Full Gait Cycle Knee Kinematics of Healthy Adults Measured Using Biplane Radiography

A dataset of knee kinematics in healthy, uninjured adults is needed to serve as a reference for comparison when evaluating the effects of injury, surgery, rehabilitation, and age. Most currently available datasets that characterize healthy knee kinematics were developed using conventional motion analysis, known to suffer from skin motion artifact. More accurate kinematics, obtained from bone pins or biplane radiography, have been reported for datasets ranging in size from 5 to 15 knees. The aim of this study was to characterize tibiofemoral kinematics and its variability in a larger sample of healthy adults. Thirty-nine knees were imaged using biplane radiography at 100 images/s during multiple trials of treadmill walking. Multiple gait trials were captured to measure stance and swing phase knee kinematics. 6DOF kinematics were determined using a validated volumetric model-based tracking process. A bootstrapping technique was used to define average and 90% prediction bands for the kinematics. The average ROM during gait was 7.0 mm, 3.2 mm, and 2.9 mm in AP, ML and PD directions, and 67.3°, 11.5° and 3.7° in FE, IE, and AbAd. Continuous kinematics demonstrated large inter-knee variability, with 90% prediction bands spanning approximately ±4 mm, ±10 mm, and ±5 mm for ML, AP, and PD translations and ±15°, ±10°, and ±6° in FE, IE, and AbAd. This dataset suggests substantial variability exists in healthy knee kinematics. This study provides a normative database for evaluating knee kinematics in patients who receive conservative or surgical treatment.

Refined Bonferroni prediction bands for autoregressive models

Joint prediction bands are often constructed using Bonferroni’s inequality. The drawback of such bands may be their large width and excessive coverage probability. The paper proposes two refinements to the basic Bonferroni method of constructing bootstrap prediction bands. These are based on higher order inequalities and optimization of the width of the band. The procedures are applied to the problem of predicting univariate autoregressive processes. Their properties are studied by means of Monte Carlo experiments. It is shown that the proposed methods lead, in many scenarios, to obtaining relatively narrow prediction bands with desired coverage probabilities.

Generating prediction bands for path forecasts from SETAR models

Prediction bands for time series are usually generated point-wise by bootstrap methods. Such bands only convey the prediction uncertainty for each horizon separately. The joint distribution is not taken into account. To represent the forecast uncertainty over the entire horizon, methods for constructing joint prediction bands for path forecasts from SETAR models are proposed. This class of nonlinear models is increasingly used in time series analysis and forecasting as it is useful for capturing nonlinear dynamics. Approaches based on statistical theory and explicit sequential and global optimization methods are both considered. Monte Carlo simulation is used to assess the performance of the proposed methods. The comparison is done with regard to the actual coverage of the constructed prediction bands for full path forecasts as well as with regard to the width of the bands. An empirical application demonstrates the relevance of the choice of bands for indicating the uncertainty of path forecasts in nonlinear models.