A data-driven framework for selecting and validating digital health metrics: use-case in neurological sensorimotor impairments

Christoph M Kanzler, Mike D Rinderknecht, Anne Schwarz, Ilse Lamers, Cynthia Gagnon, Jeremia P O Held, Peter Feys, Andreas R Luft, Roger Gassert, Olivier Lambercy, Christoph M Kanzler, Mike D Rinderknecht, Anne Schwarz, Ilse Lamers, Cynthia Gagnon, Jeremia P O Held, Peter Feys, Andreas R Luft, Roger Gassert, Olivier Lambercy

Abstract

Digital health metrics promise to advance the understanding of impaired body functions, for example in neurological disorders. However, their clinical integration is challenged by an insufficient validation of the many existing and often abstract metrics. Here, we propose a data-driven framework to select and validate a clinically relevant core set of digital health metrics extracted from a technology-aided assessment. As an exemplary use-case, the framework is applied to the Virtual Peg Insertion Test (VPIT), a technology-aided assessment of upper limb sensorimotor impairments. The framework builds on a use-case-specific pathophysiological motivation of metrics, models demographic confounds, and evaluates the most important clinimetric properties (discriminant validity, structural validity, reliability, measurement error, learning effects). Applied to 77 metrics of the VPIT collected from 120 neurologically intact and 89 affected individuals, the framework allowed selecting 10 clinically relevant core metrics. These assessed the severity of multiple sensorimotor impairments in a valid, reliable, and informative manner. These metrics provided added clinical value by detecting impairments in neurological subjects that did not show any deficits according to conventional scales, and by covering sensorimotor impairments of the arm and hand with a single assessment. The proposed framework provides a transparent, step-by-step selection procedure based on clinically relevant evidence. This creates an interesting alternative to established selection algorithms that optimize mathematical loss functions and are not always intuitive to retrace. This could help addressing the insufficient clinical integration of digital health metrics. For the VPIT, it allowed establishing validated core metrics, paving the way for their integration into neurorehabilitation trials.

Keywords: Diagnostic markers; Multiple sclerosis; Neurological disorders; Predictive markers; Prognostic markers.

Conflict of interest statement

Competing interestsThe authors declare no competing interests.

© The Author(s) 2020.

Figures

Fig. 1. Overview of the metric selection…
Fig. 1. Overview of the metric selection framework and the Virtual Peg Insertion Test (VPIT).
a The frameworks allows to select a core set of validated digital health metrics through a transparent step-by-step selection procedure. Model quality criteria C1 and C2; ROC receiver operating characteristics, AUC area under curve, ICC intra-class correlation, SRD% smallest real difference; η strength of learning effects. b The framework was applied to data recorded with the VPIT, a sensor-based upper limb sensorimotor assessment requiring the coordination of arm and hand movements as well as grip forces.
Fig. 2. Data-driven selection and validation of…
Fig. 2. Data-driven selection and validation of metrics: example of task completion time.
a The influence of age, sex, tested body side, handedness, and stereo vision deficits on each digital health metrics was removed using data from neurologically intact subjects and mixed effect models (model quality criteria C1 and C2). Models were fitted in a Box–Cox-transformed space and back-transformed for visualization. Metrics with low model quality (C1 > 15% or C2 > 25%) were removed. b The ability of a metric to discriminate between neurologically intact and affected subjects (discriminant validity) was evaluated using the area under the curve value (AUC). Metrics with AUC < 0.7 were removed. c Test–retest reliability was evaluated using the intra-class correlation coefficient (ICC) indicating the ability of a metric to discriminate between subjects across testing days. Metrics with ICC < 0.7 were removed. Additionally, metrics with strong learning effects (η > −6.35) were removed. The long horizontal red line indicates the median, whereas the short ones represent the 25th and 75th percentile. d Measurement error was defined using the smallest real difference (SRD%), indicating a range of values for that the assessment cannot discriminate between measurement error and physiological changes. The distribution of the intra-subject variability was visualized, as it strongly influences the SRD. Metrics with SRD% > 30.3 were removed.
Fig. 3. Partial correlation analysis.
Fig. 3. Partial correlation analysis.
The objective was to remove redundant information. Therefore, partial Spearman correlations were calculated between all combination of metrics while controlling for the potential influence of all other metrics. Pairs of metrics were considered for removal if the correlation was equal or above 0.5 The process was done in an iterative manner and the first a and the last b iterations are presented.
Fig. 4. Sensitivity of metrics to disability…
Fig. 4. Sensitivity of metrics to disability severity in stroke subjects.
Subjects were grouped according to the clinical disability level. The vertical axis indicates task performance based on the distance to the reference population. The population median is visualized through the black horizontal line, the interquartile range (IQR) through the boxes, and the min and max value within 1.5 IQR of the lower and upper quartiles, respectively, through the whiskers. Data points above the 95th-percentile (triangles) of neurologically intact subjects are showing abnormal behavior (black dots). Solid and dashed horizontal black lines above the box plots indicate results of the omnibus and post-hoc statistical tests, respectively. *Indicates p < 0.05 and **p < 0.001. n refers to the number of subjects in that group and N to the number of data points. Only subjects with available clinical scores were included. For the jerk peg approach, one outlier was not visualized to maintain a meaningful representation. FMA-UE Fugl-Meyer upper extremity, SPARC spectral arc length.
Fig. 5. Sensitivity of metrics to disability…
Fig. 5. Sensitivity of metrics to disability severity in MS subjects.
See Fig. 4 for a detailed description. ARAT action research arm test.
Fig. 6. Sensitivity of metrics to disability…
Fig. 6. Sensitivity of metrics to disability severity in ARSACS subjects.
See Fig. 4 for a detailed description.

References

    1. World Health Organization. International Classification of Functioning, Disability and Health: ICF. Geneva: World Health Organization; 2001.
    1. Lawrence ES, et al. Estimates of the prevalence of acute stroke impairments and disability in a multiethnic population. Stroke. 2001;32:1279–1284.
    1. Kister I, et al. Natural history of multiple sclerosis symptoms. Int. J. MS Care. 2003;15:146–158.
    1. Gagnon C, Desrosiers J, Mathieu J. Autosomal recessive spastic ataxia of charlevoix-saguenay: upper extremity aptitudes, functional independence and social participation. Int. J. Rehabilit. Res. 2004;27:253–256.
    1. Yozbatiran N, Baskurt F, Baskurt Z, Ozakbas S, Idiman E. Motor assessment of upper extremity function and its relation with fatigue, cognitive function and quality of life in multiple sclerosis patients. J. Neurol. Sci. 2006;246:117–122.
    1. Lamers I, Kelchtermans S, Baert I, Feys P. Upper limb assessment in multiple sclerosis: a systematic review of outcome measures and their psychometric properties. Arch. Phys. Med. Rehabilit. 2014;95:1184–1200.
    1. Santisteban L, et al. Upper limb outcome measures used in stroke rehabilitation studies: a systematic literature review. PLoS ONE. 2016;11:1932–6203.
    1. Burridge J, et al. A Systematic review of International Clinical Guidelines for Rehabilitation of People with neurological conditions: what recommendations are made for upper limb assessment? Front. Neurol. 2019;10:1–14.
    1. Gladstone DJ, Danells CJ, Black SE. The Fugl-Meyer assessment of motor recovery after stroke: a critical review of its measurement properties. Neurorehabil. Neural Repair. 2002;16:232–240.
    1. Chen HM, Chen CC, Hsueh IP, Huang SL, Hsieh CL. Test–retest reproducibility and smallest real difference of 5 hand function tests in patients with stroke. Neurorehabil. Neural Repair. 2009;23:435–440.
    1. Hawe RL, Scott SH, Dukelow SP. Taking proportional out of stroke recovery. Stroke. 2018;50:204–211.
    1. Hope TMH, et al. Recovery after stroke: not so proportional after all? Brain. 2019;142:15–22.
    1. Schwarz A, Kanzler CM, Lambercy O, Luft AR, Veerbeek JM. Systematic review on kinematic assessments of upper limb movements after stroke. Stroke. 2019;50:718–727.
    1. Steinhubl SR, Topol E. J. Digital medicine, on its way to being just plain medicine. npj Digit. Med. 2018;1:20175.
    1. Car J, Sheikh A, Wicks P, Williams MS. Beyond the hype of big data and artificial intelligence: building foundations for knowledge and wisdom. BMC Med. 2019;17:143.
    1. Steinhubl SR, Wolff-Hughes DL, Nilsen W, Iturriaga E, Califf RM. Digital clinical trials: creating a vision for the future. npj Digit. Med. 2019;2:126.
    1. Kelly CJ, Karthikesalingam A, Suleyman M, Corrado G, King D. Key challenges for delivering clinical impact with artificial intelligence. BMC Med. 2019;17:195.
    1. Krebs HI, et al. Robotic measurement of arm movements after stroke establishes biomarkers of motor recovery. Stroke. 2014;45:200–204.
    1. Shull PB, Jirattigalachote W, Hunt MA, Cutkosky MR, Delp SL. Quantified self and human movement: a review on the clinical impact of wearable sensing and feedback for gait analysis and intervention. Gait Posture. 2014;40:11–19.
    1. Eskofier B, et al. An overview of smart shoes in the internet of health things: gait and mobility assessment in health promotion and disease monitoring. Appl. Sci. 2017;7:986.
    1. Kwakkel G, et al. Standardized measurement of sensorimotor recovery in stroke trials: consensus-based core recommendations from the stroke recovery and rehabilitation roundtable. Neurorehabilit. Neural Repair. 2017;31:784–792.
    1. Mathews SC, et al. Digital health: a path to validation. npj Digit. Med. 2019;2:1–9.
    1. Shirota C, Balasubramanian S, Melendez-Calderon A. Technology-aided assessments of sensorimotor function: current use, barriers and future directions in the view of different stakeholders. J. Neuroeng. Rehabil. 2019;16:53.
    1. DoTran V, Dario P, Mazzoleni S. Kinematic measures for upper limb robot-assisted therapy following stroke and correlations with clinical outcome measures: a review. Med. Eng. Phys. 2018;53:13–31.
    1. Prinsen CAC, et al. COSMIN guideline for systematic reviews of patient-reported outcome measures. Qual. Life Res. 2018;27:1147–1157.
    1. Shishov N, Melzer I, Bar-Haim S. Parameters and measures in assessment of motor learning in neurorehabilitation; a systematic review of the literature. Front. Hum. Neurosci. 2017;11:1–26.
    1. Kwakkel G, et al. Standardized measurement of quality of upper limb movement after stroke: consensus-based core recommendations from the Second Stroke Recovery and Rehabilitation Roundtable. Int. J. Stroke. 2019;14:783–791.
    1. Williamson PR, et al. Developing core outcome sets for clinical trials: issues to consider. Trials. 2012;13:1–8.
    1. Boers M, et al. Developing core outcome measurement sets for clinical trials: OMERACT filter 2.0. J. Clin. Epidemiol. 2014;67:745–753.
    1. Kirkham JJ, et al. Core Outcome Set-STAndards for Development: the COS-STAD recommendations. PLoS Med. 2017;14:1–10.
    1. Saeys Y, Inza I, Larrañaga P. A review of feature selection techniques in bioinformatics. Bioinformatics. 2007;23:2507–2517.
    1. Ustun B, Rudin C. Supersparse linear integer models for optimized medical scoring systems. Mach. Learn. 2016;102:349–391.
    1. Tibshirani R. Regression shrinkage and selection via the Lasso. J. R. Stat. Soc. 1996;58:267–288.
    1. Fluet, M., Lambercy, O. & Gassert, R. Upper limb assessment using a virtual peg insertion test. In Proc. IEEE International Conference on Rehabilitation Robotics (ICORR). IEEE 1–6 (2011).
    1. Lambercy, O. et al. Assessment of upper limb motor function in patients with multiple sclerosis using the virtual peg insertion test: a pilot study. In Proc. IEEE International Conference on Rehabilitation Robotics (ICORR). IEEE 1–6 (2003).
    1. Hofmann, P., Held, J. P., Gassert, R. & Lambercy, O. Assessment of movement patterns in stroke patients: a case study with the virtual peg insertion test. In Proc International Convention on Rehabilitation Engineering & Assistive Technology (i-CREATe) 2016. Singapore Therapeutic, Assistive & Rehabilitative Technologies (START) Centre14, 1–4 (Assistive & Rehabilitative Technologies (START) Centre, Singapore Therapeutic, 2016).
    1. Tobler-Ammann BC, et al. Concurrent validity and test–retest reliability of the virtual peg insertion test to quantify upper limb function in patients with chronic stroke. J. Neuroeng. Rehabilit. 2016;13:8.
    1. Kanzler, C. M., Gomez, S. M., Rinderknecht, M. D., Gassert, R. & Lambercy, O. Influence of arm weight support on a robotic assessment of upper limb function. In Proc. 7th IEEE International Conference on Biomedical Robotics and Biomechatronics (BioRob). IEEE 1–6 (2018).
    1. Kanzler, C. M. et al. An objective functional evaluation of myoelectrically-controlled hand prostheses: a pilot study using the Virtual Peg Insertion Test. In IEEE 16th International Conference on Rehabilitation Robotics (ICORR). IEEE 392–397 (2019).
    1. Kaiser HF. A second generation little jiffy. Psychometrika. 1970;35:401–415.
    1. Kaiser HF. An index of factorial simplicity. Psychometrika. 1974;39:31–36.
    1. Prinsen CAC, et al. How to select outcome measurement instruments for outcomes included in a Core Outcome Set—a practical guideline. Trials. 2016;17:1–10.
    1. Guyon I, Elisseeff A. An introduction to variable and feature selection. J. Mach. Learn. Res. 2003;3:1157–1182.
    1. Zhou ZH. A brief introduction to weakly supervised learning. Natl Sci. Rev. 2018;5:44–53.
    1. Rinderknecht MD, Lambercy O, Raible V, Liepert J, Gassert R. Age-based model for metacarpophalangeal joint proprioception in elderly. Clin. Interv. Aging. 2017;12:635–643.
    1. Kalisch T, Kattenstroth JC, Kowalewski R, Tegenthoff M, Dinse H. Age-related changes in the joint position sense of the human hand. Clin. Interv. Aging. 2012;7:499.
    1. Herter TM, Scott SH, Dukelow SP. Systematic changes in position sense accompany normal aging across adulthood. J. Neuroeng. Rehabil. 2014;11:1–12.
    1. Tyryshkin K, et al. A robotic object hitting task to quantify sensorimotor impairments in participants with stroke. J. Neuroeng. Rehabil. 2014;11:47.
    1. Verkuilen J, Smithson M. Mixed and mixture regression models for continuous bounded responses using the beta distribution. J. Educ. Behav. Stat. 2011;37:82–113.
    1. Derksen S, Keselman HJ. Backward, forward and stepwise automated subset selection algorithms: Frequency of obtaining authentic and noise variables. Br. J. Math. Stat. Psychol. 1992;45:265–282.
    1. Steyerberg EW, Eijkemans MJC, Habbema JDF. Stepwise selection in small data sets. J. Clin. Epidemiol. 1999;52:935–942.
    1. Harrell, F.E. Regression Modeling Strategies, Vol. 27, Springer Series in Statistics (Springer, New York, NY, 2001).
    1. Whittingham MJ, Stephens PA, Bradbury RB, Freckleton RP. Why do we still use stepwise modelling in ecology and behaviour? J. Anim. Ecol. 2006;75:1182–1189.
    1. Fitts PM. The information capacity of the human motor system in controlling the amplitude of movement. J. Exp. Psychol. 1954;47:381.
    1. Harris CM, Wolpert DM. Signal-dependent noise determines motor planning. Nature. 1998;394:780–784.
    1. Dukelow SP, et al. Quantitative assessment of limb position sense following stroke. Neurorehabilit. Neural Repair. 2010;24:178–187.
    1. Flanagan RJ, Wing AM. Modulation of grip force with load force during point-to-point arm movements. Exp. Brain Res. 1993;95:301–324.
    1. Sathian K, et al. Neurological principles and rehabilitation of action disorders: common clinical deficits. Neurorehabilit. Neural Repair. 2011;25:21–32.
    1. Scott SH. Optimal feedback control and the neural basis of volitional motor control. Nat. Rev. Neurosci. 2004;5:532–546.
    1. Mukherjee A, Chakravarty A. Spasticity mechanisms—for the clinician. Front. Neurol. 2010;1:1–10.
    1. Baker SN. The primate reticulospinal tract, hand function and functional recovery. J. Physiol. 2011;589:5603–5612.
    1. Colombo R, et al. Assessing mechanisms of recovery during robot-aided neurorehabilitation of the upper limb. Neurorehabilit. Neural Repair. 2008;22:50–63.
    1. Coderre AM, et al. Assessment of upper-limb sensorimotor function of subacute stroke patients using visually guided reaching. Neurorehabilit. Neural Repair. 2010;24:528–541.
    1. Murphy MA, Willén C, Sunnerhagen KS. Movement kinematics during a drinking task are associated with the activity capacity level after stroke. Neurorehabilit. Neural Repair. 2012;26:1106–1115.
    1. Kourtis LC, Regele OB, Wright JM, Jones GB. Digital biomarkers for Alzheimeras disease: the mobile/wearable devices opportunity. npj Digit. Med. 2019;2:1–9.
    1. Viau A, Feldman AG, McFadyen BJ, Levin MF. Reaching in reality and virtual reality: a comparison of movement kinematics in healthy subjects and in adults with hemiparesis. J. Neuroeng. Rehabil. 2004;1:1–7.
    1. Magdalon EC, Michaelsen SM, Quevedo AA, Levin MF. Comparison of grasping movements made by healthy subjects in a 3-dimensional immersive virtual versus physical environment. Acta Psychol. 2011;138:126–134.
    1. Lamers I, Feys P. Patient reported outcome measures of upper limb function in multiple sclerosis: a critical overview. Mult. Scler. J. 2018;24:1792–1794.
    1. Subramanian SK, Yamanaka J, Chilingaryan G, Levin MF. Validity of movement pattern kinematics as measures of arm motor impairment poststroke. Stroke. 2010;41:2303–2308.
    1. Kanzler, C. M. et al. A data-driven framework for the selection and validation of digital health metrics: use-case in neurological sensorimotor impairments. Preprint at (2019).
    1. Mathiowetz V, Weber K, Kashman N, Volland G. Adult norms for the nine hole peg test of finger dexterity. Occup. Ther. J. Res. 1985;5:24–38.
    1. Mathiowetz V, Volland G, Kashman N, Weber K. Adult norms for the box and block test of manual dexterity. Am. J. Occup. Ther. 1985;39:386–391.
    1. Gagnon C, et al. The virtual peg insertion test as an assessment of upper limb coordination in ARSACS patients: a pilot study. J. Neurol. Sci. 2014;347:341–344.
    1. Feys P, Coninx K, Kerkhofs L, De Weyer T, Truyens V, et al. Robot-supported upper limb training in a virtual learning environment: a pilot randomized controlled trial in persons with MS. J. Neuroeng. Rehabil. 2005;12:1–12.
    1. Lamers I, et al. Intensity-dependent clinical effects of an individualized technology-supported task-oriented upper limb training program in. Relat. Disord. 2019;34:119–127.
    1. Lang JI, Lang TJ. Eye screening with the lang stereotest. Am. Orthopt. J. 1988;38:48–50.
    1. Lang CE, Bland MD, Bailey RR, Schaefer SY, Birkenmeier RL. Assessment of upper extremity impairment, function, and activity after stroke: foundations for clinical decision making. J. Hand Ther. 2003;26:104–115.
    1. Frey SH, Fogassi L, Grafton S, Picard N, Rothwell JC, et al. Neurological principles and rehabilitation of action disorders: computation, anatomy, and physiology (CAP) model. Neurorehabilit. Neural Repair. 2011;25:6S–20S.
    1. Nordin N, Xie SQ, Wünsche B, Wunsche B. Assessment of movement quality in robot- assisted upper limb rehabilitation after stroke: a review. J. Neuroeng. Rehabil. 2014;11:137.
    1. Flash T, Hogan N. The coordination of arm movements: an experimentally confirmed mathematical model. J. Neurosci. 1985;5:1688–1703.
    1. Rohrer B, et al. Movement smoothness changes during stroke recovery. J. Neurosci. 2002;22:8297–8304.
    1. Pellegrino L, Coscia M, Muller M, Solaro C, Casadio M. Evaluating upper limb impairments in multiple sclerosis by exposure to different mechanical environments. Sci. Rep. 2018;8:2110.
    1. Balasubramanian S, Melendez-Calderon A, Burdet E. A robust and sensitive metric for quantifying movement smoothness. IEEE Trans. Biomed. Eng. 2012;59:2126–2136.
    1. Balasubramanian S, Melendez-Calderon A, Roby-Brami A, Burdet E. On the analysis of movement smoothness. J. Neuroeng. Rehabil. 2005;12:112.
    1. de Graaf JB, Sittig AC, Denier van der Gon JJ. Misdirections in slow goal-directed arm movements and pointer-setting tasks. Exp. Brain Res. 1991;84:434–8.
    1. Cirstea MC, Levin MF. Compensatory strategies for reaching in stroke. Brain. 2000;123:940–953.
    1. Otaka E, et al. Clinical usefulness and validity of robotic measures of reaching movement in hemiparetic stroke patients. J. Neuroeng. Rehabil. 2005;12:66.
    1. Reinkensmeyer DJ, Iobbi MG, Kahn LE, Kamper DG, Takahashi CD. Modeling reaching impairment after stroke using a population vector model of movement control that incorporates neural firing-rate variability. Neural Comput. 2003;15:2619–2642.
    1. Mottet D, Van Dokkum LEH, Froger J, Gouaïch A, Laffont I. Trajectory formation principles are the same after mild or moderate stroke. PLoS ONE. 2017;12:1–17.
    1. Galea JM, Miall RC. Concurrent adaptation to opposing visual displacements during an alternating movement. Exp. Brain Res. 2006;175:676–688.
    1. Kurtzke JF. Rating neurologic impairment in multiple sclerosis: an expanded disability status scale (EDSS) Neurology. 1983;33:1444–1452.
    1. Fahn S, Tolosa E, Marín C. Clinical rating scale for tremor. Parkinsonas Dis. Mov. Disord. 1993;2:271–280.
    1. Kim JS. Delayed onset mixed involuntary movements after thalamic stroke Clinical, radiological and pathophysiological findings. Brain. 2001;124:299–309.
    1. Alusi SH, Worthington J, Glickman S, Bain PG. A study of tremor in multiple sclerosis. Brain. 2001;124:720–730.
    1. Manto M. Mechanisms of human cerebellar dysmetria: experimental evidence and current conceptual bases. J. Neuroeng. Rehabil. 2009;6:1–18.
    1. Carpinella I, Cattaneo D, Ferrarin M. Quantitative assessment of upper limb motor function in multiple sclerosis using an instrumented action research arm test. J. Neuroeng. Rehabil. 2014;11:1–16.
    1. Bardorfer A, Munih M, Zupan A, Primožič A. Upper limb motion analysis using haptic interface. IEEE/ASME Trans. Mechatron. 2001;6:253–260.
    1. Beer RF, Given JD, Dewald JPA. Task-dependent weakness at the elbow in patients with hemiparesis. Arch. Phys. Med. Rehabil. 1999;80:766–772.
    1. Quinn L, Reilmann R, Marder K, Gordon AM. Altered movement trajectories and force control during object transport in Huntington’s disease. Mov. Disord. 2001;16:469–480.
    1. Forssberg H, et al. Development of human precision grip i: Basic coordination of force. Exp. Brain Res. 1992;90:393–398.
    1. Hermsdörfer J, Hagl E, Nowak DA, Marquardt C. Grip force control during object manipulation in cerebral stroke. Clin. Neurophysiol. 2003;114:915–929.
    1. Wenzelburger R, et al. Hand coordination following capsular stroke. Brain. 2005;128:64–74.
    1. Lindberg PG, et al. Affected and unaffected quantitative aspects of grip force control in hemiparetic patients after stroke. Brain Res. 2012;1452:96–107.
    1. Allgöwer K, Hermsdörfer J. Fine motor skills predict performance in the Jebsen Taylor hand function test after stroke. Clin. Neurophysiol. 2017;128:1858–1871.
    1. Iyengar V, Santos MJ, Ko M, Aruin AS. Grip force control in individuals with multiple sclerosis. Neurorehabilit. Neural Repair. 2009;23:855–861.
    1. Gordon AM, Duff SV. Fingertip forces during object manipulation in children with hemiplegic cerebral palsy, I: anticipatory scaling. Dev. Med. Child Neurol. 1991;33:225–231.
    1. Lan Y, Yao J, Dewald JPA. The impact of shoulder abduction loading on volitional hand opening and grasping in chronic hemiparetic stroke. Neurorehabilit. Neural Repair. 2017;31:521–529.
    1. Bolker BM, et al. Generalized linear mixed models: a practical guide for ecology and evolution. Trends Ecol. Evol. 2009;24:127–135.
    1. Fluet, M. C., Lambercy, O. & Gassert, R. Effects of 2D/3D visual feedback and visuomotor collocation on motor performance in a virtual peg insertion test. In Proc. Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBS). IEEE 4776–4779 (2012).
    1. Gerig N, et al. Missing depth cues in virtual reality limit performance and quality of three dimensional reaching movements. PLoS ONE. 2018;13:1–18.
    1. Box GEP, Cox DR. An analysis of transformations. J. R. Stat. Soc. Ser. B. 1964;26:211–252.
    1. Leys C, Ley C, Klein O, Bernard P, Licata L. Detecting outliers: do not use standard deviation around the mean, use absolute deviation around the median. J. Exp. Soc. Psychol. 2003;49:764–766.
    1. Andersen LM. Obtaining reliable likelihood ratio tests from simulated likelihood functions. PLoS ONE. 2014;9:1–12.
    1. Roy K, Das. RN, Ambure P, Aher RB. Be aware of error measures. Further studies on validation of predictive QSAR models. Chemom. Intell. Lab. Syst. 2016;152:18–33.
    1. Hamilton DF, Ghert M, Simpson AHRW. Interpreting regression models in clinical outcome studies. Bone Jt. Res. 2005;4:152–153.
    1. Hosmer Jr DW, Lemeshow S, Sturdivant RX. Applied Logistic Regression. New Jersey: John Wiley; 2003.
    1. Lexell JE, Downham DY. How to assess the reliability of measurements in rehabilitation. J. Phys. Med. Rehabil. 2005;84:719–723.
    1. de Vet HCW, Terwee CB, Knol DL, Bouter LM. When to use agreement versus reliability measures. J. Clin. Epidemiol. 2006;59:1033–1039.
    1. Beckerman H, et al. Smallest real difference, a link between reproducibility and responsiveness. Qual. Life Res. 2001;10:571–578.
    1. Smidt N, et al. Interobserver reproducibility of the assessment of severity of complaints, grip strength, and pressure pain threshold in patients with lateral epicondylitis. Arch. Phys. Med. Rehabil. 2002;83:1145–1150.
    1. Baba K, Shibata R, Sibuya M. Partial correlation and conditional correlation as measures of conditional independence. Aust. N.Z. J. Stat. 2004;46:657–664.
    1. Kenett DY, et al. Dominating clasp of the financial sector revealed by partial correlation analysis of the stock market. PLoS ONE. 2010;5:1–14.
    1. Hinkle DE, Wiersma W, Jurs SG. Applied Statistics for the Behavioral Sciences. Boston: Houghton Mifflin; 1988.
    1. Costello AB, Osborne JW. Best practices in exploratory factor analysis : four recommendations for getting the most from your analysis. Pract. Assess. Res. Educ. 2005;10:1–9.
    1. Hayton JC, Allen DG, Scarpello V. Factor retention decisions in exploratory factor analysis: a tutorial on parallel analysis. Organ. Res. Methods. 2004;7:191–205.
    1. Franklin SB, Gibson DJ, Robertson PA, Pohlmann JT, Fralish JS. Parallel analysis: a method for determining significant principal components. J. Veg. Sci. 2006;6:99–106.
    1. Cattell R. Factors in factor analysis. Psychometrika. 1965;30:179–185.
    1. Woytowicz EJ, et al. Determining levels of upper extremity movement impairment by applying a cluster analysis to the Fugl-Meyer assessment of the upper extremity in chronic stroke. Arch. Phys. Med. Rehabil. 2017;98:456–462.
    1. Hoonhorst MH, et al. How do Fugl-Meyer arm motor scores relate to dexterity according to the action research arm test at 6 months poststroke? Arch. Phys. Med. Rehabil. 2005;96:1845–1849.

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