The probability of false positives in zero-dimensional analyses of one-dimensional kinematic, force and EMG trajectories

A false positive is the mistake of inferring an e↵ect when none exists, and although alpha controls the false positive (Type I error) rate in classical hypothesis testing, a given alpha value is accurate only if the underlying model of randomness appropriately reflects experimentally observed variance. Hypotheses pertaining to one-dimensional (1D) (e.g. time-varying) biomechanical trajectories are most often tested using a traditional zero-dimensional (0D) Gaussian model of randomness, but variance in these datasets variance is clearly 1D. The purpose of this study was to determine the likelihood that analyzing smooth 1D data with a 0D model of variance will produce false positives. We first used random field theory (RFT) to predict the probability of false positives in 0D analyses. We then validated RFT predictions via numerical simulations of smooth Gaussian 1D trajectories. Results showed that, across a range of public kinematic, force and EMG datasets, the median false positive rate was 0.382 and not the assumed alpha=0.05, even for a simple two-sample t test involving N=10 trajectories per group. The median false positive rates for experiments involving three-component vector trajectories was p=0.764. This rate increased to p=0.945 for two three-component vector trajectories, and to p=0.999 for six three-component vectors. This implies that experiments involving vector trajectories have a high probability of yielding 0D statistical significance when there is, in fact, no 1D effect. Either (a) explicit a priori identification of 0D metrics or (b) adoption of 1D methods can more tightly control alpha

On the validity of statistical parametric mapping for nonuniformly and heterogeneously smooth one-dimensional biomechanical data

Nonuniform (non-constant) temporal smoothness can arise in biomechanical processes like impacts, and heterogeneous smoothness (unequal smoothness across observations) can arise in mechanically diverse comparisons such as padded vs. unpadded impacts, where padded dynamics are generally smoother than unpadded dynamics. It has been reported that statistical parametric mapping’s (SPM’s) probability values can be invalid for such cases. The purpose of this paper was to clarify the scope of validity for SPM analysis of nonuniformly and heterogeneously smooth one-dimensional (1D) data. We simulated a variety of nonuniformly and heterogeneously smooth Gaussian 1D data over a range of smoothness values, and computed Type I error rates across 10,000 simulation iterations for each smoothness type. Results showed that, in all cases, SPM accurately controlled error at the prescribed α=0.05. Moreover, the distribution of false positives was uniform across time, implying that all regions are equally likely to produce false positives, irrespective of local roughness. We nevertheless show that cluster-level inferences (i.e., p values specific to local regions of significance) may be over-or-underestimated by approximately 0.01 (for the currently simulated scenarios), but never exceed α by definition. We conclude that SPM’s null hypothesis rejection decisions are valid for both nonuniform and heterogeneous 1D data, but that clusters’ p values may be marginally too small/large in rough/smooth regions, respectively. Since cluster-level p values never exceed α, these p value errors are negligible for hypothesis testing purposes. Nevertheless, inter-cluster p value comparisons should be avoided. Implications for statistical power and general results interpretation are discussed

Foot pressure distribution in White Rhinoceroses (Ceratotherium simum) during walking

White rhinoceroses (Ceratotherium simum) are odd-toed ungulates that belong to the group Perissodactyla. Being second only to elephants in terms of large body mass amongst extant tetrapods, rhinoceroses make fascinating subjects for the study of how large land animals support and move themselves. Rhinoceroses often are kept in captivity for protection from ivory poachers and for educational/touristic purposes, yet a detrimental side effect of captivity can be foot disease (i.e., enthesopathies and osteoarthritis around the phalanges). Foot diseases in large mammals are multifactorial, but locomotor biomechanics (e.g., pressures routinely experienced by the feet) surely can be a contributing factor. However, due to a lack of in vivo experimental data on rhinoceros foot pressures, our knowledge of locomotor performance and its links to foot disease is limited. The overall aim of this study was to characterize peak pressures and center of pressure trajectories in white rhinoceroses during walking. We asked two major questions. First, are peak locomotor pressures the lowest around the fat pad and its lobes (as in the case of elephants)? Second, are peak locomotor pressures concentrated around the areas with the highest reported incidence of pathologies? Our results show a reduction of pressures around the fat pad and its lobes, which is potentially due to the material properties of the fat pad or a tendency to avoid or limit “heel” contact at impact. We also found an even and gradual concentration of foot pressures across all digits, which may be a by-product of the more horizontal foot roll-off during the stance phase. While our exploratory, descriptive sample precluded hypothesis testing, our study provides important new data on rhinoceros locomotion for future studies to build on, and thus impetus for improved implementation in the care of captive/managed rhinoceroses

Vector field statistics for objective center-of-pressure trajectory analysis during gait, with evidence of scalar sensitivity to small coordinate system rotations

Center of pressure (COP) trajectories summarize the complex mechanical interaction between the foot and a contacted surface. Each trajectory itself is also complex, comprising hundreds of instantaneous vectors over the duration of stance phase. To simplify statistical analysis often a small number of scalars are extracted from each COP trajectory. The purpose of this paper was to demonstrate how a more objective approach to COP analysis can avoid particular sensitivities of scalar extraction analysis. A previously published dataset describing the effects of walking speed on plantar pressure (PP) distributions was re-analyzed. After spatially and temporally normalizing the data, speed effects were assessed using a vector-field paired Hotelling's T-2 test. Results showed that, as walking speed increased, the COP moved increasingly posterior at heel contact, and increasingly laterally and anteriorly between similar to 60 and 85% stance, in agreement with previous independent studies. Nevertheless, two extracted scalars disagreed with these results. Furthermore, sensitivity analysis found that a relatively small coordinate system rotation of 5.5 degrees reversed the mediolateral null hypothesis rejection decision. Considering that the foot may adopt arbitrary postures in the horizontal plane, these sensitivity results suggest that non-negligible uncertainty may exist in mediolateral COP effects. As compared with COP scalar extraction, two key advantages of the vector-field approach are: (i) coordinate system independence, (ii) continuous statistical data reflecting the temporal extents of COP trajectory changes.ArticleGAIT & POSTURE. 40(1):255-258 (2014)journal articl

Knee and Hip Joint Kinematics Predict Quadriceps and Hamstrings Neuromuscular Activation Patterns in Drop Jump Landings.

PURPOSE: The purpose was to assess if variation in sagittal plane landing kinematics is associated with variation in neuromuscular activation patterns of the quadriceps-hamstrings muscle groups during drop vertical jumps (DVJ). METHODS: Fifty female athletes performed three DVJ. The relationship between peak knee and hip flexion angles and the amplitude of four EMG vectors was investigated with trajectory-level canonical correlation analyses over the entire time period of the landing phase. EMG vectors consisted of the {vastus medialis(VM),vastus lateralis(VL)}, {vastus medialis(VM),hamstring medialis(HM)}, {hamstring medialis(HM),hamstring lateralis(HL)} and the {vastus lateralis(VL),hamstring lateralis(HL)}. To estimate the contribution of each individual muscle, linear regressions were also conducted using one-dimensional statistical parametric mapping. RESULTS: The peak knee flexion angle was significantly positively associated with the amplitudes of the {VM,HM} and {HM,HL} during the preparatory and initial contact phase and with the {VL,HL} vector during the peak loading phase (p<0.05). Small peak knee flexion angles were significantly associated with higher HM amplitudes during the preparatory and initial contact phase (p<0.001). The amplitudes of the {VM,VL} and {VL,HL} were significantly positively associated with the peak hip flexion angle during the peak loading phase (p<0.05). Small peak hip flexion angles were significantly associated with higher VL amplitudes during the peak loading phase (p = 0.001). Higher external knee abduction and flexion moments were found in participants landing with less flexed knee and hip joints (p<0.001). CONCLUSION: This study demonstrated clear associations between neuromuscular activation patterns and landing kinematics in the sagittal plane during specific parts of the landing. These findings have indicated that an erect landing pattern, characterized by less hip and knee flexion, was significantly associated with an increased medial and posterior neuromuscular activation (dominant hamstrings medialis activity) during the preparatory and initial contact phase and an increased lateral neuromuscular activation (dominant vastus lateralis activity) during the peak loading phase

A force profile analysis comparison between functional data analysis, statistical parametric mapping and statistical non-parametric mapping in on-water single sculling

Objectives: To examine whether the Functional Data Analysis (FDA), Statistical Parametric Mapping (SPM) and Statistical non-Parametric Mapping (SnPM) hypothesis testing techniques differ in their ability to draw inferences in the context of a single, simple experimental design. Design: The sample data used is cross-sectional (two-sample gender comparison) and evaluation of differences between statistical techniques used a combination of descriptive and qualitative assessments. Methods: FDA, SPM and SnPM t-tests were applied to sample data of twenty highly skilled male and female rowers, rowing at 32 strokes per minute in a single scull boat. Statistical differences for gender were assessed by applying two t-tests (one for each side of the boat). Results: The t-statistic values were identical for all three methods (with the FDA t-statistic presented as an absolute measure). The critical t-statistics (tcrit) were very similar between the techniques, with SPM tcrit providing a marginally higher tcrit than the FDA and SnPM tcrit values (which were identical). All techniques were successful in identifying consistent sections of the force waveform, where male and female rowers were shown to differ significantly (p < 0.05). Conclusions: This is the first study to show that FDA, SPM and SnPM t-tests provide consistent results when applied to sports biomechanics data. Though the results were similar, selection of one technique over another by applied researchers and practitioners should be based on the underlying parametric assumption of SPM, as well as contextual factors related to the type of waveform data to be analysed and the experimental research question of interest

Intra-subject sample size effects in plantar pressure analyses

Background Recent work using large datasets (>500 records per subject) has demonstrated seemingly high levels of step-to-step variation in peak plantar pressure within human individuals during walking. One intuitive consequence of this variation is that smaller sample sizes (e.g., 10 steps per subject) may be quantitatively and qualitatively inaccurate and fail to capture the variance in plantar pressure of individuals seen in larger data sets. However, this remains quantitatively unexplored reflecting a lack of detailed investigation of intra-subject sample size effects in plantar pressure analysis. Methods Here we explore the sensitivity of various plantar pressure metrics to intra-subject sample size (number of steps per subject) using a random subsampling analysis. We randomly and incrementally subsample large data sets (>500 steps per subject) to compare variability in three metric types at sample sizes of 5–400 records: (1) overall whole-record mean and maximum pressure; (2) single-pixel values from five locations across the foot; and (3) the sum of pixel-level variability (measured by mean square error, MSE) from the whole plantar surface. Results Our results indicate that the central tendency of whole-record mean and maximum pressure within and across subjects show only minor sensitivity to sample size >200 steps. However, 400 steps. The range in pixel-level MSE at low subsamples (500 pressure records per subject. Overall, therefore, we demonstrate a high probability that the very small sample sizes (n < 20 records), which are routinely used in human and animal studies, capture a relatively low proportion of variance evident in larger plantar pressure data set, and thus may not accurately reflect the true population mean

Simulation modeling for stratified breast cancer screening : a systematic review of cost and quality of life assumptions

BACKGROUND: The economic evaluation of stratified breast cancer screening gains momentum, but produces also very diverse results. Systematic reviews so far focused on modeling techniques and epidemiologic assumptions. However, cost and utility parameters received only little attention. This systematic review assesses simulation models for stratified breast cancer screening based on their cost and utility parameters in each phase of breast cancer screening and care. METHODS: A literature review was conducted to compare economic evaluations with simulation models of personalized breast cancer screening. Study quality was assessed using reporting guidelines. Cost and utility inputs were extracted, standardized and structured using a care delivery framework. Studies were then clustered according to their study aim and parameters were compared within the clusters. RESULTS: Eighteen studies were identified within three study clusters. Reporting quality was very diverse in all three clusters. Only two studies in cluster 1, four studies in cluster 2 and one study in cluster 3 scored high in the quality appraisal. In addition to the quality appraisal, this review assessed if the simulation models were consistent in integrating all relevant phases of care, if utility parameters were consistent and methodological sound and if cost were compatible and consistent in the actual parameters used for screening, diagnostic work up and treatment. Of 18 studies, only three studies did not show signs of potential bias. CONCLUSION: This systematic review shows that a closer look into the cost and utility parameter can help to identify potential bias. Future simulation models should focus on integrating all relevant phases of care, using methodologically sound utility parameters and avoiding inconsistent cost parameters