Clinical applicability of setup margins in radiotherapy based on non-gaussian approach: A multiple-site comparison

CT Simulation, immobilization, and treatment planning

During simulation, patients were scanned using the computed tomography CT) machine Light Speed-VCT64^TM (General Electric Medical Systems, Waukesha, Wisconsin) with a 3 mm slice thickness. Patients of all groups were scanned in the head-first supine position and immobilized with thermoplastic masks (Orfit Industries NV, Wijnegem, Belgium), mostly with vacuum cushions (Orfit Industries NV, Wijnegem, Belgium) for a few patients with cancer in the thorax and pelvis regions. A universal type carbon-fiber flat-top base plate (Orfit Industries NV, Wijnegem, Belgium) was used to fix the immobilization device during the CT simulation. For immobilization, Brain and H and N patients were secured using thermoplastic masks with 3 and 5-point fixation clamps, respectively, and with appropriate neck supports. Thorax and pelvis patients were immobilized using either vacuum cushions or 4-point thermoplastic masks with knee or ankle supports when necessary. The simulation was performed under the same treatment conditions (e.g., full bladder and empty rectum for pelvic cases) to ensure reproducibility during treatment delivery. After radiotherapy (RT) simulation, patients’ data were transferred to the treatment planning system (TPS) for RT planning. Treatments were planned using Eclipse^TM v.11.0.47 TPS (Varian Medical Systems, Palo Alto, CA, USA) and delivered using a 6-MV linear accelerator equipped with the EPID. The universal flat-top carbon-fiber base plate ensured consistent immobilization across imaging and treatment sessions.

Set up verification and imaging

Daily setup verification was performed using EPID, which acquires orthogonal images in the anterior-posterior and lateral directions. Deviations in three translational directions, i.e., lateral (R-L), superior-inferior (S-I), and anterior-posterior (A-P), were recorded. Portal images were automatically matched with digitally reconstructed radiographs (DRRs) from the planning CT, with manual adjustments made if needed. Deviations greater than 5 mm required patient repositioning and reimaging before treatment. For each patient, five fractions were analyzed, with the first two consecutive fractions imaged daily and subsequent fractions imaged weekly. A total of 800 portal images (10 images x 20 patients of each group of four sites) were registered across all treatment sites. The whole process of patient setup and imaging was done under the close observation of the medical physicist. Patient setup: first, patients were set on projections of wall-mounted lasers (in two laterals and one longitudinal direction) of the treatment room onto the fiducial marks given during simulation, and then shifted to the planning iso-center. After initial patient setup, two orthogonal portal images (PI) of setup fields in the anterior-posterior (AP) direction and lateral (LAT) direction were acquired using the EPID. Portal imaging was done by keeping the detector surface of EPID at 140 cm from the source and using the single exposure or double exposure feature (1-2 monitor units (MU)/field used). Image matching process: portal images (PI) were compared with corresponding digitally reconstructed radiographs (DRRs) generated from the planning CT. The automatic anatomy matching feature of Portal Vision software v1.6 (which is capable of calculating the difference between the intended and actual patient position in the three translational directions, such as lateral (R-L), longitudinal or superior-inferior (S-I), and vertical or anterior-posterior (A-P), specified by three Cartesian coordinates (X, Y, Z)) was used initially. For each patient, certain bony landmarks were chosen based on tumor location and contoured on DRR using a drawing tool feature; thereafter, matching was done by the radiation therapist.^[3] Radiation oncologists performed manual adjustments to align bony landmarks for fine-tuning if needed. Setup Error Recording: the deviations in the patient’s position for three translational directions: X(R-L), Y(S-I), and Z(A-P) were recorded. The rotational deviation was not accounted for in this study. The PI of the AP setup field was taken first, matched with DRR, and deviations in the X and Y directions were noted down. Next, the PI of the LAT setup field was taken, and the same matching process was repeated, and then deviations in the Y and Z directions were noted down. Shifts or calculated deviation in X, Y (deviation considered for either AP setup field or for LAT setup field, which one is larger), and Z direction were considered as daily setup shifts (Δx, Δy, Δz) in the R-L, S-I, and A-P directions, respectively, for a particular patient. Finally, treatment couch adjustment was done accordingly by applying the auto-calculated couch shifts, and treatment was completed.Imaging modality and limitations. Daily setup verification utilized EPID orthogonal images for bony-surrogate alignment due to their availability and workflow feasibility in our program.^[14,16,17] EPID does not visualize soft-tissue displacement nor quantify rotational errors; therefore, recorded setup errors represent translational components only. Organ motion, deformation, and rotations were not measured, which can bias Σ and σ downward in deformable or mobile sites (e.g., thorax, pelvis) and thus underestimate margins compared with CBCT/4D-based verification.^{[13,14,16,17]} These constraints were considered when interpreting site-specific margins.

Set up margin (SM) calculation

Statistical analysis

All statistical analyzes were conducted using Jeffrey’s Amazing Statistic Program (JASP) v0.19 software package (Netherlands).^[22] The normality of each setup error data set was checked quantitatively using the Shapiro-Wilk(S-W) test.^[23] Skewness and kurtosis analyzes were also done in addition to test normality.^[24] Histogram plots and Quantile-quantile (QQ) plots were used for qualitative validation of normality.^[21] Finally, a non-parametric paired test: the Wilcoxon signed-rank test, which is generally recommended for small, non-Gaussian samples^[25], was performed to compare conventional versus unconventional SMs. Medians^[26] and the effect size (Cohen’s d) values were calculated to correlate with clinical significance (> 1.0).^[27] Statistical significance was set at p-values < 0.05.

Conventional setup error and SM

The conventional setup errors for the population of patients were tabulated in [Table 1] (maximum values of systematic errors and random errors were highlighted). Maximum values of systematic errors were observed along the A-P direction for the brain case and along the S-I direction for all other sites. Similarly, maximum random errors were observed in the R-L direction for the pelvis case and along the S-I direction for other cases. Following the setup error calculation, setup margins (SM) were estimated using the conventional SM calculation formula given by van Herk’s methodology.^[7] As mentioned in the materials and methods section, the results were tabulated in [Table 2] (maximum values highlighted). The setup margins observed across the four tumorsites were highest for the thorax cases and lowest for the brain cases [Table 2].

Unconventional setup error and SM

Normality check

In this study, the setup data of the patient population wereanalyzedqualitatively and quantitatively to check normality. Tumorsite-wise, the means of daily shifts of setup across fractions for each patient in each direction (i.e., R-L, S-I, A-P) were considered for evaluation. To check the normality of the data qualitatively, histogram plots and corresponding Q-Q plots were evaluated for each site in each direction, as given in [Figure 1] (A. Brain, B. H and N,C. Thorax, D. Pelvis). By visual inspection of the histograms and Q-Q plots, it can be noted that the histograms are not symmetric and not at all bell-shaped, whereas the data points are mostly semi-linear in the Q-Q plots.

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Figure 1:

Histogram plots and Q-Q plots of shifts (daily setup deviation) across three translational directions (Lateral, Longitudinal and Transverse) for Brain, Head and Neck, Thorax, and Pelvis sites: contains a combined plot for (A) Brain, (B) Head and Neck, (C) Thorax, (D) Pelvis sites showing (a) Histograms with Gaussian fit and corresponding (b) probability plots (Q-Q plots) for Lateral shifts (R-L), Longitudinal shifts (S-I), and Transverse shifts (A-P) respectively. Theoretical quantiles are plotted against sample quantiles in Q-Q plots to assess normality for each site in three translational directions. Large deviations from the diagonal line indicate non-normality. Note: Shifts: R-L (Lateral), S-I (Longitudinal), and A-P (Transverse) represent the three translational directions of setup adjustments. For each patient, the mean daily shifts across all fractions were calculated for each translational direction (R-L, S-I, A-P). This resulted in a total of 12 datasets (3 axes × 4 tumor sites), three for each treatment site. Hence, histograms and Q-Q plots of these 12 datasets were obtained. Gaussian Fit: the smooth curve fitted over the histogram represents the best-fitting normal distribution for the observed data. Theoretical Quantiles: Represent the expected values of a perfectly normal distribution. Sample Quantiles: Derived from the observed data. H:Head, N:Neck, Q-Q: Quantile-quantile

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Conventional versus Unconventional SM

The largest values of conventional SMs(using van Herk’s formalism) among three translational directions (i.e. R-L, S-I, A-P) across all tumor sites differ by 1.65 mm for the brain case, 1.94 mm for the H and N case, 3.63 mm for the thorax case, and 2.74 mm for the pelvis case in comparison with the unconventional SMs by comparing values from Tables 2 and 4. However, the largest values of conventional SMs for all the tumor sites except the pelvis case were observed in the S-I direction, whereas for the unconventional SMs, the highest values were observed in the S-I direction for all the sites. Also, the unconventional SM was highest for the thorax and least for the brain case, similar to the observation of the conventional methods (i.e., Thorax>Pelvis>H and N>Brain). A non-parametric paired test, i.e. Wilcoxon signed rank test,which is generally recommended to test two methods without assuming normality.^[25] The statistical comparison of SMs estimated by the unconventional methodand the conventional method was tabulated in Table 5. For skewed setup error distributions found in this study, the median was prioritized over the mean as a measure of central tendency, as it is less influenced by outliers.^[20] This aligns with recommendations for analyzing non-Gaussian data in clinical studies.^[26] Therefore, median values of SMs for each translational direction (R-L, S-I, A-P) across all tumor sites,along with p-values, are given in Table 5. Median values of setup margins across all tumor sites and directions for the conventional method were 2.71 mm,whereas for the unconventional method, it was 4.21 mm.Comparison results were found statistically significant (p<0.05) except for the pelvis (A-P) case, and also the effect size (i.e., the difference between two means divided by pooled standard deviation, which translates statistical significance (p-value) into clinical relevance). Cohen’s d > 1 implies a large practical difference between methods.^[27]

Systematic and random errors

Systematic setup errors calculated using the conventional method are less than 1 mm across all the tumor sites in this work [Table 1], which is similar to the previously reported EPID-based studies.^[32-35] The maximum random errors for the brain, H and N, and pelvis cases found in this work [Table 1] are also comparable to the previous EPID-based studies.^[36-38] However, for the thorax case, the maximum random error observed was 5.02 mm, which is larger compared to similar EPID-based studies.^[32,39] Differences in results for random errors for the thorax may arise due to the differences in the expertise of individual radiation professionals.^[28]

Conventional setup margins

The maximum conventional SMs for the brain, H and N, thorax,and pelvis cases [Table 2] found in this study are similar to the EPID-based multi-site study.^[33] However, the results of the current study [Table 2] slightly differ from some other EPID-based single-site studies.^[35-38] The small differences observed with other EPID-based studies may arise due to various factors such as institute-specific imaging protocol, individual experience or expertise, type of imaging modality,andimmobilization.^{[28,29,31,40]} To find specific reasons, a robust and specific study may be needed, which was out of the scope of the present study. Moreover, results for the conventional margin analysis of the current study [Table 2] agree with CBCT-based previous studies^[41,42] in the case of brain or H and N sites, but for the thorax or pelvis sites, SMs are smaller comparatively.Margins for the thorax or pelvis may be underestimated in the present EPID-based measurement due to the non-accountability of organ motion and rotational inaccuracy, which are more reliable and understandable in CBCT-based imaging.^[13]

Normality test

Conventional methods of setup margin calculation assume that setup errors are distributed normally^[4], Where as the unconventional method does not assume that setup errors are necessarily normally distributed.^[10] The result of the S-W test [Table 3a] is statistically insignificant as the p-values are more than 0.05 except for the brain (R-L) case, thorax (A-P) case, and pelvis (A-P) case.However,samples from a normal population distribution do not necessarily appear normal, especially when the sample size is small.^[21,43] Therefore, with the small data size evaluated in this work, it may be difficult to decide whether the data is normally distributed or not solely by the S-W statistics. In such a situation, a quantitative assessment of the skewness and kurtosis of the distribution and visual inspections using histograms and Q-Q plots, in addition, may be useful to determine the normality of the data.^[21,24] The skew values and excess kurtosis values (i.e., kurtosis minus three) as given in Table 3b differed from their ideal values or reference values stated,^[24] Indicating that the setup data sets deviate from normality. Moreover, by visual inspection of the histograms and Q-Q plots, it can be noted that histograms are not symmetric and not at all bell-shaped, whereas data points are mostly semi-linear in Q-Q plots [Figure 1]. Therefore, the setup error data sets in the present work do not necessarily belong to a normal distribution and hence, are eligible for unconventional margin estimation.

Unconventional setup margins

This study expands on the methodology proposed by Suzuki et al.^[10], with key differences in imaging techniques, sample cancer cohort, which may be considered as a larger sample size, offering strong statistical robustness. In comparison, this study analyzed 200 images per group, which may have impacted the statistical results for normality and contributed to semi-linearity in Q-Q plots.^[21] Another notable methodological divergence is data correction: Suzuki et al.^[10] Adjusted their setup data by subtracting systematic sizes, and analytical approaches. Suzuki et al.^[10] employed kilo-voltage (KV) imaging, integrating x-ray and optical infrared tracking for setup verification, while our study used a megavoltage (MV) Electronic Portal Imaging Device (EPID), which is widely available in routine clinical settings, especially in low-resource environments and smaller clinics.^[44] Suzuki et al.^[10] Analyzed 555 setup images for a prostate errors before constructing histograms, whereas we used uncorrected daily average shifts to generate histograms [Figure 1] and directly compute 90% ranges of setup errors (RSE). Further, in this work, unconventional setup margins (SMs) were compared against the conventional SMs, which were calculated using the 90% population-based van Herk’s method.^[4] To ensure consistency, 90%RSE values were used in the unconventional SM estimations, whereas Suzuki et al.^[10] used 95% RSEs. These methodological differences likely explain the lower unconventional SMs reported in the present study compared to Suzuki et al. ^[10] However, this direct comparison may not be enough because the present study is a multi-site evaluation, and unconventional setup margins (i.e., 90% RSEs) were compared with the existing conventional setup margins recipes, whereas Suzuki et al.^[10] Compared the 95% RSEs with the 95% CI of the normal distribution for a specific tumorsite (prostate case only).

Conventional versus unconventional SMs

A statistical comparison [Table 5] between the unconventional SM approach and the conventional SM formalism (van Herk’s) was performed in this study using the Wilcoxon signed-rank test(a non-parametric paired test). Although the pattern of SMs (i.e., SMs for Thorax > Pelvis > H and N >Brain cases) is the same for both types of methods, which (i.e., pattern) agrees with previous studies^[42,43], it can be observed from [Table 5] that the higher z-scores were obtained, which indicates stronger evidence against the null hypothesis (no difference). Hence, quantifies the magnitude of difference between the two methods (unconventional vs. conventional). It was found that error distributions are skewed in this study; hence, the median was prioritized over the mean as a measure of central tendency.^[26] The differences in the median values for SMs [Table 5] indicate that the conventional method underestimates the setup margins compared to the unconventional method, with statistically significant results (p<0.05) in the present study. However, Cohen’s d values are reported for completeness, but a large effect size value (Cohen’s d) > 1.0 does not necessarily imply clinical importance To separate statistical from clinical importance, we pre-specified a clinically meaningful difference in margin as ≥ 2 mm, consistent with common IGRT precision considerations and the population-coverage objective underlying margin recipes Inferences about clinical relevance were based primarily on the pre-specified ≥ 2 mm threshold and anatomical context (dose fall-off near the PTV edge, proximity of OARs, and risk of target under-coverage), rather than on effect-size magnitude alone. Using this criterion, differences meeting ≥ 2 mm were observed for thorax S–I (Δ = 3.63 mm), pelvis S–I (Δ = 2.90 mm), and pelvis R–L (Δ = 2.17 mm); other site-direction pairs showed smaller discrepancies (< 2 mm). The median values of setup margins across tumor sites and direction evaluated by these two types of methods (unconventional vs conventional) differ by 1.5 mm,which may result in insufficient target coverage or excess dose to surrounding organs and hence impact clinical outcomes. However, in this EPID-based geometric uncertainty analysis, systematic (Ʃ) and random (σ) errors were defined exclusively as systematic and random setup errors, respectively, when applying van Herk’s margin formalism as discussed in the materials and methods section. Portal images capture the combined effects of setup errors and phantom transfer error, but not delineation error or organ motion error, as the organ itself is not visible in portal images.^[12] This simplification introduces a limitation, as delineation error and organ motion error—neither measured nor included using literature references in this study—were excluded from conventional setup margin calculations and may have influenced the difference in SMs (unconventional vs. conventional).

The primary outcome of this study shows that SMs derived from conventional methods underestimate the margins when setup error data do not follow a normal distribution, as observed in this study. Moreover, the current estimation of EPID-based setup margins using the unconventional method is closer to or comparable to the results of advanced imaging modality (CBCT) based studies.^[41,42] One of the most important advantages of the unconventional method is its adaptability to various data distributions. The 90% RSE approach, which does not rely on normality assumptions, inherently accommodates extreme values, offering a conservative estimate that safeguards against under-dosing. This attribute makes the unconventional method a viable option in resource-limited clinical environments, where patient data may be limited, or for early-phase clinical trials where standardizing setup procedures across a smaller cohort is challenging.In that sense, it may be stated that the unconventional method is more appropriate and practically useful when compared to the conventional method, where setup data is not normally distributed or in a situation where a smaller number of patient data is considered or available. However, the unconventional method used in this study is a statistical-geometrical methodology that depends more on the extremes (i.e., 5% and 95% edges) of the population distribution,whereas the conventional methods are based on either dose coverage probability or dose-population-based methodology, which considers the concept of finite penumbra width.^[4,7] EPID captures bony, translational shifts only and does not quantify soft-tissue motion/deformation or rotations; true uncertainty—particularly in thorax/pelvis— may therefore be underestimated, and these unmeasured components likely explain part of the larger unconventional margins observed here.Moreover, EPID-based measurements may be considered inferior when compared to other high-end techniques like CBCT-based measurements.^[45] These points may be considered as the limitations of the present work—practical adoption. In practice, we recommend using the unconventional percentile margin anisotropically where Δ ≥ 2 mm—in our cohort, thorax S–I and pelvis S–I/R–L—to safeguard CTV coverage in heavy-tail directions better while avoiding unnecessary expansion elsewhere. Therefore, to validate the appropriateness of the unconventional method over the conventional methods, more rigorous and robust investigations will be required.