis for diabetic retinopathy assessment
Ahmad Fadzil Mohamad Hani, Dileep Kumar in Optical Imaging for Biomedical and Clinical Applications, 2017
It can be seen from Table 5.2 that the intensity means of the three components are different in each colour channel. The macular pigment and melanin have the lowest and the highest means, respectively. The difference in intensity means of macular pigment, haemoglobin and melanin is expected due to different spectral absorbance of these three components. This characteristic is useful to separate these three components using ICA. Standard deviation and minimum–maximum intensities also vary among these three components. Standard deviations and intensity ranges shown in the table indicate the homogeneity of intensity distribution of each component in each channel. A small standard deviation indicates that intensity distribution tends to centre on the mean indicating a more homogeneous intensity distribution. Conversely, a high standard deviation implies that data intensities are spread out over a large range of values indicating a more inhomogeneous intensity distribution. The variation of standard deviation and intensity range is expected and implies that the contrast of the retinal fundus image is varied. Like standard deviation, the highest intensity range belongs to the red channel followed by the green and the blue channel. It implies that intensity variation mostly occurs in the red channels rather than in the other two colour channels.
Selection of preferred thermal environment and cold-avoidance responses in rats rely on signals transduced by the dorsal portion of the lateral funiculus of the spinal cord
Published in Temperature, 2023
Robson C.L. Vizin, Maria C. Almeida, Renato N. Soriano, Andrej A. Romanovsky
The effects of bilateral DLF transection on the spontaneous innate behavior of selecting Tpr were studied in the thermogradient apparatus over a 24-h period. While the Tpr and Tc dynamics in funiculotomized rats were similar to those in sham-operated rats (Figure 2, Table 1), there was a notable difference. The fluctuations of Tpr were markedly greater in funiculotomized rats than in sham-operated controls, especially during the light (inactive) phase of the diurnal cycle (Figure 2, Table 1). Furthermore, in funiculotomized rats, the changes at the effector level (greater fluctuations in Tpr) translated into the greater amplitude of Tc fluctuations and greater Tc variability (as measured by standard deviation) during the light phase (Table 1). Standard deviation is a measure of data dispersion, or variability, and is often used as such in the thermophysiological literature (see, e.g., Ref. [34]). The wider fluctuations in both Tpr and Tc suggest that funiculotomized rats were less sensitive to environmental thermal changes, and that their behavioral thermoregulation was less precise.
Efficacy of non-surgical treatments for androgenetic alopecia in men and women: a systematic review with network meta-analyses, and an assessment of evidence quality
Published in Journal of Dermatological Treatment, 2022
Aditya K. Gupta, Mary A. Bamimore, Kelly A. Foley
Our point estimate of interest was mean change in hair count from baseline, in units of hairs per square centimeter (hairs/cm2), and our measure of variability was the standard deviation (±SD). For studies that did not directly provide this point estimate (nor its standard deviation), we used various techniques to estimate them. When the mean difference was not directly provided, baseline and follow-up values of mean hair count, sample size and standard deviation were used to compute the mean change in hair count from baseline (±SD); the difference was estimated with a two-sample t-test in the NCSS statistical software (15). When the standard deviation was not directly provided, it was estimated using the range rule which states that the value of the standard deviation is approximately equivalent to: the quotient of the absolute difference, between the minimum and maximum, divided by 4 (16). When standard error of the mean was provided, the standard deviation was computed by multiplying the square root of sample size with the standard error. When the 95% confidence interval of the mean was provided, the standard deviation was estimated by applying the following equation (17):
Debridement, antibiotics and implant retention (DAIR) is successful in the management of acutely infected unicompartmental knee arthroplasty: a case series
Published in Annals of Medicine, 2023
Angela Brivio, Talal Al-Jabri, Jurgen Martin, David Barrett, Nicola Maffulli
Patients failing to complete the therapeutic regimen through non-attendance or failure of therapy were excluded, and recurrence of infection was noted. Failure to eradicate the infection was defined as recurrent infection from the same or different organisms. FU was continued in successful cases until inflammatory markers had returned to normal and the patient reported cessation of infective symptoms. Yearly FU appointments were then scheduled. The overall survivorship free from reoperation for infection and the overall survivorship free from reoperation for any reason is reported. The mean and standard deviations are provided using a population standard deviation formula. We used a Kaplan Meier survivorship curve to present survivorship free from reinfection following the primary DAIR procedure. This mode of analysis is similar to that used in previous literature in this field and allows direct comparison to other previous publications and different techniques for treating PJI.
Related Knowledge Centers
- Margin of Error
- Statistical Dispersion
- Expected Value
- Sampling
- Margin of Error
- Statistical Significance
- Average
- Height
- Sample Mean & Covariance
- Unbiased Estimation of Standard Deviation
- Accuracy & Precision