Denoising Your Monte Carlo Renders: Recent Advances in Image Space-Adaptive Sampling and Reconstruction

With the ongoing shift in the computer graphics industry toward Monte Carlo rendering, there is a need for effective, practical noise-reduction techniques that are applicable to a wide range of rendering effects and easily integrated into existing production pipelines. This course surveys recent advances in image-space adaptive sampling and reconstruction algorithms for noise reduction, which have proven very effective at reducing the computational cost of Monte Carlo techniques in practice. These approaches leverage advanced image-filtering techniques with statistical methods for error estimation. They are attractive because they can be integrated easily into conventional Monte Carlo rendering frameworks, they are applicable to most rendering effects, and their computational overhead is modest.

Prophylactic mastectomy and oophorectomy for women at risk of breast and ovarian cancer: Incorporating preferences in a decision analysis

The discoveries of the BRCA1 and BRCA2 genes have made it possible for women of families with hereditary breast/ovarian cancer to determine if they carry cancer-predisposing genetic mutations. Women with germline mutations have significantly higher probabilities of developing both cancers than the general population. Since the presence of a BRCA1 or BRCA2 mutation does not guarantee future cancer development, the appropriate course of action remains uncertain for these women. Prophylactic mastectomy and oophorectomy remain controversial since the underlying premise for surgical intervention is based more upon reduction in the estimated risk of cancer than on actual evidence of clinical benefit. Issues that are incorporated in a woman's decision making process include quality of life without breasts, ovaries, attitudes toward possible surgical morbidity as well as a remaining risk of future development of breast/ovarian cancer despite prophylactic surgery. The incorporation of patient preferences into decision analysis models can determine the quality-adjusted survival of different prophylactic approaches to breast/ovarian cancer prevention. Monte Carlo simulation was conducted on 4 separate decision models representing prophylactic oophorectomy, prophylactic mastectomy, prophylactic oophorectomy/mastectomy and screening. The use of 3 separate preference assessment methods across different populations of women allows researchers to determine how quality adjusted survival varies according to clinical strategy, method of preference assessment and the population from which preferences are assessed. ^

A 3-D CT assisted Monte Carlo evaluation of intracavitary brachytherapy implants

Intracavitary brachytherapy (ICB) combined with external beam irradiation for treatment of cervical cancer is highly successful in achieving local control. The M.D. Anderson Cancer Center employs Fletcher Suit Delclos (FSD) applicators. FSD applicators contain shields to limit dose to critical structures. Dosimetric evaluation of ICB implants is limited to assessing dose at reference points. These points serve as surrogates for treatment intensity and critical structure dose. Several studies have mentioned that the ICRU38 reference points inadequately characterize the dose distribution. Also, the ovoid shields are rarely considered in dosimetry. ^ The goal of this dissertation was to ascertain the influence of the ovoid shields on patient dose distributions. Monte Carlo dosimetry (MCD) was applied to patient computed tomography(CT) scans. These data were analyzed to determine the effect of the shields on dose to standard reference points and the bladder and rectum. The hypothesis of this work is that the ICRU38 bladder and rectal points computed conventionally are not clinically acceptable surrogates for the maximum dose points as determined by MCD. ^ MCD was applied to the tandem and ovoids. The FSD ovoids and tandem were modeled in a single input file that allowed dose to be calculated for any patient. Dose difference surface histograms(DDSH) were computed for the bladder and rectum. Reference point doses were compared between shielded and unshielded ovoids, and a commercial treatment planning system. ^ The results of this work showed the tandem tip screw caused a 33% reduction in dose. The ovoid shields reduced the dose by a maximum of 48.9%. DDSHs revealed on average 5% of the bladder surface area was spared 53 cGy and 5% of the rectal surface area was spared 195 cGy. The ovoid shields on average reduced the dose by 18% for the bladder point and 25% for the rectal point. The Student's t-test revealed the ICRU38 bladder and rectal points do not predict the maximum dose for these organs. ^ It is concluded that modeling the tandem and ovoid internal structures is necessary for accurate dose calculations, the bladder shielding segments may not be necessary, and that the ICRU38 bladder point is irrelevant. ^

Verification of intensity modulated stereotactic radiotherapy using Monte Carlo calculations and EPID dosimetry

The purpose of this work was to develop a comprehensive IMSRT QA procedure that examined, using EPID dosimetry and Monte Carlo (MC) calculations, each step in the treatment planning and delivery process. These steps included verification of the field shaping, treatment planning system (RTPS) dose calculations, and patient dose delivery. Verification of each step in the treatment process is assumed to result in correct dose delivery to the patient. ^ The accelerator MC model was verified against commissioning data for field sizes from 0.8 × 0.8 cm 2 to 10 × 10 cm 2. Depth doses were within 2% local percent difference (LPD) in low gradient regions and 1 mm distance to agreement (DTA) in high gradient regions. Lateral profiles were within 2% LPD in low gradient regions and 1 mm DTA in high gradient regions. Calculated output factors were within 1% of measurement for field sizes ≥1 × 1 cm2. ^ The measured and calculated pretreatment EPID dose patterns were compared using criteria of 5% LPD, 1 mm DTA, or 2% of central axis pixel value with ≥95% of compared points required to pass for successful verification. Pretreatment field verification resulted in 97% percent of the points passing. ^ The RTPS and Monte Carlo phantom dose calculations were compared using 5% LPD, 2 mm DTA, or 2% of the maximum dose with ≥95% of compared points required passing for successful verification. RTPS calculation verification resulted in 97% percent of the points passing. ^ The measured and calculated EPID exit dose patterns were compared using criteria of 5% LPD, 1 mm DTA, or 2% of central axis pixel value with ≥95% of compared points required to pass for successful verification. Exit dose verification resulted in 97% percent of the points passing. ^ Each of the processes above verified an individual step in the treatment planning and delivery process. The combination of these verification steps ensures accurate treatment delivery to the patient. This work shows that Monte Carlo calculations and EPID dosimetry can be used to quantitatively verify IMSRT treatments resulting in improved patient care and, potentially, improved clinical outcome. ^

Monte Carlo and analytical dose calculations for ocular proton therapy

Uveal melanoma is a rare but life-threatening form of ocular cancer. Contemporary treatment techniques include proton therapy, which enables conservation of the eye and its useful vision. Dose to the proximal structures is widely believed to play a role in treatment side effects, therefore, reliable dose estimates are required for properly evaluating the therapeutic value and complication risk of treatment plans. Unfortunately, current simplistic dose calculation algorithms can result in errors of up to 30% in the proximal region. In addition, they lack predictive methods for absolute dose per monitor unit (D/MU) values. ^ To facilitate more accurate dose predictions, a Monte Carlo model of an ocular proton nozzle was created and benchmarked against measured dose profiles to within ±3% or ±0.5 mm and D/MU values to within ±3%. The benchmarked Monte Carlo model was used to develop and validate a new broad beam dose algorithm that included the influence of edgescattered protons on the cross-field intensity profile, the effect of energy straggling in the distal portion of poly-energetic beams, and the proton fluence loss as a function of residual range. Generally, the analytical algorithm predicted relative dose distributions that were within ±3% or ±0.5 mm and absolute D/MU values that were within ±3% of Monte Carlo calculations. Slightly larger dose differences were observed at depths less than 7 mm, an effect attributed to the dose contributions of edge-scattered protons. Additional comparisons of Monte Carlo and broad beam dose predictions were made in a detailed eye model developed in this work, with generally similar findings. ^ Monte Carlo was shown to be an excellent predictor of the measured dose profiles and D/MU values and a valuable tool for developing and validating a broad beam dose algorithm for ocular proton therapy. The more detailed physics modeling by the Monte Carlo and broad beam dose algorithms represent an improvement in the accuracy of relative dose predictions over current techniques, and they provide absolute dose predictions. It is anticipated these improvements can be used to develop treatment strategies that reduce the incidence or severity of treatment complications by sparing normal tissue. ^

Outcome-based adaptive randomization for binary data in clinical trials---Compare and contrast

Monte Carlo simulation has been conducted to investigate parameter estimation and hypothesis testing in some well known adaptive randomization procedures. The four urn models studied are Randomized Play-the-Winner (RPW), Randomized Pôlya Urn (RPU), Birth and Death Urn with Immigration (BDUI), and Drop-the-Loses Urn (DL). Two sequential estimation methods, the sequential maximum likelihood estimation (SMLE) and the doubly adaptive biased coin design (DABC), are simulated at three optimal allocation targets that minimize the expected number of failures under the assumption of constant variance of simple difference (RSIHR), relative risk (ORR), and odds ratio (OOR) respectively. Log likelihood ratio test and three Wald-type tests (simple difference, log of relative risk, log of odds ratio) are compared in different adaptive procedures. ^ Simulation results indicates that although RPW is slightly better in assigning more patients to the superior treatment, the DL method is considerably less variable and the test statistics have better normality. When compared with SMLE, DABC has slightly higher overall response rate with lower variance, but has larger bias and variance in parameter estimation. Additionally, the test statistics in SMLE have better normality and lower type I error rate, and the power of hypothesis testing is more comparable with the equal randomization. Usually, RSIHR has the highest power among the 3 optimal allocation ratios. However, the ORR allocation has better power and lower type I error rate when the log of relative risk is the test statistics. The number of expected failures in ORR is smaller than RSIHR. It is also shown that the simple difference of response rates has the worst normality among all 4 test statistics. The power of hypothesis test is always inflated when simple difference is used. On the other hand, the normality of the log likelihood ratio test statistics is robust against the change of adaptive randomization procedures. ^

Bayesian and survival model for tumor relapse status and disease-specific survival, with applications to breast cancer

Breast cancer is the most common non-skin cancer and the second leading cause of cancer-related death in women in the United States. Studies on ipsilateral breast tumor relapse (IBTR) status and disease-specific survival will help guide clinic treatment and predict patient prognosis.^ After breast conservation therapy, patients with breast cancer may experience breast tumor relapse. This relapse is classified into two distinct types: true local recurrence (TR) and new ipsilateral primary tumor (NP). However, the methods used to classify the relapse types are imperfect and are prone to misclassification. In addition, some observed survival data (e.g., time to relapse and time from relapse to death)are strongly correlated with relapse types. The first part of this dissertation presents a Bayesian approach to (1) modeling the potentially misclassified relapse status and the correlated survival information, (2) estimating the sensitivity and specificity of the diagnostic methods, and (3) quantify the covariate effects on event probabilities. A shared frailty was used to account for the within-subject correlation between survival times. The inference was conducted using a Bayesian framework via Markov Chain Monte Carlo simulation implemented in softwareWinBUGS. Simulation was used to validate the Bayesian method and assess its frequentist properties. The new model has two important innovations: (1) it utilizes the additional survival times correlated with the relapse status to improve the parameter estimation, and (2) it provides tools to address the correlation between the two diagnostic methods conditional to the true relapse types.^ Prediction of patients at highest risk for IBTR after local excision of ductal carcinoma in situ (DCIS) remains a clinical concern. The goals of the second part of this dissertation were to evaluate a published nomogram from Memorial Sloan-Kettering Cancer Center, to determine the risk of IBTR in patients with DCIS treated with local excision, and to determine whether there is a subset of patients at low risk of IBTR. Patients who had undergone local excision from 1990 through 2007 at MD Anderson Cancer Center with a final diagnosis of DCIS (n=794) were included in this part. Clinicopathologic factors and the performance of the Memorial Sloan-Kettering Cancer Center nomogram for prediction of IBTR were assessed for 734 patients with complete data. Nomogram for prediction of 5- and 10-year IBTR probabilities were found to demonstrate imperfect calibration and discrimination, with an area under the receiver operating characteristic curve of .63 and a concordance index of .63. In conclusion, predictive models for IBTR in DCIS patients treated with local excision are imperfect. Our current ability to accurately predict recurrence based on clinical parameters is limited.^ The American Joint Committee on Cancer (AJCC) staging of breast cancer is widely used to determine prognosis, yet survival within each AJCC stage shows wide variation and remains unpredictable. For the third part of this dissertation, biologic markers were hypothesized to be responsible for some of this variation, and the addition of biologic markers to current AJCC staging were examined for possibly provide improved prognostication. The initial cohort included patients treated with surgery as first intervention at MDACC from 1997 to 2006. Cox proportional hazards models were used to create prognostic scoring systems. AJCC pathologic staging parameters and biologic tumor markers were investigated to devise the scoring systems. Surveillance Epidemiology and End Results (SEER) data was used as the external cohort to validate the scoring systems. Binary indicators for pathologic stage (PS), estrogen receptor status (E), and tumor grade (G) were summed to create PS+EG scoring systems devised to predict 5-year patient outcomes. These scoring systems facilitated separation of the study population into more refined subgroups than the current AJCC staging system. The ability of the PS+EG score to stratify outcomes was confirmed in both internal and external validation cohorts. The current study proposes and validates a new staging system by incorporating tumor grade and ER status into current AJCC staging. We recommend that biologic markers be incorporating into revised versions of the AJCC staging system for patients receiving surgery as the first intervention.^ Chapter 1 focuses on developing a Bayesian method to solve misclassified relapse status and application to breast cancer data. Chapter 2 focuses on evaluation of a breast cancer nomogram for predicting risk of IBTR in patients with DCIS after local excision gives the statement of the problem in the clinical research. Chapter 3 focuses on validation of a novel staging system for disease-specific survival in patients with breast cancer treated with surgery as the first intervention. ^

Standard Errors for the Blinder-Oaxaca Decomposition

The decomposition technique introduced by Blinder (1973) and Oaxaca (1973) is widely used to study outcome differences between groups. For example, the technique is commonly applied to the analysis of the gender wage gap. However, despite the procedure's frequent use, very little attention has been paid to the issue of estimating the sampling variances of the decomposition components. We therefore suggest an approach that introduces consistent variance estimators for several variants of the decomposition. The accuracy of the new estimators under ideal conditions is illustrated with the results of a Monte Carlo simulation. As a second check, the estimators are compared to bootstrap results obtained using real data. In contrast to previously proposed statistics, the new method takes into account the extra variation imposed by stochastic regressors.

Object Kinetic Monte Carlo calculations of irradiated Fe-Cr dilute alloys: The effect of the interaction radius between substitutional Cr and self-interstitial Fe

ObjectKineticMonteCarlo models allow for the study of the evolution of the damage created by irradiation to time scales that are comparable to those achieved experimentally. Therefore, the essential ObjectKineticMonteCarlo parameters can be validated through comparison with experiments. However, this validation is not trivial since a large number of parameters is necessary, including migration energies of point defects and their clusters, binding energies of point defects in clusters, as well as the interactionradii. This is particularly cumbersome when describing an alloy, such as the Fe–Cr system, which is of interest for fusion energy applications. In this work we describe an ObjectKineticMonteCarlo model for Fe–Cr alloys in the dilute limit. The parameters used in the model come either from density functional theory calculations or from empirical interatomic potentials. This model is used to reproduce isochronal resistivity recovery experiments of electron irradiateddiluteFe–Cr alloys performed by Abe and Kuramoto. The comparison between the calculated results and the experiments reveal that an important parameter is the capture radius between substitutionalCr and self-interstitialFe atoms. A parametric study is presented on the effect of the capture radius on the simulated recovery curves.

The Risk of Using the Q Heterogeneity Estimator for Software Engineering Experiments

All meta-analyses should include a heterogeneity analysis. Even so, it is not easy to decide whether a set of studies are homogeneous or heterogeneous because of the low statistical power of the statistics used (usually the Q test). Objective: Determine a set of rules enabling SE researchers to find out, based on the characteristics of the experiments to be aggregated, whether or not it is feasible to accurately detect heterogeneity. Method: Evaluate the statistical power of heterogeneity detection methods using a Monte Carlo simulation process. Results: The Q test is not powerful when the meta-analysis contains up to a total of about 200 experimental subjects and the effect size difference is less than 1. Conclusions: The Q test cannot be used as a decision-making criterion for meta-analysis in small sample settings like SE. Random effects models should be used instead of fixed effects models. Caution should be exercised when applying Q test-mediated decomposition into subgroups.

Comparative analysis of meta-analysis methods: when to use which?

Background: Several meta-analysis methods can be used to quantitatively combine the results of a group of experiments, including the weighted mean difference, statistical vote counting, the parametric response ratio and the non-parametric response ratio. The software engineering community has focused on the weighted mean difference method. However, other meta-analysis methods have distinct strengths, such as being able to be used when variances are not reported. There are as yet no guidelines to indicate which method is best for use in each case. Aim: Compile a set of rules that SE researchers can use to ascertain which aggregation method is best for use in the synthesis phase of a systematic review. Method: Monte Carlo simulation varying the number of experiments in the meta analyses, the number of subjects that they include, their variance and effect size. We empirically calculated the reliability and statistical power in each case Results: WMD is generally reliable if the variance is low, whereas its power depends on the effect size and number of subjects per meta-analysis; the reliability of RR is generally unaffected by changes in variance, but it does require more subjects than WMD to be powerful; NPRR is the most reliable method, but it is not very powerful; SVC behaves well when the effect size is moderate, but is less reliable with other effect sizes. Detailed tables of results are annexed. Conclusions: Before undertaking statistical aggregation in software engineering, it is worthwhile checking whether there is any appreciable difference in the reliability and power of the methods. If there is, software engineers should select the method that optimizes both parameters.