Distinct error rates for reference and nonreference genotypes estimated by pedigree analysis

Errors in genotype calling can have perverse effects on genetic analyses, confounding association studies, and obscuring rare variants. Analyses now routinely incorporate error rates to control for spurious findings. However, reliable estimates of the error rate can be difficult to obtain because of their variance between studies. Most studies also report only a single estimate of the error rate even though genotypes can be miscalled in more than one way. Here, we report a method for estimating the rates at which different types of genotyping errors occur at biallelic loci using pedigree information. Our method identifies potential genotyping errors by exploiting instances where the haplotypic phase has not been faithfully transmitted. The expected frequency of inconsistent phase depends on the combination of genotypes in a pedigree and the probability of miscalling each genotype. We develop a model that uses the differences in these frequencies to estimate rates for different types of genotype error. Simulations show that our method accurately estimates these error rates in a variety of scenarios. We apply this method to a dataset from the whole-genome sequencing of owl monkeys (Aotus nancymaae) in three-generation pedigrees. We find significant differences between estimates for different types of genotyping error, with the most common being homozygous reference sites miscalled as heterozygous and vice versa. The approach we describe is applicable to any set of genotypes where haplotypic phase can reliably be called and should prove useful in helping to control for false discoveries.     

Shared uncertainty in measurement error problems, with application to Nevada Test Site fallout data

In radiation epidemiology, it is often necessary to use mathematical models in the absence of direct measurements of individual doses. When complex models are used as surrogates for direct measurements to estimate individual doses that occurred almost 50 years ago, dose estimates will be associated with considerable error, this error being a mixture of (a) classical measurement error due to individual data such as diet histories and (b) Berkson measurement error associated with various aspects of the dosimetry system. In the Nevada Test Site(NTS) Thyroid Disease Study, the Berkson measurement errors are correlated within strata. This article concerns the development of statistical methods for inference about risk of radiation dose on thyroid disease, methods that account for the complex error structure inherence in the problem. Bayesian methods using Markov chain Monte Carlo and Monte-Carlo expectation-maximization methods are described, with both sharing a key Metropolis-Hastings step. Regression calibration is also considered, but we show that regression calibration does not use the correlation structure of the Berkson errors. Our methods are applied to the NTS Study, where we find a strong dose-response relationship between dose and thyroiditis. We conclude that full consideration of mixtures of Berkson and classical uncertainties in reconstructed individual doses are important for quantifying the dose response and its credibility/confidence interval. Using regression calibration and expectation values for individual doses can lead to a substantial underestimation of the excess relative risk per gray and its 95% confidence intervals.     

Improved error detection using a divided treatment plan in volume modulated arc therapy

AimWe sought to improve error detection ability during volume modulated arc therapy (VMAT) by dividing and evaluating the treatment plan.BackgroundVMAT involves moving a beam source delivering radiation to tumor tissue through an arc, which significantly decreases treatment time. Treatment planning for VMAT involves many parameters. Quality assurance before treatment is a major focus of research.Materials and methodsWe used an established VMAT prostate treatment plan and divided it into 12° × 30° sections. In all the sections, only image data that generated errors in one segment and those that were integrally acquired were evaluated by a gamma analysis. This was done with five different patient plans.ResultsThe integrated image data resulting from errors in each section was 100% (tolerance 0.5 mm/0.5%) in the gamma analysis result in all image data. Division of the treatment plans produced a shift in the mean value of each gamma analysis in the cranial, left, and ventral directions of 94.59%, 98.83%, 96.58%, and the discrimination ability improved.ConclusionThe error discrimination ability was improved by dividing and verifying the portal imaging.     

Radiomics analysis of EPID measurements for patient positioning error detection in thyroid associated ophthalmopathy radiotherapy

PurposeElectronic portal imaging detector (EPID)-based patient positioning verification is an important component of safe radiotherapy treatment delivery. In computer simulation studies, learning-based approaches have proven to be superior to conventional gamma analysis in the detection of positioning errors. To approximate a clinical scenario, the detectability of positioning errors via EPID measurements was assessed using radiomics analysis for patients with thyroid-associated ophthalmopathy.MethodsTreatment plans of 40 patients with thyroid-associated ophthalmopathy were delivered to a solid anthropomorphic head phantom. To simulate positioning errors, combinations of 0-, 2-, and 4-mm translation errors in the left–right (LR), superior-inferior (SI), and anterior-posterior (AP) directions were introduced to the phantom. The positioning errors-induced dose differences between measured portal dose images were used to predict the magnitude and direction of positioning errors. The detectability of positioning errors was assessed via radiomics analysis of the dose differences. Three classification models—support vector machine (SVM), k-nearest neighbors (KNN), and XGBoost—were used for the detection of positioning errors (positioning errors larger or smaller than 3 mm in an arbitrary direction) and direction classification (positioning errors larger or smaller than 3 mm in a specific direction). The receiver operating characteristic curve and the area under the ROC curve (AUC) were used to evaluate the performance of classification models.ResultsFor the detection of positioning errors, the AUC values of SVM, KNN, and XGBoost models were all above 0.90. For LR, SI, and AP direction classification, the highest AUC values were 0.76, 0.91, and 0.80, respectively.ConclusionsCombined radiomics and machine learning approaches are capable of detecting the magnitude and direction of positioning errors from EPID measurements. This study is a further step toward machine learning-based positioning error detection during treatment delivery with EPID measurements.     

Comparison of three commercial dosimetric systems in detecting clinically significant VMAT delivery errors

AimTo study the sensitivity of three commercial dosimetric systems, Delta4, Multicube and Octavius4D, in detecting Volumetric Modulated Arc Therapy (VMAT) delivery errors.MethodsFourteen prostate and head and neck (H&N) VMAT plans were considered for this study. Three types of errors were introduced into the original plans: gantry angle independent and dependent MLC errors, and gantry angle dependent dose errors. The dose matrix measured by each detector system for the no-error and error introduced delivery were compared with the reference Treatment Planning System (TPS) calculated dose matrix for no-error plans using gamma (γ) analysis with 2%/2 mm tolerance criteria. The ability of the detector system in identifying the minimum error in each scenario was assessed by analysing the gamma pass rates of no error delivery and error delivery using a Wilcoxon signed-rank test. The relative sensitivity of the system was assessed by determining the slope of the gamma pass line for studied error magnitude in each error scenario.ResultsIn the gantry angle independent and dependent MLC error scenario the Delta4, Multicube and Octavius4D systems detected a minimum 2 mm error. In the gantry angle dependent dose error scenario all studied systems detected a minimum 3% and 2% error in prostate and H&N plans respectively. In the studied detector systems Multicube showed relatively less sensitivity to the errors in the majority of error scenarios.ConclusionThe studied systems identified the same magnitude of minimum errors in all considered error scenarios.     

Bias and error in using survey records for ponderosa pine landscape restoration

Aim Public land survey records are commonly used to reconstruct historical forest structure over large landscapes. Reconstruction studies have been criticized for using absolute measures of forest attributes, such as density and basal area, because of potential selection bias by surveyors and unknown measurement error. Current methods to identify bias are based upon statistical techniques whose assumptions may be violated for survey data. Our goals were to identify and directly estimate common sources of bias and error, and to test the accuracy of statistical methods to identify them. Location Forests in the western USA: Mogollon Plateau, Arizona; Blue Mountains, Oregon; Front Range, Colorado. Methods We quantified both selection bias and measurement error for survey data in three ponderosa pine landscapes by directly comparing measurements of bearing trees in survey notes with remeasurements of bearing trees at survey corners (384 corners and 812 trees evaluated). Results Selection bias was low in all areas and there was little variability among surveyors. Surveyors selected the closest tree to the corner 95% to 98% of the time, and hence bias may have limited impacts on reconstruction studies. Bourdo’s methods were able to successfully detect presence or absence of bias most of the time, but do not measure the rate of bias. Recording and omission errors were common but highly variable among surveyors. Measurements for bearing trees made by surveyors were generally accurate. Most bearings were less than 5° in error and most distances were within 5% of our remeasurements. Many, but not all, surveyors in the western USA probably estimated diameter of bearing trees at stump height (0.3 m). These estimates deviated from reconstructed diameters by a mean absolute error of 7.0 to 10.6 cm. Main conclusions Direct comparison of survey data at relocated corners is the only method that can determine if bias and error are meaningful. Data from relocated trees show that biased selection of trees is not likely to be an important source of error. Many surveyor errors would have no impact on reconstruction studies, but omission errors have the potential to have a large impact on results. We suggest how to reduce potential errors through data screening.     

Consideration of a priori information and type of an experimental error using the method of system identification based on the minimal quadratic discrepancy criterion

The variants of the identification method were considered that take the a priori information about the evolution of a system under study and the type of experimental errors of the dynamic parameters of the system into account. An example of using this method for the identification of a biochemical reaction is given where the error in measuring the dynamic parameters (concentration of substances) has both an absolute and a relative components.     

Delivering RapidArc®: A comprehensive study on accuracy and long term stability

PurposeTo establish the reliability and accuracy of a UNIQUE Linac in delivering RapidArc treatments and assess its long term stability.Materials and methodsUNIQUE performance was monitored and analyzed for a period of nearly two years. 2280 Dynalog files, related to 179 clinical RapidArc treatments were collected. Different tumor sites and dose scheduling were included, covering the full range of our treatment plans. Statistical distributions of MLC motion error, gantry rotation error and MU delivery error were evaluated. The stochastic and systematic nature of each error was investigated together with their variation in time.ResultsAll the delivery errors are found to be small and more stringent tolerances than those proposed by TG142 are suggested. Unlike MLC positional errors, where a linear relationship with leaf speed holds, other Volumetric Modulated Arc Therapy (VMAT) parameters reveal a random nature and, consequently, a reduced clinical relevance. MLC errors are linearly related only to leaf speed no matter the shape of the MLC apertures. Gantry rotation and MU delivery are as accurate as major competing Linacs. UNIQUE was found to be reliable and accurate throughout the investigation period, regardless of the specific tumor sites and fractionation schemes.ConclusionsThe accuracy of RapidArc treatments delivered with UNIQUE has been established. The stochastic nature of delivery errors is proven. Long term statistics of the delivery parameter errors do not show significant variations, confirming the reliability of the VMAT delivery system.     

Technical note: The effect of midshaft location on the error ranges of femoral and tibial cross‐sectional parameters

In comparing long‐bone cross‐sectional geometric properties between individuals, percentages of bone length are often used to identify equivalent locations along the diaphysis. In fragmentary specimens where bone lengths cannot be measured, however, these locations must be estimated more indirectly. In this study, we examine the effect of inaccurately located femoral and tibial midshafts on estimation of geometric properties. The error ranges were compared on 30 femora and tibiae from the Eneolithic and Bronze Age. Cross‐sections were obtained at each 1% interval from 60 to 40% of length using CT scans. Five percent of deviation from midshaft properties was used as the maximum acceptable error. Reliability was expressed by mean percentage differences, standard deviation of percentage differences, mean percentage absolute differences, limits of agreement, and mean accuracy range (MAR) (range within which mean deviation from true midshaft values was less than 5%). On average, tibial cortical area and femoral second moments of area are the least sensitive to positioning error, with mean accuracy ranges wide enough for practical application in fragmentary specimens (MAR = 40–130 mm). In contrast, tibial second moments of area are the most sensitive to error in midshaft location (MAR = 14–20 mm). Individuals present significant variation in morphology and thus in error ranges for different properties. For highly damaged fossil femora and tibiae we recommend carrying out additional tests to better establish specific errors associated with uncertain length estimates. Am J Phys Anthropol 2010. © 2009 Wiley‐Liss, Inc.     

The potential costs of accounting for genotypic errors in molecular parentage analyses

Genotypic errors, whether due to mutation or laboratory error, can cause the genotypes of parents and their offspring to appear inconsistent with Mendelian inheritance. As a result, molecular parentage analyses are expected to benefit when allowances are made for the presence of genotypic errors. However, a cost of allowing for genotypic errors might also be expected under some analytical conditions, primarily because parentage analyses that assume nonzero genotypic error rates can neither assign nor exclude parentage with certainty. The goal of this work was therefore to determine whether or not such costs might be important under conditions relevant to parentage analyses, particularly in natural populations. Simulation results indicate that the costs may often outweigh the benefits of accounting for nonzero error rates, except in situations where data are available for many marker loci. Consequently, the most powerful approach to handling genotypic errors in parentage analyses might be to apply likelihood equations with error rates set to values substantially lower than the rates at which genotypic errors occur. When applying molecular parentage analyses to natural populations, we advocate an increased consideration of optimal strategies for handling genotypic errors. Currently available software packages contain procedures that can be used for this purpose.     

Accounting for data errors discovered from an audit in multiple linear regression

A data coordinating team performed onsite audits and discovered discrepancies between the data sent to the coordinating center and that recorded at sites. We present statistical methods for incorporating audit results into analyses. This can be thought of as a measurement error problem, where the distribution of errors is a mixture with a point mass at 0. If the error rate is nonzero, then even if the mean of the discrepancy between the reported and correct values of a predictor is 0, naive estimates of the association between two continuous variables will be biased. We consider scenarios where there are (1) errors in the predictor, (2) errors in the outcome, and (3) possibly correlated errors in the predictor and outcome. We show how to incorporate the error rate and magnitude, estimated from a random subset (the audited records), to compute unbiased estimates of association and proper confidence intervals. We then extend these results to multiple linear regression where multiple covariates may be incorrect in the database and the rate and magnitude of the errors may depend on study site. We study the finite sample properties of our estimators using simulations, discuss some practical considerations, and illustrate our methods with data from 2815 HIV-infected patients in Latin America, of whom 234 had their data audited using a sequential auditing plan.     

A novel validation and calibration method for motion capture systems based on micro-triangulation

Motion capture systems are widely used to measure human kinematics. Nevertheless, users must consider system errors when evaluating their results. Most validation techniques for these systems are based on relative distance and displacement measurements. In contrast, our study aimed to analyse the absolute volume accuracy of optical motion capture systems by means of engineering surveying reference measurement of the marker coordinates (uncertainty: 0.75 mm). The method is exemplified on an 18 camera OptiTrack Flex13 motion capture system. The absolute accuracy was defined by the root mean square error (RMSE) between the coordinates measured by the camera system and by engineering surveying (micro-triangulation). The original RMSE of 1.82 mm due to scaling error was managed to be reduced to 0.77 mm while the correlation of errors to their distance from the origin reduced from 0.855 to 0.209. A simply feasible but less accurate absolute accuracy compensation method using tape measure on large distances was also tested, which resulted in similar scaling compensation compared to the surveying method or direct wand size compensation by a high precision 3D scanner. The presented validation methods can be less precise in some respects as compared to previous techniques, but they address an error type, which has not been and cannot be studied with the previous validation methods.     

Susceptibility of biallelic haplotype and genotype frequencies to genotyping error

With the availability of fast genotyping methods and genomic databases, the search for statistical association of single nucleotide polymorphisms with a complex trait has become an important methodology in medical genetics. However, even fairly rare errors occurring during the genotyping process can lead to spurious association results and decrease in statistical power. We develop a systematic approach to study how genotyping errors change the genotype distribution in a sample. The general M-marker case is reduced to that of a single-marker locus by recognizing the underlying tensor-product structure of the error matrix. Both method and general conclusions apply to the general error model; we give detailed results for allele-based errors of size depending both on the marker locus and the allele present. Multiple errors are treated in terms of the associated diffusion process on the space of genotype distributions. We find that certain genotype and haplotype distributions remain unchanged under genotyping errors, and that genotyping errors generally render the distribution more similar to the stable one. In case-control association studies, this will lead to loss of statistical power for nondifferential genotyping errors and increase in type I error for differential genotyping errors. Moreover, we show that allele-based genotyping errors do not disturb Hardy-Weinberg equilibrium in the genotype distribution. In this setting we also identify maximally affected distributions. As they correspond to situations with rare alleles and marker loci in high linkage disequilibrium, careful checking for genotyping errors is advisable when significant association based on such alleles/haplotypes is observed in association studies.     

Predicting and correcting bias caused by measurement error in line transect sampling using multiplicative error models

Line transect sampling is one of the most widely used methods for animal abundance assessment. Standard estimation methods assume certain detection on the transect, no animal movement, and no measurement errors. Failure of the assumptions can cause substantial bias. In this work, the effect of error measurement on line transect estimators is investigated. Based on considerations of the process generating the errors, a multiplicative error model is presented and a simple way of correcting estimates based on knowledge of the error distribution is proposed. Using beta models for the error distribution, the effect of errors and of the proposed correction is assessed by simulation. Adequate confidence intervals for the corrected estimates are obtained using a bootstrap variance estimate for the correction and the delta method. As noted by Chen (1998, Biometrics 54, 899-908), even unbiased estimators of the distances might lead to biased density estimators, depending on the actual error distribution. In contrast with the findings of Chen, who used an additive model, unbiased estimation of distances, given a multiplicative model, lead to overestimation of density. Some error distributions result in observed distance distributions that make efficient estimation impossible, by removing the shoulder present in the original detection function. This indicates the need to improve field methods to reduce measurement error. An application of the new methods to a real data set is presented.     

Observer error in sampling a rare plant population

Background: Estimation of abundance in vegetation sampling involving observers is almost always characterised by observer error, although such error is rarely reported.

Aims: To quantify observer error in population estimation of the rare plant species Physaria filiformis in Missouri, USA.

Methods: The abundance of P. filiformis was estimated within 25-m² plots by six trained observers with varying experience levels over 10 years. Observers assigned plots to six predefined density classes. A total of 477 plots were estimated annually, and actual counts were conducted on ca. 10% of the plots to assess per cent agreement of estimates with counts.

Results: Over a third of the estimates of plant abundance evaluated for accuracy (36.4%) deviated from exhaustive counts. The majority of the misestimates were underestimates by one density class (29.4%). The number and type of misestimates varied systematically with density class.

Conclusions: Observer error could be explained to some degree by variation in population density, but not by experience. It appears that inherent differences exist among observers that cannot be entirely compensated for by experience or training. Observer error in this system represents a systematic bias, and can be compensated for by use of correction factors, which would ideally be both density class-dependent and observer-specific.     

Toward error analysis of large-scale forest carbon budgets

Quantification of forest carbon sources and sinks is an important part of national inventories of net greenhouse gas emissions. Several such forest carbon budgets have been constructed, but little effort has been made to analyse the sources of error and how these errors propagate to determine the overall uncertainty of projected carbon fluxes. We performed an error analysis for estimates of tree volume and volume change determined by repeated measurements of permanent sample plots for the South‐eastern United States as a step toward assessing errors in the carbon budget constructed by the USDA Forest Service. Error components recognized were: sampling error for sample plot selection; measurement error for tree height and diameter; and regression error for tree volume. Most of the propagated error in volume and volume change estimation was due to sampling error. Error estimates depended on the size of the area examined (single state to region) and the degree to which tree growth and recruit‐ment balanced mortality and harvesting. Approximate regional 95% confidence intervals were 3 455 073 000 ± 39 606 000 (1.1%) m³ for current growing‐stock volume, and 10 616 000 ± 4210 000 (39.7%) m³ years^?1 for growing‐stock volume change. These methods should be useful in further analysis of the sources of error and overall uncertainty in national efforts to quantify carbon fluxes associated with forests and land cover dynamics.     

Measurement error in a random walk model with applications to population dynamics

Population abundances are rarely, if ever, known. Instead, they are estimated with some amount of uncertainty. The resulting measurement error has its consequences on subsequent analyses that model population dynamics and estimate probabilities about abundances at future points in time. This article addresses some outstanding questions on the consequences of measurement error in one such dynamic model, the random walk with drift model, and proposes some new ways to correct for measurement error. We present a broad and realistic class of measurement error models that allows both heteroskedasticity and possible correlation in the measurement errors, and we provide analytical results about the biases of estimators that ignore the measurement error. Our new estimators include both method of moments estimators and "pseudo"-estimators that proceed from both observed estimates of population abundance and estimates of parameters in the measurement error model. We derive the asymptotic properties of our methods and existing methods, and we compare their finite-sample performance with a simulation experiment. We also examine the practical implications of the methods by using them to analyze two existing population dynamics data sets.     

农业环境中土壤取样误差研究

对自然条件下8种土壤类型、39个取样地块的25个土壤理化参数的取样误差进行了综合研究。结果表明,不同地块间,按累计取样误差大小排序为:池塘>地块边缘>自留地>林地>商品菜地>旱地>水田>滩地。在所有地块测定项目中,取样误差最大的是Cl^-,平均高达70%以上,其次是土壤有效磷,除滩地外取样误差基本上都超过30%;有效钾和全硫的取样误差也多在20%以上;取样误差最小的理化参数与成土母质有关,其中包括各种重金属和全量P、K、Mg以及pH和砂粒等,除极个别外,误差都在10%以下;2种粒度的土壤水分、碳酸钙、粉砂、粘粒、有机碳、全量N、Na、Ca、B和As等11项理化参数的取样误差居中,误差变动于10%～20%之间。聚类分析可以将不同测定项目大致分为3类,客观反映了人类活动对土壤理化参数分布均匀性的影响。     

Optimum Sorption Isotherm by Linear and Nonlinear Methods for Safranin onto Alkali-Treated Rice Husk

Rice husk, a lignocellulosic by-product of the agroindustry, was treated with alkali and used as a low-cost adsorbent for the removal of safranin from aqueous solution in batch adsorption procedure. In order to estimate the equilibrium parameters, the equilibrium adsorption data were analyzed using the following two-parameter isotherms: Freundlich, Langmuir, and Temkin. A comparison of linear and nonlinear regression methods in selecting the optimum adsorption isotherm was applied on the experimental data. Six linearized isotherm models (including four linearized Langmuir models) and three nonlinear isotherm models are thus discussed in this paper. In order to determine the best-fit isotherm predicted by each method, seven error functions namely, coefficient of determination (r ²), the sum of the squares of the errors (SSE), sum of the absolute errors (SAE), average relative error (ARE), hybrid fractional error-function (HYBRID), Marquardt's percent standard deviation (MPSD), and the chi-square test (χ²) were used. It was concluded that the nonlinear method is a better way to obtain the isotherm parameters and the data were in good agreement with the Langmuir isotherm model.     

Estimation of accuracy of patient-specific musculoskeletal modelling: case study on a post polio residual paralysis subject

For patients with patterns ranging out of anthropometric standard values, patient-specific musculoskeletal modelling becomes crucial for clinical diagnosis and follow-up. However, patient-specific modelling using imaging techniques and motion capture systems is mainly subject to experimental errors. The aim of this study was to quantify these experimental errors when performing a patient-specific musculoskeletal model. CT scan data were used to personalise the geometrical model and its inertial properties for a post polio residual paralysis subject. After having performed a gait-based experimental protocol, kinematics data were measured using a VICON motion capture system with six infrared cameras. The musculoskeletal model was computed using a direct/inverse algorithm (LifeMod software). A first source of errors was identified in the segmentation procedure in relation to the calculation of personalised inertial parameters. The second source of errors was subject related, as it depended on the reproducibility of performing the same type of gait. The impact of kinematics, kinetics and muscle forces resulting from the musculoskeletal modelling was quantified using relative errors and the absolute root mean square error. Concerning the segmentation procedure, we found that the kinematics results were not sensitive to the errors (relative error < 1%). However, a strong influence was noted on the kinetics results (deviation up to 71%). Furthermore, the reproducibility error showed a significant influence (relative mean error varying from 5 to 30%). The present paper demonstrates that in patient-specific musculoskeletal modelling variations due to experimental errors derived from imaging techniques and motion capture need to be both identified and quantified. Therefore, the paper can be used as a guideline.