Model-based Roentgen stereophotogrammetry of orthopaedic implants

Attaching tantalum markers to prostheses for Roentgen stereophotogrammetry (RSA) may be difficult and is sometimes even impossible. In this study, a model-based RSA method that avoids the attachment of markers to prostheses is presented and validated. This model-based RSA method uses a triangulated surface model of the implant. A projected contour of this model is calculated and this calculated model contour is matched onto the detected contour of the actual implant in the RSA radiograph. The difference between the two contours is minimized by variation of the position and orientation of the model. When a minimal difference between the contours is found, an optimal position and orientation of the model has been obtained. The method was validated by means of a phantom experiment. Three prosthesis components were used in this experiment: the femoral and tibial component of an Interax total knee prosthesis (Stryker Howmedica Osteonics Corp., Rutherfort, USA) and the femoral component of a Profix total knee prosthesis (Smith & Nephew, Memphis, USA). For the prosthesis components used in this study, the accuracy of the model-based method is lower than the accuracy of traditional RSA. For the Interax femoral and tibial components, significant dimensional tolerances were found that were probably caused by the casting process and manual polishing of the components surfaces. The largest standard deviation for any translation was 0.19mm and for any rotation it was 0.52 degrees. For the Profix femoral component that had no large dimensional tolerances, the largest standard deviation for any translation was 0.22mm and for any rotation it was 0.22 degrees. From this study we may conclude that the accuracy of the current model-based RSA method is sensitive to dimensional tolerances of the implant. Research is now being conducted to make model-based RSA less sensitive to dimensional tolerances and thereby improving its accuracy.     

Image-based RSA: Roentgen stereophotogrammetric analysis based on 2D-3D image registration

Image-based Roentgen stereophotogrammetric analysis (IBRSA) integrates 2D-3D image registration and conventional RSA. Instead of radiopaque RSA bone markers, IBRSA uses 3D CT data, from which digitally reconstructed radiographs (DRRs) are generated. Using 2D-3D image registration, the 3D pose of the CT is iteratively adjusted such that the generated DRRs resemble the 2D RSA images as closely as possible, according to an image matching metric. Effectively, by registering all 2D follow-up moments to the same 3D CT, the CT volume functions as common ground. In two experiments, using RSA and using a micromanipulator as gold standard, IBRSA has been validated on cadaveric and sawbone scapula radiographs, and good matching results have been achieved. The accuracy was: |mu |< 0.083 mm for translations and |mu| < 0.023 degrees for rotations. The precision sigma in x-, y-, and z-direction was 0.090, 0.077, and 0.220 mm for translations and 0.155 degrees , 0.243 degrees , and 0.074 degrees for rotations. Our results show that the accuracy and precision of in vitro IBRSA, performed under ideal laboratory conditions, are lower than in vitro standard RSA but higher than in vivo standard RSA. Because IBRSA does not require radiopaque markers, it adds functionality to the RSA method by opening new directions and possibilities for research, such as dynamic analyses using fluoroscopy on subjects without markers and computer navigation applications.     

Markerless Roentgen Stereophotogrammetric Analysis for in vivo implant migration measurement using three dimensional surface models to represent bone

Recent studies have shown that model-based RSA using implant surface models to detect in vivo migration is as accurate as the classical marker-based RSA method. Use of bone surface models would be a further advancement of the model-based method by decreasing complications arising from marker insertion. The aim of this pilot investigation was to assess the feasibility of a "completely markerless" model-based RSA in detecting migration of an implant using bone surface models instead of bone markers. A total knee arthroplasty (TKA) was performed on a human cadaver knee, which was subsequently investigated by repeated RSA measurements performed by one observer. The cadaver knee was CT scanned prior to implantation of the TKA. Tibia-fibular surface models were created using two different commercially available software packages to investigate the effect of segmentation software on the accuracy of repeated migration measures of zero displacement by one observer. Reverse engineered surface models of the TKA tibial component were created. The analysis of the RSA images was repeated 10 times by one individual observer. For the markerless method, the greatest apparent migration observed about the three anatomical axes investigated was between -2.08 and 1.35 mm (SD ≤ 0.88) for z-axis translation, and -4.57° to 7.86° (SD ≤ 3.17) for R(y)-axis rotation, which were well beyond out of the range of what is typically considered adequate for clinically relevant RSA measurements. Use of tibia-fibular surface models of the bone instead of markers could provide practical advantages in evaluating implant migration. However, we found the accuracy and precision of the markerless approach to be lower than that of marker-based RSA, to a degree which precludes the use of this method for measuring implant migration in its present form.     

Handling modular hip implants in model-based RSA: combined stem-head models

Migration measurements of hip prostheses using marker-based Roentgen stereophotogrammetric analysis (RSA) require the attachment of markers to the prostheses. The model-based approach, which does not require these markers, is, however, less precise. One of the reasons may be the fact that the spherical head has not been modelled. Therefore, we added a 3D surface model of the spherical head and estimated the position and orientation of the combined stem-head model. The new method using a combined stem-head model was compared in a phantom study on five prostheses (of different types) and in a clinical study using double examinations of implanted hip prostheses, with two existing methods: a standard model-based approach and one using elementary geometrical shapes. The combined model showed the highest precision for the rotation about the longitudinal axis in the phantom experiments. With a standard deviation of 0.69 degrees it showed a significant improvement (p=0.02) over the model-based approach (0.96 degrees ) on the phantom data, but no improvement on the clinical data. Overall, the use of elementary geometrical shapes was worse with respect to the model-based approach, with a standard deviation of 1.02 degrees on the phantom data and 0.79 degrees on the clinical data. This decrease in precision was significant (p<0.01) on the clinical data. With relatively small differences in the other migration directions, these results demonstrate that the new method with a combined stem-head model can be a useful alternative to the standard model-based approach.     

A simplified radiographic method for measuring bone-component motion in total knees.

Measurement of the relative motion between an implant and the surrounding bone over different time periods is valuable for assessing and comparing the component stability and predicting the potential future outcome. The RSA method, where small beads are implanted in the bone adjacent to the component, can measure implant-bone position to an accuracy of about 0.1 mm. However, the method involves special radiographic views and analytical software, not readily available. For purposes of component assessment on a more routine basis and for multi-centre trials, a method was developed where standard A-P and M-L radiographs were used. Computer software was written which estimated the out-of-plane rotations of the component relative to the plane of the film, and then carried out corrections to enhance the accuracy of calculation of the bead heights relative to the component. The theoretical errors were shown to be less than 0.04 mm for the expected range of out-of-plane rotations. When radiographs of components in simulated bones were taken at a range of rotations, the 95% confidence limits for axial displacement were found to be less than +0.3 mm, and for rotation in the plane to be 0.6 degrees. This indicated that the method was useful for studying knee components where the sinkage could reach a range of 0.5-2 mm in a 2 year period.     

Implementation and validation of an implant-based coordinate system for RSA migration calculation

An in vitro radiostereometric analysis (RSA) phantom study of a total knee replacement was carried out to evaluate the effect of implementing two new modifications to the conventional RSA procedure: (i) adding a landmark of the tibial component as an implant marker and (ii) defining an implant-based coordinate system constructed from implant landmarks for the calculation of migration results. The motivation for these two modifications were (i) to improve the representation of the implant by the markers by including the stem tip marker which increases the marker distribution (ii) to recover clinical RSA study cases with insufficient numbers of markers visible in the implant polyethylene and (iii) to eliminate errors in migration calculations due to misalignment of the anatomical axes with the RSA global coordinate system. The translational and rotational phantom studies showed no loss of accuracy with the two new measurement methods. The RSA system employing these methods has a precision of better than 0.05 mm for translations and 0.03° for rotations, and an accuracy of 0.05 mm for translations and 0.15° for rotations. These results indicate that the new methods to improve the interpretability, relevance, and standardization of the results do not compromise precision and accuracy, and are suitable for application to clinical data.     

The robustness and accuracy of in vivo linear wear measurements for knee prostheses based on model-based RSA

Accurate in vivo measurements methods of wear in total knee arthroplasty are required for a timely detection of excessive wear and to assess new implant designs. Component separation measurements based on model-based Roentgen stereophotogrammetric analysis (RSA), in which 3-dimensional reconstruction methods are used, have shown promising results, yet the robustness of these measurements is unknown. In this study, the accuracy and robustness of this measurement for clinical usage was assessed. The validation experiments were conducted in an RSA setup with a phantom setup of a knee in a vertical orientation. 72 RSA images were created using different variables for knee orientations, two prosthesis types (fixed-bearing Duracon knee and fixed-bearing Triathlon knee) and accuracies of the reconstruction models. The measurement error was determined for absolute and relative measurements and the effect of knee positioning and true seperation distance was determined. The measurement method overestimated the separation distance with 0.1mm on average. The precision of the method was 0.10mm (2*SD) for the Duracon prosthesis and 0.20mm for the Triathlon prosthesis. A slight difference in error was found between the measurements with 0° and 10° anterior tilt. (difference=0.08mm, p=0.04). The accuracy of 0.1mm and precision of 0.2mm can be achieved for linear wear measurements based on model-based RSA, which is more than adequate for clinical applications. The measurement is robust in clinical settings. Although anterior tilt seems to influence the measurement, the size of this influence is low and clinically irrelevant.     

Comparative accuracy of radiostereometric and optical tracking systems

This study aims to quantify and compare the accuracy of traditional radiostereometric analysis (RSA), fluoroscopic RSA (fRSA), and optical tracking systems. Three phantoms were constructed, each having three stainless steel spheres and three reflective markers. One phantom was mounted to the base of a precision cross-slide table, one to the base of a precision rotation table, and the third was mounted to each moveable tabletop. Two dial-gauges, rigidly mounted to the cross-slide table and rotation table, quantified translations and rotations. Two fluoroscopy units placed orthogonally tracked the steel spheres while a four-camera optical motion capture system tracked the reflective markers in three-dimensional space. RSA was performed with both digital radiography and fluoroscopy. Three axes of translation were tested: parallel to one fluoroscopy image, parallel to the other fluoroscopy image, and at approximately 45° to each image. One axis of rotation was tested. Intraclass correlation coefficients indicated excellent agreement between the actual (dial-gauge) and measured translations for all modalities (ICCs>0.99) and excellent agreement between actual and measured rotations for RSA and fRSA (ICCs>0.99). Standard errors of measurement ranged from 0.032 mm and 0.121° for RSA, to 0.040 mm and 0.229° for fRSA, and to 0.109 mm and 0.613° for optical tracking. Differences between actual and measured translations along the 45° axis were significantly smaller than the two parallel axes. These findings suggest that under ideal conditions, accuracy of fRSA is comparable to traditional RSA, and superior to optical tracking. Accuracy is highest when measured at 45° to the fluoroscopy units.     

Validation of radiostereometric analysis in six degrees of freedom for use with reverse total shoulder arthroplasty

A phantom study was conducted to determine bias in motion and bias at zero motion of radiostereometric analysis (RSA) for evaluating implant relative displacement in reverse total shoulder arthroplasty (RTSA). A Sawbones shoulder phantom was fitted with a RTSA implant set and 13 tantalum markers. The model was fixed to a manual micrometer, providing controlled movements though fifteen known increments in translation and twelve increments in rotation (0.02–5.00 mm and 0.1–6.0°), along each translation and rotation axis. Movement between the glenoid and humerus was assessed using beads vs. beads (B/B), model vs. beads (M/B), and model vs. model (M/M) measurement methods in a model-based RSA environment. Bias in motion and bias at zero motion were defined as the difference between measured and accepted reference values, and the difference between double examinations with a theoretical displacement of zero, respectively. Bias in motion ranged from 0.054 ± 0.010 to 0.129 ± 0.014 mm and 0.076 ± 0.025 to 0.126 ± 0.025° (B/B), 0.023 ± 0.009 to 0.126 ± 0.016 mm and 0.111 ± 0.033 to 0.794 ± 0.251° (M/B), and 0.029 ± 0.010 to 0.135 ± 0.030 mm and 0.243 ± 0.088 to 0.384 ± 0.153° (M/M). Bias at zero motion ranged from 0.120 to 0.156 mm and 0.075 to 0.206° (B/B), 0.074 to 0.149 mm and 0.067 to 1.953° (M/B), and 0.069 to 0.259 mm and 0.284 to 1.273° (M/M). This is the first RSA for RTSA study, with results comparable to those validating the use of RSA for hip and knee arthroplasties (accepted as 0.05–0.50 mm and 0.15–1.15°), justifying the potential use of RSA as a tool for measuring implant displacement in the shoulder.     

Validation of a low-dose hybrid RSA and fluoroscopy technique: Determination of accuracy, bias and precision

Analyzing skeletal kinematics with radiostereometric analysis (RSA) following corrective orthopedic surgery allows the quantitative comparison of different implant designs. The purpose of this study was to validate a technique for dynamically estimating the relative position and orientation of skeletal segments using RSA and single plane X-ray fluoroscopy. Two micrometer-based in vitro phantom models of the skeletal segments in the hip and knee joints were used. The spatial positions of tantalum markers that were implanted into each skeletal segment were reconstructed using RSA. The position and orientation of each segment were determined in fluoroscopy images by minimizing the difference between the markers measured and projected in the image plane. Accuracy was determined in terms of bias and precision by analyzing the deviation between the applied displacement protocol and measured pose estimates. Measured translational accuracy was less than 100 microm parallel to the image plane and less than 700 microm in the direction orthogonal to the image plane. The measured rotational error was less than 1 degrees . Measured translational and rotational bias was not statistically significant at the 95% level of confidence. The technique allows real-time kinematic skeletal measurements to be performed on human subjects implanted with tantalum markers for quantitatively measuring the motion of normal joints and different implant designs.     

Radiostereometric analysis using clinical radiographic views: Development of a universal calibration object

Radiostereometric analysis (RSA) is a highly accurate technique used to provide three-dimensional (3D) measurements of orthopaedic implant migration for clinical research applications, yet its implementation in routine clinical examinations has been limited. Previous studies have introduced a modified RSA procedure that separates the calibration examinations from the patient examinations, allowing routine clinical radiographs to be analyzed using RSA. However, in order to calibrate the wide range of clinical views, a new calibration object is required. In this study, a universal, isotropic calibration object was designed to calibrate any pair of radiographic views used in the clinic for RSA. A numerical simulation technique was used to design the calibration object, followed by a phantom validation test of a prototype to verify the performance of the novel object, and to compare the measurement reliability to the conventional calibration cage. The 3D bias for the modified calibration method using the new calibration object was 0.032 ± 0.006 mm, the 3D repeatability standard deviation was 0.015 mm, and the 3D repeatability limit was 0.042 mm. Although statistical differences were present between the universal calibration object and the conventional cage, the differences were considered to be not clinically meaningful. The 3D bias and repeatability values obtained using the universal calibration object were well under the threshold acceptable for RSA, therefore it was successfully validated. The universal calibration object will help further the adoption of RSA into a more routine practice, providing the opportunity to generate quantitative databases on joint replacement performance.     

Development of an RSA calibration system with improved accuracy and precision

In this study, a new radiostereometric analysis (RSA) calibration cage was developed with the aim of improving the accuracy and precision of RSA. This development consisted of three steps: a numerical simulation technique was first used to design the new cage; a synthetic imaging method was then implemented to predict the performance of the designed cage before it was actually fabricated; and an experimental phantom test was finally conducted to verify the actual performance of the new cage and compare with two currently widely used cages. Accuracy was calculated as the 95% prediction intervals from regression analyses between the measured and actual displacements, and precision was defined as the standard deviation of repeated measurements. The final experimental phantom tests showed that the accuracy and precision of the new calibration cage were improved by about 40% over an existing biplanar cage and by about 70% compared to a uniplanar cage design. This new cage can be used with any skeletal joints, in either static or kinematic examination, which is helpful for the standardization of the RSA application.     

A combined RSA and FE study of the implanted proximal tibia: correlation of the post-operative mechanical environment with implant migration

There is strong evidence to suggest that inducible displacements, migration and implant loosening are closely related to the initial mechanical environment of the implanted tibia. If this is true, then it should be possible to predict the likelihood of implant migration using patient-specific finite element models. Finite element models of the proximal implanted tibiae were analysed based on pre-operative quantitative computed tomography data of four patients entered into a radiographic migration study. These four patients were also part of an radiostereometric analysis (RSA) study. A variety of load cases were analysed and the risk of bone failure determined for a 2 mm layer of bone immediately beneath the tibial tray. The results were compared with the RSA data measured 1 year post-operatively for each patient. For each patient, an appropriate load case was selected based on patient weight and on the varus-valgus migrations observed in the migration study. The two patients with press-fit implants were predicted to have the highest risk of failure and were found to migrate the most. The two patients with bonded implants (one HA coated and one cemented) were found to have a low risk of failure and these implants migrated the least. This study suggests that the degree of implant migration is dependent on the initial mechanical environment and can be determined using patient-specific finite element analysis.     

Improved execution efficiency of model-based roentgen stereophotogrammetric analysis: simplification and segmentation of model meshes

Recently, the model-based roentgen stereophotogrammetric analysis (RSA) method has been developed as an in vivo tool to estimate static pose and dynamic motion of the instrumented prostheses. The two essential inputs for the RSA method are prosthetic models and roentgen images. During RSA calculation, the implants are often reversely scanned and input in the form of meshes to estimate the outline error between prosthetic projection and roentgen images. However, the execution efficiency of the RSA iterative calculation may limit its clinical practicability, and one reason for inefficiency may be very large number of meshes in the model. This study uses two methods of mesh manipulation to improve the execution efficiency of RSA calculation. The first is to simplify the model meshes and the other is to segment and delete the meshes of insignificant regions. An index (i.e. critical percentage) of an optimal element number is defined as the trade-off between execution efficiency and result accuracy. The predicted results are numerically validated by total knee prosthetic system. The outcome shows that the optimal strategy of the mesh manipulation is simplification and followed by segmentation. On average, the element number can even be reduced to 1% of the original models. After the mesh manipulation, the execution efficiency can be increased about 75% without compromising the accuracy of the predicted RSA results (the increment of rotation and translation error: 0.06° and 0.02 mm). In conclusion, prosthetic models should be manipulated by simplification and segmentation methods prior to the RSA calculation to increase the execution efficiency and then to improve clinical applicability of the RSA method.     

A model-free feature-based bi-planar RSA method for kinematic analysis of total knee arthroplasty

Fluoroscopic imaging is commonly used for assessing relative motions of orthopaedic implants. One limiting factor to in vivo model-based roentgen stereophotogrammetric analysis of total knee arthroplasty is the need for 3D models of the implants.The 3D models of the implant components must be reverse-engineered, if not provided by the company, which makes this method impractical for a clinical study involving many types or sizes of implants. This study introduces a novel feature-based methodology that registers the features at the implant-bone or implant-cement interface of the components that have elementary shapes. These features include pegs with hemispherical heads, and straight, circular or curved edges located on flat faces of the box of the femoral component or the stem geometry of the tibial component. Software was developed to allow easy registration of these features through a graphical user interface. The accuracy and precision of registration for multiple flexion angles from 0 to 120 deg was determined with reference to registered poses of the implants through experiments on bone replica models and also on a cadaver specimen implanted with total knee prostheses. When compared to an equivalent bi-planar model-based registration, the results were comparable: The mean accuracy of this feature-based method was 1.45 deg and 1.03 mm (in comparison to 0.95 deg and 1.32 mm for the model-based approach), and the mean precision was 0.57 deg and 0.26 mm (in comparison to 0.42 deg and 0.44 mm for the model-based approach).The methodology and the developed software can easily accommodate different design of implants with various fixation features. This method can facilitate in vivo kinematic analysis of total knee arthroplasty by eliminating the need for 3D models of the implant components.     

Three-dimensional computer simulation of radiostereometric analysis (RSA) in distal radius fractures

Physical phantom models have conventionally been used to determine the accuracy and precision of radiostereometric analysis (RSA) in various orthopaedic applications. Using a phantom model of a fracture of the distal radius it has previously been shown that RSA is a highly accurate and precise method for measuring both translation and rotation in three-dimensions (3-D). The main shortcoming of a physical phantom model is its inability to mimic complex 3-D motion. The goal of this study was to create a realistic computer model for preoperative planning of RSA studies and to test the accuracy of RSA in measuring complex movements in fractures of the distal radius using this new model. The 3-D computer model was created from a set of tomographic scans. The simulation of the radiographic imaging was performed using ray-tracing software (POV-Ray). RSA measurements were performed according to standard protocol. Using a two-part fracture model (AO/ASIF type A2), it was found that for simple movements in one axis, translations in the range of 25microm-2mm could be measured with an accuracy of +/-2microm. Rotations ranging from 16 degrees to 2 degrees could be measured with an accuracy of +/-0.015 degrees . Using a three-part fracture model the corresponding values of accuracy were found to be +/-4microm and +/-0.031 degrees for translation and rotation, respectively. For complex 3-D motion in a three-part fracture model (AO/ASIF type C1) the accuracy was +/-6microm for translation and +/-0.120 degrees for rotation. The use of 3-D computer modelling can provide a method for preoperative planning of RSA studies in complex fractures of the distal radius and in other clinical situations in which the RSA method is applicable.     

Imaging knee position using MRI, RSA/CT and 3D digitisation

The purpose of this study was to compare 3 methods of imaging knee position. Three fresh cadaver knees were imaged at 6 flexion angles between 0 degrees and 120 degrees by MRI, a combination of RSA and CT and 3D digitisation (in two knees). Virtual models of all 42 positions were created using suitable computer software. Each virtual model was aligned to a newly defined anatomically based Cartesian coordinate system. The angular rotations around the 3 coordinate system axes were calculated directly from the aligned virtual models using rigid body kinematics and found to be equally accurate for the 3 methods. The 3 rotations in each knee could be depicted using anatomy-based diagrams for all 3 methods. We conclude that the 3 methods of data acquisition are equally and adequately accurate in vitro. MRI may be the most useful in vivo.     

Validation of a new model-based tracking technique for measuring three-dimensional, in vivo glenohumeral joint kinematics

Shoulder motion is complex and significant research efforts have focused on measuring glenohumeral joint motion. Unfortunately, conventional motion measurement techniques are unable to measure glenohumeral joint kinematics during dynamic shoulder motion to clinically significant levels of accuracy. The purpose of this study was to validate the accuracy of a new model-based tracking technique for measuring three-dimensional, in vivo glenohumeral joint kinematics. We have developed a model-based tracking technique for accurately measuring in vivo joint motion from biplane radiographic images that tracks the position of bones based on their three-dimensional shape and texture. To validate this technique, we implanted tantalum beads into the humerus and scapula of both shoulders from three cadaver specimens and then recorded biplane radiographic images of the shoulder while manually moving each specimen's arm. The position of the humerus and scapula were measured using the model-based tracking system and with a previously validated dynamic radiostereometric analysis (RSA) technique. Accuracy was reported in terms of measurement bias, measurement precision, and overall dynamic accuracy by comparing the model-based tracking results to the dynamic RSA results. The model-based tracking technique produced results that were in excellent agreement with the RSA technique. Measurement bias ranged from -0.126 to 0.199 mm for the scapula and ranged from -0.022 to 0.079 mm for the humerus. Dynamic measurement precision was better than 0.130 mm for the scapula and 0.095 mm for the humerus. Overall dynamic accuracy indicated that rms errors in any one direction were less than 0.385 mm for the scapula and less than 0.374 mm for the humerus. These errors correspond to rotational inaccuracies of approximately 0.25 deg for the scapula and 0.47 deg for the humerus. This new model-based tracking approach represents a non-invasive technique for accurately measuring dynamic glenohumeral joint motion under in vivo conditions. The model-based technique achieves accuracy levels that far surpass all previously reported non-invasive techniques for measuring in vivo glenohumeral joint motion. This technique is supported by a rigorous validation study that provides a realistic simulation of in vivo conditions and we fully expect to achieve these levels of accuracy with in vivo human testing. Future research will use this technique to analyze shoulder motion under a variety of testing conditions and to investigate the effects of conservative and surgical treatment of rotator cuff tears on dynamic joint stability.     

Comparison of random-effects meta-analysis models for the relative risk in the case of rare events: A simulation study

Pooling the relative risk (RR) across studies investigating rare events, for example, adverse events, via meta-analytical methods still presents a challenge to researchers. The main reason for this is the high probability of observing no events in treatment or control group or both, resulting in an undefined log RR (the basis of standard meta-analysis). Other technical challenges ensue, for example, the violation of normality assumptions, or bias due to exclusion of studies and application of continuity corrections, leading to poor performance of standard approaches. In the present simulation study, we compared three recently proposed alternative models (random-effects [RE] Poisson regression, RE zero-inflated Poisson [ZIP] regression, binomial regression) to the standard methods in conjunction with different continuity corrections and to different versions of beta-binomial regression. Based on our investigation of the models' performance in 162 different simulation settings informed by meta-analyses from the Cochrane database and distinguished by different underlying true effects, degrees of between-study heterogeneity, numbers of primary studies, group size ratios, and baseline risks, we recommend the use of the RE Poisson regression model. The beta-binomial model recommended by Kuss (2015) also performed well. Decent performance was also exhibited by the ZIP models, but they also had considerable convergence issues. We stress that these recommendations are only valid for meta-analyses with larger numbers of primary studies. All models are applied to data from two Cochrane reviews to illustrate differences between and issues of the models. Limitations as well as practical implications and recommendations are discussed; a flowchart summarizing recommendations is provided.     

Linear regression models for solvent accessibility prediction in proteins.

The relative solvent accessibility (RSA) of an amino acid residue in a protein structure is a real number that represents the solvent exposed surface area of this residue in relative terms. The problem of predicting the RSA from the primary amino acid sequence can therefore be cast as a regression problem. Nevertheless, RSA prediction has so far typically been cast as a classification problem. Consequently, various machine learning techniques have been used within the classification framework to predict whether a given amino acid exceeds some (arbitrary) RSA threshold and would thus be predicted to be "exposed," as opposed to "buried." We have recently developed novel methods for RSA prediction using nonlinear regression techniques which provide accurate estimates of the real-valued RSA and outperform classification-based approaches with respect to commonly used two-class projections. However, while their performance seems to provide a significant improvement over previously published approaches, these Neural Network (NN) based methods are computationally expensive to train and involve several thousand parameters. In this work, we develop alternative regression models for RSA prediction which are computationally much less expensive, involve orders-of-magnitude fewer parameters, and are still competitive in terms of prediction quality. In particular, we investigate several regression models for RSA prediction using linear L1-support vector regression (SVR) approaches as well as standard linear least squares (LS) regression. Using rigorously derived validation sets of protein structures and extensive cross-validation analysis, we compare the performance of the SVR with that of LS regression and NN-based methods. In particular, we show that the flexibility of the SVR (as encoded by metaparameters such as the error insensitivity and the error penalization terms) can be very beneficial to optimize the prediction accuracy for buried residues. We conclude that the simple and computationally much more efficient linear SVR performs comparably to nonlinear models and thus can be used in order to facilitate further attempts to design more accurate RSA prediction methods, with applications to fold recognition and de novo protein structure prediction methods.