Proportion Of Outliers Research Articles

Outliers in nutrient intake data for U.S. adults: national health and nutrition examination survey 2017-2018.

An important step in preparing data for statistical analysis is outlier detection and removal, yet no gold standard exists in current literature. The objective of this study is to identify the ideal decision test using the National Health and Nutrition Examination Survey (NHANES) 2017-2018 dietary data. We conducted a secondary analysis of NHANES 24-h dietary recalls, considering the survey's multi-stage cluster design. Six outlier detection and removal strategies were assessed by evaluating the decision tests' impact on the Pearson's correlation coefficient among macronutrients. Furthermore, we assessed changes in the effect size estimates based on pre-defined sample sizes. The data were collected as part of the 2017-2018 24-h dietary recall among adult participants (N=4,893). Effect estimate changes for macronutrients varied from 6.5 % for protein to 39.3 % for alcohol across all decision tests. The largest proportion of outliers removed was 4.0 % in the large sample size, for the decision test, >2 standard deviations from the mean. The smallest sample size, particularly for alcohol analysis, was most affected by the six decision tests when compared to no decision test. This study, the first to use 2017-2018 NHANES dietary data for outlier evaluation, emphasizes the importance of selecting an appropriate decision test considering factors such as statistical power, sample size, normality assumptions, the proportion of data removed, effect estimate changes, and the consistency of estimates across sample sizes. We recommend the use of non-parametric tests for non-normally distributed variables of interest.

PG-Net: Progressive Guidance Network via Robust Contextual Embedding for Efficient Point Cloud Registration

Building high-quality correspondences is critical in the feature-based point cloud registration pipelines. However, existing single-sequence learning frameworks are difficult to accurately and adequately capture contextual information, leaving a large proportion of outliers between two low-overlap scenes. In this paper, we present a progressive guidance network (PG-Net) to gather rich contextual information and exclude outliers. Specifically, we design a novel iterative structure that exploits the inlier probabilities of correspondences to guide the classification of initial correspondences progressively. This structure can mitigate outlier effects with robust contextual information to obtain more accurate model estimation. In addition, to sufficiently capture contextual information, we propose a grouped dense fusion attention feature embedding module to enhance the representation of inliers and significant channel-spatial. Meanwhile, we propose a two-stage neural spectral matching module to compute the inlier probability of each correspondence and estimate a 3D transformation model in a coarse-to-fine manner. Experiments results on indoor and outdoor datasets using distinct 3D local descriptors demonstrate that our PG-Net surpasses state-of-the-art outlier removal methods. Especially compared to the recent outlier removal network PointDSC, our PG-Net improves the registration recall by 4.06% on the indoor dataset with the FPFH descriptor. Source code: https://github.com/changcaiyang/PG-Net.

The Estimating of the Conditional Density with Application to the Mode Function in Scalar-On-Function Regression Structure: Local Linear Approach with Missing at Random

The aim of this research was to study a nonparametric estimator of the density and mode function of a scalar response variable given a functional variable, when the observations are i.i.d. This proposed estimator is given by combining Missing At Random (MAR) with the local linear approach. Finally, a comparison study based on simulated data is also provided to illustrate the finite sample performances and the usefulness of the local linear approach with MAR to the presence of even a small proportion of outliers in the data.

Measuring sampling fairness and geochemical consensus for blasthole assays within grade-block mining units

In the mining industry, current grade control practices lack a standardised framework that can assess the reliability of average grade estimates computed for selective mining units (otherwise known as grade-blocks) within a mining bench. This article describes two measures that can quantify sampling fairness and geochemical consensus. Concretely, sampling fairness considers spatial factors such as sampling density and bias in the spatial distribution of blastholes whereas geochemical consensus considers the agreement between the assay samples within a grade-block. Geochemical disparity is measured using a robust distance estimator and a masking formula that takes into account the proportion of outliers and magnitude of differences observed above a threshold. The efficacy of the consensus measure is demonstrated through validation experiments. The results confirm the MCD (minimum covariance determinant) robust estimator can breakdown when the fraction of outliers exceeds (n−k−1)/(2n). For k≥2 variables and a sample size n≥10, this typically leads to an underestimation of the true extent and impact of outliers when they exceed 40%. An extension based on split-sequence analysis is proposed to overcome this limitation. The method is evaluated using production data from an open-pit iron ore deposit. An open-source implementation of the proposed algorithms is available on GitHub.

The heterogeneous amyloid‐positive brain: mapping individualised patterns of atrophy in amyloid‐positive Alzheimer’s disease patients using neuroanatomical normative models

AbstractBackgroundPatterns of atrophy in the brain highly differ between individual Alzheimer’s Disease (AD) patients, however, most clinical research focuses on group‐level differences (Verdi et al., 2021). Here we used a novel technique, neuroanatomical normative modelling, to reveal individual patterns of cortical thickness by quantifying deviations from the normative range. We applied a hierarchical Bayesian regression (HBR) normative model (Kia et al., 2021), to amyloid‐positive AD patients who had clinical amyloid PET imaging at the Imperial Memory Clinic (IMC). Patients had either AD dementia or mild cognitive impairment due to AD. We hypothesised that there would be individual differences in patterns of cortical atrophy in these patients.MethodCortical thickness across 148 regions of interest (ROIs) was generated using FreeSurfer from n=130 (102 AD patients and 28 healthy controls) T1‐weighted MRIs acquired from the IMC. A reference HBR normative model was trained on a separate dataset of n=34,490 healthy individuals to index population variability, which predicted cortical thickness at each ROI using age and sex. This generated cortical thickness z‐scores for each ROI, per patient (z‐score < ‐1.96 = outlier).ResultThe patterns of cortical atrophy outliers were highly varied in amyloid‐positive AD patients. For instance, the largest proportion of outliers in a region was 60% within the superior temporal sulci, if atrophy were homogenous we would expect 100% of outliers to be here (Fig.1). This heterogeneity was also seen when comparing how similar outlier patterns were between patients (Fig.2). We also found that the proportions of outliers differ according to disease severity, e.g. the highest percentage of outliers was 70% within superior temporal sulci within the AD dementia subgroup, and 50% in superior temporal sulci in the mild cognitive impairment due to AD subgroup (Fig.3).ConclusionAmyloid‐positivity results in heterogenous patterns of cortical atrophy. This is more pronounced in AD dementia, though still present in people with mild cognitive impairment due to AD. Neuroanatomical normative maps have the potential to be individualised markers of disease, and with application to longitudinal data could track individual disease progression.

Alignment accuracy and functional outcomes between hand-held navigation and conventional instruments in TKA: a randomized controlled trial

BackgroundThis study assessed surgical accuracy and functional outcomes using hand-held accelerometer-based navigation following total knee arthroplasty (TKA). Question: (1) Does hand-held navigation (the iAssist system) improve surgical accuracy (assessed with five parameters commonly used to evaluate surgical alignment: the hip-knee-ankle angle (HKA), femoral coronal angle (FCA), tibial coronal angle (TCA), femoral sagittal angle (FSA), and tibial slope angle (TSA)) compared to conventional instruments in TKA? (2) Which surgical alignment parameters among HKA, FCA, TCA, FSA, and TSA can obtain the most advantage from the iAssist system? (3) Does the iAssist system lead to better functional outcomes at two years of follow-up after TKA?MethodsThis parallel-group double-blinded randomized controlled trial recruited 60 patients (30 patients each in the iAssist and conventional group) with osteoarthritis who underwent primary TKA by a single surgeon at Siriraj Hospital. There was no loss to follow-up in the study. All procedures in both groups were performed using similar surgical exposure, prosthesis implant, perioperative and postoperative protocols. Participants in the iAssist group received the iAssist system as an assistive technique, while those in the conventional group only had conventional instruments. Surgical alignments (HKA, FCA, TCA, FSA, and TSA) were recorded using CT scan at six weeks post-operation. Functional outcomes were assessed with knee ROM, KSS, and EQ-5D at 6 months, 1 year and 2 years post-operation. Baseline characteristics including age, sex, the affected knee side, and body mass index were comparable between the two groups, similar to preoperative ROM, KSS, and EQ-5D.ResultsThe mean operative time was relatively longer in the iAssist than the conventional group, although not statistically significant (88.1 ± 13.7 versus 83.4 ± 21.3; p = 0.314). Among the surgical alignment parameters evaluated, FCA was the only radiographic parameter with a statistically significant difference between the two groups and was closer to 90º in the iAssist group (89.4 ± 2.2 in the iAssist versus 87.2 ± 2.1 in the conventional group; p = 0.003). Also, there was a higher proportion of outliers in the conventional than the iAssist group (23.3% versus 10%; p = 0.086). Nonetheless, HKA and TCA did not differ between the two groups (p = 0.25 and 0.096, respectively), although the percentages of outliers were higher in the conventional than the iAssist group (HKA: 26.7% vs. 13.3%; p = 0.101 and TCA: 6.7% versus 0%; p = 0.078). Likewise, we observed other radiographic parameters had no significant group differences, including FSA and TSA. Furthermore, at two years post-operation, we found no differences between the iAssist and the conventional group in knee ROM (106.7 ± 14.6 versus 108.2 ± 12.7; p = 0.324), KSS (82.5 ± 6.4 versus 83.8 ± 3.4; p = 0.324), and EQ-5D (0.9 ± 0.2 versus 1.0 ± 0.1; p = 0.217). All functional outcomes were also comparable at 6 months and 12 months of follow-up postoperatively.ConclusionThe iAssist technology increase surgical precision by allowing for a more precise FCA with fewer outliers than conventional equipment. iAssist had longer operative time. Functional outcomes and quality of life were not different.Level of evidence:I

Outlier Detection Using t-test in Rasch IRT Equating under NEAT Design.

In equating practice, the existence of outliers in the anchor items may deteriorate the equating accuracy and threaten the validity of test scores. Therefore, stability of the anchor item performance should be evaluated before conducting equating. This study used simulation to investigate the performance of the t-test method in detecting outliers and compared its performance with other outlier detection methods, including the logit difference method with 0.5 and 0.3 as the cutoff values and the robust z statistic with 2.7 as the cutoff value. The investigated factors included sample size, proportion of outliers, item difficulty drift direction, and group difference. Across all simulated conditions, the t-test method outperformed the other methods in terms of sensitivity of flagging true outliers, bias of the estimated translation constant, and the root mean square error of examinee ability estimates.

RI-LPOH: Rotation-Invariant Local Phase Orientation Histogram for Multi-Modal Image Matching

To better cope with the significant nonlinear radiation distortions (NRD) and severe rotational distortions in multi-modal remote sensing image matching, this paper introduces a rotationally robust feature-matching method based on the maximum index map (MIM) and 2D matrix, which is called the rotation-invariant local phase orientation histogram (RI-LPOH). First, feature detection is performed based on the weighted moment equation. Then, a 2D feature matrix based on MIM and a modified gradient location orientation histogram (GLOH) is constructed and rotational invariance is achieved by cyclic shifting in both the column and row directions without estimating the principal orientation separately. Each part of the sensed image’s 2D feature matrix is additionally flipped up and down to obtain another 2D matrix to avoid intensity inversion, and all the 2D matrices are concatenated by rows to form the final 1D feature vector. Finally, the RFM-LC algorithm is introduced to screen the obtained initial matches to reduce the negative effect caused by the high proportion of outliers. On this basis, the remaining outliers are removed by the fast sample consensus (FSC) method to obtain optimal transformation parameters. We validate the RI-LPOH method on six different types of multi-modal image datasets and compare it with four state-of-the-art methods: PSO-SIFT, MS-HLMO, CoFSM, and RI-ALGH. The experimental results show that our proposed method has obvious advantages in the success rate (SR) and the number of correct matches (NCM). Compared with PSO-SIFT, MS-HLMO, CoFSM, and RI-ALGH, the mean SR of RI-LPOH is 170.3%, 279.8%, 81.6%, and 25.4% higher, respectively, and the mean NCM is 13.27, 20.14, 1.39, and 2.42 times that of the aforementioned four methods.

Deep learning-based landmark recognition and angle measurement of full-leg plain radiographs can be adopted to assess lower extremity alignment.

Evaluating lower extremity alignment using full-leg plain radiographs is an essential step in diagnosis and treatment of patients with knee osteoarthritis. The study objective was to present a deep learning-based anatomical landmark recognition and angle measurement model, using full-leg radiographs, and validate its performance. A total of 11,212 full-leg plain radiographs were used to create the model. To train the data, 15 anatomical landmarks were marked by two orthopaedic surgeons. Mechanical lateral distal femoral angle (mLDFA), medial proximal tibial angle (MPTA), joint line convergence angle (JLCA), and hip-knee-ankle angle (HKAA) were then measured. For inter-observer reliability, the inter-observer intraclass correlation coefficient (ICC) was evaluated by comparing measurements from the model, surgeons, and students, to ground truth measurements annotated by an orthopaedic specialist with 14years of experience. To evaluate test-retest reliability, all measurements were made twice by each measurer. Intra-observer ICCs were then derived. Performance evaluation metrics used in previous studies were also derived for direct comparison of the model's performance. Inter-observer ICCs for all angles of the model were 0.98 or higher (p < 0.001). Intra-observer ICCs for all angles were 1.00, which was higher than that of the orthopaedic specialist (0.97-1.00). Measurements made by the model showed no significant systemic variation. Except for JLCA, angles were precisely measured with absolute error averages under 0.52 degrees and proportion of outliers under 4.26%. The deep learning model is capable of evaluating lower extremity alignment with performance as accurate as an orthopaedic specialist with 14years of experience. III, retrospective cohort study.

Testing the Presence of Outliers in Regression Models*

We propose two sets of tests for the overall presence of outliers in regression models. First, ‘simple’ tests on whether the proportion and the number of detected outliers deviate from their expected values. Second, ‘scaling’ tests on whether the proportion of outliers decreases with the cut‐off used to detect outliers. We apply our tests to a panel difference‐in‐differences model of transport CO2 emissions in response to the introduction of North America's first major carbon tax. Our tests show the presence of significant outliers in the un‐taxed control group, which results in an overestimation of the estimated impacts of the tax.

Robust Dynamic Pricing with Demand Learning in the Presence of Outlier Customers

Dynamic pricing is a core problem in revenue management. Most existing literature assumes that the demand follows a probabilistic model, with an unknown demand curve as the mean. However, in practice, customers may not always behave according to such a model. In “Robust Dynamic Pricing with Demand Learning in the Presence of Outlier Customers,” Chen and Wang study the dynamic pricing problem under model misspecification. To characterize the behavior of outlier customers, an ε-contamination model—the most fundamental model in robust statistics and machine learning, is adopted. The challenges brought by the presence of outlier customers are mainly due to the fact that arrivals of outliers and their exhibited demand behaviors are completely arbitrary. To address these challenges, the authors propose robust dynamic pricing policies that can handle any outlier arrival and demand patterns. The proposed policies are fully adaptive without requiring prior knowledge of the outlier proportion parameter.

Outlier detection in multivariate functional data through a contaminated mixture model

In an industrial context, the activity of sensors is recorded at a high frequency. A challenge is to automatically detect abnormal measurement behavior. Considering the sensor measures as functional data, the problem can be formulated as the detection of outliers in a multivariate functional data set. Due to the heterogeneity of this data set, the proposed contaminated mixture model both clusters the multivariate functional data into homogeneous groups and detects outliers. The main advantage of this procedure over its competitors is that it does not require to specify the proportion of outliers. Model inference is performed through an Expectation-Conditional Maximization algorithm, and the BIC is used to select the number of clusters. Numerical experiments on simulated data demonstrate the high performance achieved by the inference algorithm. In particular, the proposed model outperforms the competitors. Its application on the real data which motivated this study allows to correctly detect abnormal behaviors.

A new robust multivariate mode estimator for eye-tracking calibration.

We propose in this work a new method for estimating the main mode of multivariate distributions, with application to eye-tracking calibration. When performing eye-tracking experiments with poorly cooperative subjects, such as infants or monkeys, the calibration data generally suffer from high contamination. Outliers are typically organized in clusters, corresponding to fixations in the time intervals when subjects were not looking at the calibration points. In this type of multimodal distributions, most central tendency measures fail at estimating the principal fixation coordinates (the first mode), resulting in errors and inaccuracies when mapping the gaze to the screen coordinates. Here, we developed a new algorithm to identify the first mode of multivariate distributions, named BRIL, which relies on recursive depth-based filtering. This novel approach was tested on artificial mixtures of Gaussian and Uniform distributions, and compared to existing methods (conventional depth medians, robust estimators of location and scatter, and clustering-based approaches). We obtained outstanding performances, even for distributions containing very high proportions of outliers, both grouped in clusters and randomly distributed. Finally, we demonstrate the strength of our method in a real-world scenario using experimental data from eye-tracking calibrations with Capuchin monkeys, especially for highly contaminated distributions where other algorithms typically lack accuracy.

Robustness and Tractability for Non-convex M-estimators

We investigate two important properties of M-estimator, namely, robustness and tractability, in linear regression setting, when the observations are contaminated by some arbitrary outliers. Specifically, robustness means the statistical property that the estimator should always be close to the underlying true parameters {\em regardless of the distribution of the outliers}, and tractability indicates the computational property that the estimator can be computed efficiently, even if the objective function of the M-estimator is {\em non-convex}. In this article, by learning the landscape of the empirical risk, we show that under mild conditions, many M-estimators enjoy nice robustness and tractability properties simultaneously, when the percentage of outliers is small. We further extend our analysis to the high-dimensional setting, where the number of parameters is greater than the number of samples, $p \gg n$, and prove that when the proportion of outliers is small, the penalized M-estimators with {\em $L_1$} penalty will enjoy robustness and tractability simultaneously. Our research provides an analytic approach to see the effects of outliers and tuning parameters on the robustness and tractability for some families of M-estimators. Simulation and case study are presented to illustrate the usefulness of our theoretical results for M-estimators under Welsch's exponential squared loss.

No Difference in Clinical Outcomes and Survivorship for Robotic, Navigational, and Conventional Primary Total Knee Arthroplasty with a Minimum Follow-up of 10 Years.

Computer-assisted surgery, including robotic and navigational total knee arthroplasty (TKA), has been proposed as a technique used to improve alignment of implants. The purpose of this study was to compare the clinical and radiological outcomes during a minimum follow-up period of 10 years among robotic, navigational, and conventional TKA. A total of 855 knees (robotic group, 194; conventional group, 270; and navigational group, 391) were available for physical and radiological examinations over a mean follow-up period of 10 years. The survival rate was analyzed using the Kaplan-Meier method based on the survival endpoint. The Hospital for Special Surgery score, Western Ontario and McMaster Universities Osteoarthritis Index, Knee Society Score, and range of motion were used for clinical evaluation. The hip-knee-ankle (HKA) axis angle, the coronal inclination of femoral and tibial components, and the presence of radiolucent lines were also assessed at the final follow-up. All clinical assessments at the final follow-up revealed improvements in the three groups without any significant difference among the groups (p > 0.05). The cumulative 10-year survival rate was 97.4% in the robotic group, 96.6% in the conventional group, and 98.2% in the navigational group, with no significant difference (p = 0.447). The rates of complication-associated surgery were not significantly different among the groups (p = 0.907). Only the proportion of outliers in the HKA axis angle showed a significant difference (p = 0.001), but other radiological outcomes were not significantly different among the three groups. Our study demonstrated satisfactory survival rates for robotic, navigational, and conventional TKAs and similar clinical outcomes during the long-term follow-up. Larger studies with continuous serial data are needed to confirm these findings.

Reliability of the Posterior Condylar Axis as an Alternative Reference for Femoral Rotation in Japanese Patients with Varus Knee Osteoarthritis Undergoing Total Knee Arthroplasty

Background: This study aimed to assess the reliability of the posterior condylar axis (PCA), the most widely used alternative reference for the surgical transepicondylar axis (sTEA), as a reference for appropriate femoral rotational alignment in total knee arthroplasty (TKA) by comparing variances with other alternative reference axes. Methods: A total of 305 knees in 233 Japanese patients who underwent TKA due to varus knee osteoarthritis were assessed in this study. Variances and relationships between alternative references were determined. Angles of alternative reference axes relative to the sTEA in the axial plane were measured using computer software based on computed tomography. Results: The PCA line was 3.0°±1.8° (range, -2.1° to 8.8°) internally rotated relative to the sTEA. No significant differences were observed in the PCA angle relative to the sTEA angle between males and females. The variance with respect to the sTEA was significantly smaller in the order of anatomical transepicondylar axis (aTEA), PCA, and antero-posterior axis (APA). The variance of the APA and that of the femoral anterior tangent line (FAT) did not significantly differ, while the variance of the FAT was significantly smaller than that of the trochlear anterior line (TAL). The proportion of outliers for PCA (&gt;3° away from the average value) was 9.8%. The PCA was weakly correlated with the aTEA, APA, FAT, and TAL. Conclusions: In terms of variance with respect to the sTEA, the PCA was second to aTEA in reliability as an alternative reference axis, and was on average 3.0°±1.8° internally rotated relative to the sTEA. Our findings suggest that the PCA is a reliable and reproducibly identifiable alternative axis for accurately determining femoral rotational alignment in TKA.

The initial learning curve for the ROSA\xae Knee System can be achieved in 6-11 cases for operative time and has similar 90-day complication rates with improved implant alignment compared to manual instrumentation in total knee arthroplasty

PurposeThe purpose of this study was to determine the learning curve for total operative time using a novel cutting guide positioning robotic assistant for total knee arthroplasty (raTKA). Additionally, we compared complications and final limb alignment between raTKA and manual TKA (mTKA), as well as accuracy to plan for raTKA cases.MethodsWe performed a retrospective cohort study on a series of patients (n = 180) that underwent raTKA (n = 90) using the ROSA Total Knee System or mTKA (n = 90) by one of three high-volume (> 200 cases per year) orthopaedic surgeons between December 2019 and September 2020, with minimum three-month follow-up. To evaluate the learning curve surgical times and postoperative complications were reviewed.ResultsThe cumulative summation analysis for total operative time revealed a change point of 10, 6, and 11 cases for each of three surgeons, suggesting a rapid learning curve. There was a significant difference in total operative times between the learning raTKA and both the mastered raTKA and mTKA groups (p = 0.001) for all three surgeons combined. Postoperative complications were minimal in all groups. The proportion of outliers for the final hip-knee-ankle angle compared to planned was 5.2% (3/58) for the mastered raTKA compared to 24.1% (19/79) for mTKA (p = 0.003). The absolute mean difference between the validated and planned resections for all angles evaluated was < 1 degree for the mastered raTKA cases.ConclusionAs the digital age of medicine continues to develop, advanced technologies may disrupt the industry, but should not disrupt the care provided. This cutting guide positioning robotic system can be integrated relatively quickly with a rapid initial learning curve (6-11 cases) for operative times, similar 90-day complication rates, and improved component positioning compared to mTKA. Proficiency of the system requires additional analysis, but it can be expected to improve over time.Level of evidenceLevel III Retrospective Therapeutic Cohort Study.

Accuracy of different navigation systems for femoral and tibial implantation in total knee arthroplasty: a randomised comparative study.

It remains to be established whether optical computed tomography (CT)-free and acceleration-based navigation systems differ in terms of implantation accuracy and clinical outcomes for total knee arthroplasty. This randomised prospective study compared the implantation accuracy of these two navigation systems in total knee arthroplasty. Optical CT-free navigation (ExactechGPS) or acceleration-based navigation (KneeAlign2) was randomly assigned to the left or right knee of 45 patients who underwent a single-stage bilateral total knee arthroplasty: the ExactechGPS (n = 45) and KneeAlign2 groups (n = 45) were compared. Component alignments were evaluated using three-dimensional computed tomography and radiography at pre- and post-surgery. Implantation accuracy of the component alignment, proportion of outliers, postoperative range of motion, and Japanese Orthopaedic Association (JOA) score were compared between the systems. The implantation accuracies of the lower-extremity mechanical alignment, coronal femoral component angle, coronal tibial component angle, sagittal femoral component, axial femoral angle, and axial tibial angle had no significant difference between the groups. The implantation accuracy of the sagittal tibial component angle was superior in the ExactechGPS than the KneeAlign2 group (1.3° vs. 1.8°, P = 0.034). The proportions of outliers, range of motion, and JOA score had no significant difference between the groups. In the tibial sagittal plane, there was a significant difference in the implantation accuracy, but its difference did not affect the clinical outcomes. Both navigation systems have clinically acceptable implantation accuracy.

Detection of Outliers in Anchor Items Using Modified Rasch Fit Statistics

ABSTRACT The existence of outliers in the anchor items can be detrimental to the estimation of examinee ability and undermine the validity of score interpretation across forms. However, in practice, anchor item performance can become distorted due to various reasons. This study compares the performance of modified INFIT and OUTFIT Rasch statistics with the Logit Difference approach with 0.3 and 0.5 as the predetermined cutoff values, and the Robust z statistic with 1.645 and 2.7 as the cutoff values through a simulation study by varying the sample size, proportion of outliers, item difficulty drift direction, and group difference magnitude. The results suggest that both modified INFIT and OUTFIT statistics perform very similarly and outperform the other methods in all aspects, including sensitivity of flagging outliers, specificity of flagging non-outliers, recovery of translation constant, and recovery of examinee ability in all simulated conditions.

Comparison of Axis Determination With Different Toric Intraocular Lens Power Calculation Methods.

To compare the axis position of the measured total corneal astigmatism (TCA) with the axis of the anterior keratometry and the calculated axis position of different toric intraocular lens (IOL) calculators. A total of 163 astigmatic eyes of 163 patients were retrospectively analyzed. The axis of the actual TCA, measured with anterior segment optical coherence tomography, was compared to the anterior keratometric value (Group I) and three different methods of TCA calculation for toric IOL power determination: Abulafia-Koch regression formula (Group II), Barrett Toric Calculator V2.0 (Group III), and Barrett Toric Calculator V2.0 including measured posterior keratometric value (Group IV). Eyes were assigned to three subgroups: with-the-rule, against-the-rule, and oblique astigmatism. The mean deviation calculated from measured TCA was +0.56° (Group I), -0.32° (Group II), -0.37° (Group III), and -1.00° (Group IV). For with-the-rule astigmatism, the TCA axis agreed most with Group I (6.5% outliers > 5° deviation). For against-the-rule astigmatism, Group IV and Group II were closest to the measured TCA axis (1.5% and 3% outliers with > 5° deviation). The means of the calculated axis were similar to the measured TCA, but the proportion of outliers with an axis deviation of greater than 5° showed remarkable differences. Isolated anterior keratometric value measurements showed the fewest outliers in with-the-rule astigmatism. In against-the-rule astigmatism, Abulafia-Koch calculation should be used for axis determination. [J Refract Surg. 2021;37(9):642-647.].