Lina Schelin

Spatially Balanced Sampling through the Pivotal Method

A simple method to select a spatially balanced sample using equal or unequal inclusion probabilities is presented. For populations with spatial trends in the variables of interest, the estimation can be much improved by selecting samples that are well spread over the population. The method can be used for any number of dimensions and can hence also select spatially balanced samples in a space spanned by several auxiliary variables. Analysis and examples indicate that the suggested method achieves a high degree of spatial balance and is therefore efficient for populations with trends.

One-leg hop kinematics 20 years following anterior cruciate ligament rupture: Data revisited using functional data analysis

BACKGROUND Despite interventions, anterior cruciate ligament ruptures can cause long-term deficits. To assist in identifying and treating deficiencies, 3D-motion analysis is used for objectivizing data. Conventional statistics are commonly employed to analyze kinematics, reducing continuous data series to discrete variables. Conversely, functional data analysis considers the entire data series. METHODS Here, we employ functional data analysis to examine and compare the entire time-domain of knee-kinematic curves from one-leg hops between and within three groups. All subjects (n=95) were part of a long-term follow-up study involving anterior cruciate ligament ruptures treated ~20 years ago conservatively with physiotherapy only or with reconstructive surgery and physiotherapy, and matched knee-healthy controls. FINDINGS Between-group differences (injured leg, treated groups; non-dominant leg, controls) were identified during the take-off and landing phases, and in the sagittal (flexion/extension) rather than coronal (abduction/adduction) and transverse (internal/external) planes. Overall, surgical and control groups demonstrated comparable knee-kinematic curves. However, compared to controls, the physiotherapy-only group exhibited less flexion during the take-off (0-55% of the normalized phase) and landing (44-73%) phase. Between-leg differences were absent in controls and the surgically treated group, but observed during the flight (4-22%, injured leg>flexion) and the landing (57-85%, injured leg<internal rotation) phases in the physiotherapy-only group. INTERPRETATION Functional data analysis identified specific functional knee-joint deviations from controls persisting 20 years post anterior cruciate ligament rupture, especially when treated conservatively. This approach is suggested as a means for comprehensively analyzing complex movements, adding to previous analyses.

The Arm Posture Score for assessing arm swing during gait: An evaluation of adding rotational components and the effect of different gait speeds

In 3D gait analysis, quantification of leg movements is well established, whereas a measure of arm swing has been lacking. Recently, the Arm Posture Score (APS) was introduced to characterize arm movements in children with cerebral palsy, including information from four variables (APS4) in the sagittal and frontal planes. A potential limitation of the APS is that it does not include rotational movements and has not yet been evaluated with regard to gait speed. The aims of this study were (i) to investigate the effect on APS of adding two components of arm rotation (APS6) and (ii) to determine the influence of gait speed on the APS measures, when applied to non-disabled adults. Forty-two subjects walked 10 m at a self-selected speed (1.34 m/s), and in addition a subgroup of 28 subjects walked at a slow speed (0.66 m/s) set by a metronome. Data were collected from markers in a whole-body set up and by eight optoelectronic cameras. The results demonstrated significantly higher APS6 than APS4 values for both arms, irrespective of gait speed. Speed condition, whether self-selected or slow, had a significant effect on both APS measures. The two additional arm components are suggested to provide relevant information about arm swing during walking. However, APS6 needs to be implemented in gait analysis of individuals with gait arm pathologies in order to further examine its utility. We recommend that gait speed should to be taken into account when using APS measures to quantify arm swing during gait.

Spatial prediction in the presence of left-censoring

Environmental (spatial) monitoring of different variables often involves left-censored observations falling below the minimum detection limit (MDL) of the instruments used to quantify them. Several methods to predict the variables at new locations given left-censored observations of a stationary spatial process are compared. The methods use versions of kriging predictors, being the best linear unbiased predictors minimizing the mean squared prediction errors. A semi-naive method that determines imputed values at censored locations in an iterative algorithm together with variogram estimation is proposed. It is compared with a computationally intensive method relying on Gaussian assumptions, as well as with two distribution-free methods that impute the MDL or MDL divided by two at the locations with censored values. Their predictive performance is compared in a simulation study for both Gaussian and non-Gaussian processes and discussed in relation to the complexity of the methods from a users perspective. The method relying on Gaussian assumptions performs, as expected, best not only for Gaussian processes, but also for other processes with symmetric marginal distributions. Some of the (semi-)naive methods also work well for these cases. For processes with skewed marginal distributions (semi-)naive methods work better. The main differences in predictive performance arise for small true values. For large true values no difference between methods is apparent.

Curve analyses reveal altered knee, hip, and trunk kinematics during drop–jumps long after anterior cruciate ligament rupture

BACKGROUND Anterior cruciate ligament (ACL) ruptures may lead to knee dysfunctions later in life. Single-leg tasks are often evaluated, but bilateral movements may also be compromised. Our aim was to use curve analyses to examine double-leg drop-jump kinematics in ACL-reconstructed, ACL-deficient, and healthy-knee cohorts. METHODS Subjects with unilateral ACL ruptures treated more than two decades ago (17-28years) conservatively with physiotherapy (ACLPT, n=26) or in combination with reconstructive surgery (ACLR, n=28) and healthy-knee controls (n=25) performed 40-cm drop-jumps. Three-dimensional knee, hip, and trunk kinematics were analyzed during Rebound, Flight, and Landing phases. Curves were time-normalized and compared between groups (injured and non-injured legs of ACLPT and ACLR vs. non-dominant and dominant legs of controls) and within groups (between legs) using functional analysis of variance methods. RESULTS Compared to controls, ACL groups exhibited less knee and hip flexion on both legs during Rebound and greater knee external rotation on their injured leg at the start of Rebound and Landing. ACLR also showed less trunk flexion during Rebound. Between-leg differences were observed in ACLR only, with the injured leg more internally rotated at the hip. Overall, kinematic curves were similar between ACLR and ACLPT. However, compared to controls, deviations spanned a greater proportion of the drop-jump movement at the hip in ACLR and at the knee in ACLPT. CONCLUSIONS Trunk and bilateral leg kinematics during double-leg drop-jumps are still compromised long after ACL-rupture care, independent of treatment. Curve analyses indicate the presence of distinct compensatory mechanisms in ACLPT and ACLR compared to controls.

A statistically compiled test battery for feasible evaluation of knee function after rupture of the Anterior Cruciate Ligament - derived from long-term follow-up data.

Purpose Clinical test batteries for evaluation of knee function after injury to the Anterior Cruciate Ligament (ACL) should be valid and feasible, while reliably capturing the outcome of rehabilitation. There is currently a lack of consensus as to which of the many available assessment tools for knee function that should be included. The present aim was to use a statistical approach to investigate the contribution of frequently used tests to avoid redundancy, and filter them down to a proposed comprehensive and yet feasible test battery for long-term evaluation after ACL injury. Methods In total 48 outcome variables related to knee function, all potentially relevant for a long-term follow-up, were included from a cross-sectional study where 70 ACL-injured (17–28 years post injury) individuals were compared to 33 controls. Cluster analysis and logistic regression were used to group variables and identify an optimal test battery, from which a summarized estimator of knee function representing various functional aspects was derived. Results As expected, several variables were strongly correlated, and the variables also fell into logical clusters with higher within-correlation (max ρ = 0.61) than between clusters (max ρ = 0.19). An extracted test battery with just four variables assessing one-leg balance, isokinetic knee extension strength and hop performance (one-leg hop, side hop) were mathematically combined to an estimator of knee function, which acceptably classified ACL-injured individuals and controls. This estimator, derived from objective measures, correlated significantly with self-reported function, e.g. Lysholm score (ρ = 0.66; p<0.001). Conclusions The proposed test battery, based on a solid statistical approach, includes assessments which are all clinically feasible, while also covering complementary aspects of knee function. Similar test batteries could be determined for earlier phases of ACL rehabilitation or to enable longitudinal monitoring. Such developments, established on a well-grounded consensus of measurements, would facilitate comparisons of studies and enable evidence-based rehabilitation.