The reliability and validity of three nonradiological measures of thoracic kyphosis and their relations to the standing radiological Cobb angle.  
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PMID: 20938766 Owner: NLM Status: MEDLINE 
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INTRODUCTION: The objective of this study is to describe the reliability of three nonradiological kyphosis measures (Debrunner kyphosis angle, flexicurve kyphosis index, and flexicurve kyphosis angle) and their validity compared to the Cobb angle and to approximate a Cobb angle from nonradiological kyphosis measures. METHODS: We analyzed data from 113 participants aged ≥ 60 years with kyphosis angle ≥ 40°. Cobb angle was measured on a standing lateral thoracolumbar radiograph using bounds at T4 and T12. Nonradiological measures of kyphosis were made three times by a single rater and a 4th time by a blinded second rater. RESULTS: Intra and interrater reliabilities for nonradiological assessments were high (intraclass correlations of 0.96 to 0.98) and did not differ from each other. Pearson correlations, estimating validity, ranged from 0.62 to 0.69 and did not differ. The Debrunner angle was close to the Cobb angle, with scaling factor of 1.067 and an offset of 5°. The Flexicurve kyphosis angle had to be scaled by 1.53 to obtain the equivalent Cobb angle. The scaling factor for the Flexicurve kyphosis index to Cobb angle was 315, with an offset of 5°. Compared to the measured Cobb angle, Cobb angles predicted using the nonradiological measures had similar magnitude errors (standard deviations of the differences ranging between 10.24 and 11.26). CONCLUSIONS: Each nonradiological measurement had similar reliability and validity. Low cost, ease of use, and robustness to variations in spine contour argue for the Flexicurve in longitudinal kyphosis assessments. The approximate conversion factors provided will permit translation of nonradiological measures to Cobb angles. 
Authors:

G A Greendale; N S Nili; MH Huang; L Seeger; A S Karlamangla 
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Publication Detail:

Type: Journal Article; Randomized Controlled Trial; Research Support, N.I.H., Extramural; Validation Studies Date: 20101012 
Journal Detail:

Title: Osteoporosis international : a journal established as result of cooperation between the European Foundation for Osteoporosis and the National Osteoporosis Foundation of the USA Volume: 22 ISSN: 14332965 ISO Abbreviation: Osteoporos Int Publication Date: 2011 Jun 
Date Detail:

Created Date: 20110512 Completed Date: 20120223 Revised Date: 20130703 
Medline Journal Info:

Nlm Unique ID: 9100105 Medline TA: Osteoporos Int Country: England 
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Languages: eng Pagination: 1897905 Citation Subset: IM 
Affiliation:

Division of Geriatrics, David Geffen School of Medicine, University of California, 10945 Le Conte Avenue, Suite 2339, Los Angeles, CA 900951687, USA. ggreenda@mednet.ucla.edu 
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MeSH Terms  
Descriptor/Qualifier:

Aged Aged, 80 and over Female Humans Kyphosis / diagnosis*, radiography Male Middle Aged Observer Variation Physical Examination / methods Reproducibility of Results Severity of Illness Index Thoracic Vertebrae / pathology*, radiography 
Grant Support  
ID/Acronym/Agency:

1P30 AG028748/AG/NIA NIH HHS; 5 R01HD045834/HD/NICHD NIH HHS 
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Journal Information Journal ID (nlmta): Osteoporos Int ISSN: 0937941X ISSN: 14332965 Publisher: SpringerVerlag, London 
Article Information Download PDF © The Author(s) 2010 Received Day: 25 Month: 5 Year: 2010 Accepted Day: 9 Month: 9 Year: 2010 Electronic publication date: Day: 12 Month: 10 Year: 2010 pmcrelease publication date: Day: 12 Month: 10 Year: 2010 Print publication date: Month: 6 Year: 2011 Volume: 22 Issue: 6 First Page: 1897 Last Page: 1905 ID: 3092935 PubMed Id: 20938766 Publisher Id: 1422 DOI: 10.1007/s001980101422z 
The reliability and validity of three nonradiological measures of thoracic kyphosis and their relations to the standing radiological Cobb angle  
G. A. Greendale1 
Address: +13108258253 +13107942199 ggreenda@mednet.ucla.edu 
N. S. Nili1  
M.H. Huang1  
L. Seeger2  
A. S. Karlamangla1  
1Division of Geriatrics, David Geffen School of Medicine, University of California, 10945 Le Conte Avenue, Suite 2339, Los Angeles, CA 900951687 USA 

2Department of Radiology, Division of Musculoskeletal Imaging, David Geffen School of Medicine at UCLA, University of California, Los Angeles, CA USA 
Adverse consequences of hyperkyphosis (excessive thoracic kyphosis) include physical functional limitations [^{1}–^{4}], injurious falls [^{5}], back pain [^{6}], respiratory compromise [^{7}], restricted spinal motion [^{8}], fractures [^{9}, ^{10}], and mortality [^{11}–^{13}]. However, a recent randomized, controlled trial found that hyperkyphosis was remediable, encouraging further study of its prevention and treatment [^{14}].
Impediments to largescale hyperkyphosis research are the difficulties inherent in obtaining the criterion standard measurement, the modified Cobb angle [^{15}–^{19}], including expense, limited portability of Xray equipment, Xray exposure, and the time necessary to procure and read the radiographic image.
To facilitate hyperkyphosis research, investigators have developed inexpensive and Xrayfree kyphosis measures, such as the Debrunner kyphometer and the flexicurve ruler. The Debrunner kyphometer consists of a protractor mounted on two arms, the ends of which are positioned on specified bony landmarks; kyphosis angle is read from the protractor [^{6}, ^{20}]. While those with advanced training may readily recognize the landmarks, other research staff may have a difficult time accurately and reproducibly identifying the correct levels. The flexicurve ruler, gently pressed onto the back, adopts the thoracic and lumbar contours of the participant. The researcher then traces the ruler’s retained shape onto paper and calculates the kyphosis index (Fig. 1) [^{21}]. One can also calculate an inscribed angle of kyphosis from the tracing, using geometric formulae (Fig. 1) [^{14}].
Although the nonradiological kyphosis measures minimize cost and obviate radiation, they have enjoyed limited adoption. One explanation may be that they are not calibrated to the Cobb angle, which limits their clinical interpretation. A metric that translates a nonradiological kyphosis result into an approximate Cobb angle would allow estimation of clinical severity from nonCobb measures. Demonstrations of the reliability and validity of the nonradiological measures, especially in older persons, have been minimal, a possible second reason for limited use [^{13}, ^{20}, ^{22}–^{24}].
Therefore, we designed this study to describe: (1) the intrarater and interrater reliability of three nonradiological kyphosis measures, the Debrunner kyphosis angle, the flexicurve kyphosis index, and the flexicurve kyphosis angle; (2) the validity of each nonradiological measure using the modified Cobb angle as the criterion standard; and (3) a translational formula that provides an approximate Cobb angle based on results of the nonradiological measures. We used baseline data from the Yoga for Kyphosis trial, during which we performed standing lateral radiographs to assess modified Cobb angle as well as multiple, sameday, intrarater and interrater measures of the nonradiological assessments.
The analysis sample came from the Yoga for Kyphosis Trial, a single masked, randomized, controlled trial (RCT) of Yoga intended to improve thoracic hyperkyphosis [^{14}]. The trial enrolled 118 participants aged ≥60 years with Debrunner kyphometerassessed kyphosis angle ≥40°. Major RCT exclusions were: serious comorbidity; use of an assistive device; or unable to pass a movementsafety screen. Of 118 persons enrolled in the RCT, 113 had a standing radiological Cobb angle and at least one nonradiological assessment of kyphosis at RCT baseline, making them eligible for this analysis.
All kyphosis measures were made on the same day, within a 4h window. The modified Cobb angle, based on the technique originally described by Cobb to quantify scoliosis, was measured on standing lateral thoracolumbar radiographs [^{17}–^{19}], specifying the limit vertebrae at T4 and T12 [^{18}]. Because some radiographs did not permit use of specified limit vertebrae (e.g., due to overlying structures) Cobb angles from 20 films were based on eight vertebrae (T4–T11 or T5–T12) and Cobb angles from six films were based on seven vertebrae (T5–T11). Nonradiological measures of kyphosis included the Debrunner kyphometer angle, the Flexicurve kyphosis index, and the Flexicurve kyphosis angle. The upper arm of the Debrunner kyphometer was placed on C7 and the lower arm on T12. The circumscribed kyphosis angle was read from the protractor [^{6}, ^{20}]. Debrunner measurements were flagged as problematic in eight cases, because it was difficult to get the base of the arms flush on the landmarks. The Flexicurve kyphosis index was measured using a Flexicurve [^{21}, ^{25}]. The cephalic end of the Flexicurve was placed on C7, and it was molded to the spine in the caudal direction. The shape was traced onto paper, and the apex kyphosis height was estimated relative to the length of the entire thoracic spine; this is the Flexicurve kyphosis index (Fig. 1). Using geometric formulae, the Flexicurve kyphosis angle was also calculated from the Flexicurve tracing. By definition, this inscribed angle is systematically less than the circumscribed angle (Fig. 1).
Research staff had baccalaureate degrees, but none had formal training in anatomy. Staff training consisted of an initial didactic and demonstration (with the aid of volunteer subjects) by Principal Investigator (GAG). It included: review of basic spine anatomy using illustrations; instruction in how to find landmarks by palpation; demonstration of the placement of the kyphometer and how to read the angle from the instrument’s protractor; demonstration of how to apply the flexible ruler and how to make measurements from it. Each staff member then practiced identifying landmarks and conducting the measures. In aggregate, the didactics and staff practice took approximately 40 min. During the conduct of the study, each Debrunner measurement took between 1 and 2 min to make and record, depending on the degree of difficulty ascertaining landmarks. Each flexible ruler measure took 30 s to make; subsequent tracing of the shape on paper and taking the measurements to calculate the angle and index took 2.5 min.
Each clinical kyphosis assessment was made three times for each participant (with repositioning) by the same staff person; the average was the primary value. These three measures also permitted evaluation of intrarater reliability. For interrater reliability, immediately following the first set of measures, one other masked research associate made a 4th assessment, with repositioning, in 54 participants. (Interrater sample size ranged from 51 to 54 due to missing values.)
We examined the withinrater, intraclass correlation coefficients (ICC = betweenperson variance divided by total variance) for each of the nonradiological kyphosis measures using the three measurements made on each participant by the primary rater. In the 54 participants in the interrater subset, who had paired ratings made by a single first and a single second rater, we compared the average of the three measures from the primary rater with the single measure from the secondary rater, calculating interrater ICCs. Both intrarater and interrater ICCs were also examined after stratification by kyphosis severity, defined by Cobb angle median split: moderate if <53°, severe if ≥53°. To compare the nonradiological kyphosis measures with the Cobb angle criterion standard, we examined Pearson correlations between each nonradiological measure and Cobb angle. These analyses were repeated after first excluding 26 participants whose Cobb angles did not span T4–T12 and then excluding seven individuals whose Debrunner measurements were flagged as problematic. In each of these samples, correlations were also examined after stratification by kyphosis severity. We created mathematical formulae to convert the nonradiological results to equivalent Cobb angles. Formulae were created by simple linear regression of the Cobb angle on each of the nonradiological measures in the sample that excluded participants whose Cobb angles did not span T4–T12 and whose Debrunner measurements were flagged as problematic. To test if Cobb angles measured using alternate landmarks had systematic error, in the 20 participants whose Cobb angle measurements spanned either T5–T12 or T4–T11, we compared the measured Cobb angle with the Cobb angle predicted by the clinical measures, using the paired t test. Finally, in the sample in which we derived the Cobb angle prediction equations (Table 5), we conducted Bland–Altman analyses. Bland–Altman analysis consists of the examinations of two graphs. The first graph is an identity plot, a scatter plot of the two measurements along with the line y = x. If the measurements agree closely, then the scatter plot points will line up near to the line y = x. The identity plot was produced only for measured Cobb angle and the measured Debrunner kyphosis angle, because they measure the same thing (circumscribed kyphosis angle) and use the same metric (degrees). The second graph is a Bland–Altman plot, a scatter plot of the variable’s means plotted on the horizontal axis and the variable’s differences plotted on the vertical axis; it includes approximate 95% confidence bands (the confidence bands assume normality of differences). The Bland–Altman plot illustrates the amount of disagreement between the measures being compared. Bland–Altman plots were created for the measured Cobb angle and each of the following: measured Debrunner kyphosis angle; Debrunnerpredicted Cobb angle; Flexicurve kyphosis indexpredicted Cobb angle; and Flexicurve kyphosis anglepredicted Cobb angle. The scientific importance of these differences is judged qualitatively; however, we also computed the standard deviation of the mean difference between the Cobb angle and each comparator to gauge the magnitude of the error [^{26}].
The mean age of the study sample was 75.3 years, average body mass index was 26.5, and 80.5% were women. These and other characteristics of the full sample and the interrater reliability sample are summarized in Table 1.
Shown in Table 2, the mean Cobb angle in the full sample was 53.76°. In the 87 cases with T4–T12 Cobb angles, the mean Cobb angle value was 55.43. Average Debrunner kyphosis angle was similar to the average Cobb angle. As expected, the inscribed flexicurve kyphosis angle averaged about 20° less than the circumscribed Cobb and Debrunner angles.
In the full sample, intra and interrater reliabilities (ICCs) were uniformly high for all kyphosis assessments, 0.96 to 0.98 (Table 3). We also computed ICCs in subsamples, using the median value of the sample Cobb angle to define severity. Restriction of range in subsamples compared to the full sample systematically lowers the ICC value, but ICCs of the two subsamples can be compared to each other: reliabilities were similar in those with moderate and severe kyphosis. We also calculated the interrater reliability based on only the first measurement from the rater one and the 4th from rater two; results did not differ (data not shown). Analyses excluding eight cases that were flagged for difficult kyphometer placement did not alter the intra or interrater reliability estimates for that device (data not shown).
The modified Cobb angle was our criterion measurement; nonradiological measures were compared to it to gauge their validity (Table 4). In the full sample, the Pearson correlations between the nonradiological kyphosis measures and the Cobb angle ranged from 0.62 to 0.69 (95% confidence Interval [CI] for each estimate was ±0.184). Correlations between each nonradiological measure in the 87 persons with T4–T12 Cobb angles were approximately 0.72, somewhat higher than the correlations based on the entire sample. In the sample that was also restricted to those whose Debrunner measures were not flagged as difficult (N = 80), the Pearson correlations between the clinical kyphosis measures and the Cobb angle were even higher, and ranged from 0.762 to 0.758. In aggregate, there was a trend towards higher correlations as the samples were progressively restricted. Comparing the severity subsamples, correlations between each nonradiological measure and the Cobb angle were somewhat higher in those with severe compared to those with moderate hyperkyphosis, but overlapping CIs did not support a statistically significant difference between them.
Nonradiological tests were calibrated to the Cobb angle, using linear regression: the T4–T12 Cobb angle was the outcome and each nonradiological kyphosis measure was the predictor (Table 5). The R^{2} was 0.57–0.58 for each of the measures. Except for a systematic bias of about 5°, the Debrunner kyphosis angle was very similar to the Cobb angle: the beta coefficient, or scaling factor, to convert Debrunner angle to Cobb angle was 1.067. As expected, the flexicurve angle was systematically smaller than the Cobb angle; it had to be scaled by 1.53 to get the equivalent Cobb angle. The kyphosis index may also be approximated to the Cobb angle by using the conversion factor (about 315) and an offset of about 5°.
In the 20 individuals with Cobb angle measurements that spanned one less vertebral body (i.e., T4–T11 or T5–T12), mean Cobb angle was smaller than the Cobb angle predicted by the clinical kyphosis measures by about 8° in each case (data not shown), indicating that when the Cobb angle measure spans fewer vertebral bodies, the Cobb angle is systematically underestimated.
An identity plot graphically displays the agreement between the measured Cobb angle and the Debrunner angle (Fig. 2a). To graphically portray the disagreement between the kyphosis measures, Bland–Altman plots, scatter plots of the variable means on the horizontal axis and the variable differences on the vertical axis, were created. These plots include approximate 95% confidence bands. We also computed the standard deviation (SD) of the mean difference between the Cobb angle and each comparator to gauge the magnitude of the error. Figure 2b, c, displays Bland–Altman plots for the measured Cobb angle and each of the following: measured Debrunner kyphometer angle (SD of mean difference, 11.4); Cobb anglepredicted using the Debrunner angle (SD of mean difference, 10.96); Cobb anglepredicted using the Flexicurve kyphosis index (SD of mean difference, 11.26); and Cobb anglepredicted using the Flexicurve kyphosis angle (SD of mean difference, 10.24).
The overarching goals of this study were to calculate the reliability and validity of the Debrunner kyphometer angle, flexicurve kyphosis index, and flexicurve kyphosis angle and to calibrate each to the Cobb angle. Intra and interrater reliabilities for the three nonradiological kyphosis assessments were uniformly high (0.96 to 0.98) and did not differ statistically from each other. Comparing the nonradiological kyphosis measurements to the Cobb angle also yielded validity estimates that were not distinguishable; all correlations were moderate (0.62 to 0.69). Our derived regression equations that scaled the nonradiological kyphosis estimates to the Cobb angle had robust R^{2} values, between 0.57 and 0.58.
This study’s high interrater and intrarater reliabilities of Debrunner kyphometer and the Flexicurve kyphosis index, based on ICC values, mirrored reliabilities developed in a sample of 26 postmenopausal women with osteoporosis (but whose age range and degree of kyphosis was not specified); in that sample, interrater and intrarater ICCs between 0.89 and 0.99 were found for each test [^{20}]. The present analysis expands upon prior work by including a greater sample size, older subjects (in whom measurements may be more challenging), and a broad range of kyphosis over which reliabilities were assessed. The two studies agree, however: inter and intrarater reliabilities approach perfect and do not differ between the Debrunner kyphometer and the Flexicurve kyphosis index [^{27}]. Although Ohlen examined reliability of the Debrunner kyphometer in 31 young volunteers and Ettinger tested reliability of the Flexicurve kyphosis index in 75 women aged 65–91 years, these two studies used different statistical methods to quantify reliability than those used in the present study, precluding direct comparison of their reliability estimates to ours [^{22}, ^{24}].
To our knowledge, published work has not reported the validity of the Debrunner kyphometer or the Flexicurve kyphosis index compared to the standing Cobb angle. Based on a subsample of 120 women from the Fracture Intervention Trial, Kado et al. calculated an ICC of 0.68 for the kyphosis index compared to a supine Cobb angle; however, the supine position would be expected to lessen the angle of kyphosis and lower the validity estimate [^{28}].
Creating a mathematical formula that approximates Cobb angle based on a nonradiological kyphosis measure is not a novel idea and its value in avoiding radiation and facilitating longitudinal measurement has been recognized [^{23}]. However, crosscalibration has been done only for the Debrunner instrument in an adolescent sample [^{23}]. The present study offers metrics that allow researchers and clinicians to scale the Debrunner angle, Flexicurve kyphosis index, and the newly developed Flexicurve kyphosis angle to a standing radiological Cobb angle in adults with hyperkyphosis. For example, the Flexicurve kyphosis index–Cobb translations could enhance the interpretation of an important finding from the Study of Osteoporotic Fractures (SOF): that greater Flexicurve kyphosis indices predicted higher mortality independently of vertebral fracture [^{13}]. It is now possible to approximate the Cobb angles that these indices represented: using the current study’s metric, the SOF sample’s mean predicted Cobb angle would be 43.8° (standard deviation, 10.7). Thus, the relative mortality hazard per kyphosis index standard deviation developed in SOF can be roughly translated to a 15% increase in mortality per each 10.7° increment in Cobb angle.
This study intended to inform deliberations about which of the three nonradiological tests used in the Yoga for Kyphosis project might be best suited to large observational or interventional kyphosis studies, in which sizable numbers of participants would be evaluated at multiple times. Because these types of studies necessitate multiple raters, the first consideration is the inter and intrarater reliabilities. On this basis, all three assessments performed nearly perfectly and equally. A second basis for ranking the three tests is validity, but this also did not discriminate among them. Finally, when compared to the criterion standard measured Cobb angle, Cobb angles predicted using each of the nonradiological measures had similar magnitude errors according to the Bland–Altman plots. Therefore, factors such as simplicity of use and sensitivity to anatomical variability may suggest the most favorable approach. The flexicurve may be easier for research staff without medical training, as it does not require identification of caudal landmarks. The flexicurve traces the contour of the entire spine; the inflection points between the cervical lordosis, thoracic kyphosis, and lumbar lordosis define the spinal curves. In contrast, the Debrunner kyphometer must be placed on palpated landmarks [^{6}]. Despite careful protocols, the inferior landmark can be particularly difficult to discern, especially when lumbar lordosis has reversed [^{21}]. The Cobb and Debrunner angles base their measurements entirely on the two ends of the spinal curve. If there are no problems at these locations (such as endplate tilt of limit vertebrae or difficult Debrunner placement), dependence on the terminal portions of the curve will not be strongly influential [^{29}]. However, when anatomical abnormalities are present, then an instrument such as the Flexicurve, which uses the entire spinal contour, will be more robust because deformities in part of the spine will not introduce large errors. In this regard, the Flexicurve is akin to the centroid angle, which computes kyphosis using the midpoints of all vertebral bodies from T1–T12 [^{29}]. Indicative of the error introduced by difficult landmark determination was the trend toward higher a correlation between the Debrunner and Cobb angles when eight individuals with difficult Debrunner measures were omitted from the validity computation (Table 4).
Use of the T4–T12 constrained Cobb angle had merits and limitations. In favor of the constrained Cobb is that the uppermost thoracic vertebrae are often poorly visualized due to overlying tissue density. Another attribute of the constrained technique is that the identification of the most inclined vertebral body, which marks the transition from the thoracic to the lumbar curves, can be difficult, leading to low intrarater reliability for determination of limit vertebrae, a problem circumvented by using the constrained Cobb technique [^{30}, ^{31}]. It must be acknowledged that the constrained method will misestimate the true kyphosis angle when the transition vertebra is not at the same level as the specified level. In aggregate, the potential measurement errors in the Cobb angle degrade the accuracy of the criterion standard, conservatively biasing this study’s validity estimates.
The reliability and validity estimates of the nonradiological measures of kyphosis calculated from this sample cannot be assumed to apply to all instances in which these measuring devices are used; they are not immutable characteristics of the tests themselves [^{32}]. Deterioration of reliability and validity may occur due to subject characteristics (e.g., obesity hampers landmark location) or to operator characteristics (e.g., staff capability). Because the research associates who performed the measures in the current study had no formal training in anatomy and likely comparable to other entrylevel research or clinical staff, we believe that operator characteristics are unlikely to be influential in other settings.
The metrics developed in this study to scale the nonradiological tests to the standing Cobb angle must be viewed as approximations, intended to give investigators and clinicians a “feel” for what the values of the nonradiological tests mean in Cobb angle terms. They are not intended to translate individual patient’s nonradiological measures to Cobb angle values in clinical practice. Rather, these approximate conversion formulae are meant to help researchers get a handle on what the nonradiological tests mean in Cobb angle terms, which will inform the general clinical translation of research results.
In summary, in our study sample, we found that the Debrunner kyphometer, the flexicurve kyphosis angle and the flexicurve kyphosis index had strong and similar validity and reliability. Its low cost, ease of use by entrylevel research staff, short measurement time, and relative robustness to variations in spine contour and deformity argue for use of the Flexicurve in longitudinal assessments of kyphosis. This study also provides approximate conversion factors that permit translation of results from three nonradiological kyphosis measures to an approximate Cobb angle value, which will assist researchers in interpreting the clinical meaning of the nonradiological tests.
Conflicts of interest None.
Source of funding Funding for conduct of the Yoga for Kyphosis Trial and this analysis was provided by NIH/NICHHD (5 R01 HD045834). Dr. Karlamangla was also supported by funding from the UCLAClaude D. Pepper Older Americans Independence Center (1P30 AG028748).
Open Access This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Figures
[Figure ID: Fig1] 
Fig. 1
Three methods of quantifying thoracic kyphosis angles are illustrated. The modified T_{4}–T_{12} Cobb angle (dotted lines) measures the angle created by lines drawn parallel to the limit vertebrae visualized on a lateral standing thoracolumbar radiograph. In this case, the limit vertebrae are prespecified at T4 and T12. The Flexicurve kyphosis index and angle are computed using measurements taken from the flexicurve tracing of the thoracic curve, represented here by the solid dark curve posterior to the thoracic vertebral bodies. To calculate the Flexicurve kyphosis index, the apex kyphosis height (E) is divided by the length of the entire thoracic curve (L). The Flexicurve kyphosis angle, Theta (θ), is calculated using lines drawn perpendicular to the short sides of the triangle inscribed by the thoracic curve. This triangle is demarcated by points a (Apex), b (at the cranial end of the curve), and c (at the caudal end). Theta equals arc tan (E/L_{1}) + arc tan (E/L_{2}) 
[Figure ID: Fig2] 
Fig. 2
Identity plot of the measured Cobb angle and the measured Debrunner angle (a). Bland–Altman plots of the measured Cobb angle and each of the following: measured Debrunner angle (b); Cobb angle predicted using the Debrunner angle (c); Cobb angle predicted using the Flexicurve kyphosis Index (d); and Cobb angle predicted using the Flexicurve kyphosis angle (e). Bland–Altman plots include approximate 95% confidence bands and also provide the SD of the difference between the Cobb angle and each comparator. Please see Methods for details 
Tables
Baseline demographic, behavioral and medical characteristics of study participants
Characteristic  Full sample (N = 113)  Interrater reliability sample ^{a} (N = 54) 

Age (years)  75.3 ± 7.5  75.5 ± 7.7 
Height (cm)  160.7 ± 8.9  161.1 ± 9.0 
Weight (kg)  68.8 ± 15.1  68.3 ± 14.3 
Body mass index (kg/m^{2})  26.5 ± 4.5  26.1 ± 4.3 
Female gender: % (N)  80.5 (91)  81.8 (45) 
Usual physical activity  2.3 ± 0.5  2.3 ± 0.6 
Chronic conditions (#)  5.6 ± 3.8  5.4 ± 2.9 
Vertebral fractures ^{b,c}  
None % (N)  75.2 (85)  74.6 (41) 
Thoracic % (N)  19.5 (22)  20.0 (11) 
Lumbar % (N)  7.1 (8)  9.1 (5) 
^{a}All P values for full vs. interrater samples >0.05
^{b}Percentage of lumbar and thoracic fractures sum to greater than 100% because some participants had fractures of both spinal regions
^{c}Vertebral fractures defined as ≥25% decrement in interior, middle, or posterior vertebral body height
Average values and distributions of standing Cobb angle and nonradiological kyphosis measurements
Kyphosis measurement  Sample size  Mean  Standard deviation  Median 

Cobb angle, entire sample^{a} (degrees)  113  53.76  14.76  53.10 
Cobb angle, subset in which T4–T12 landmarks were used (degrees)  87  55.43  13.62  53.1 
Debrunner kyphosis angle (degrees)  113  57.68  9.60  58.00 
Flexicurve kyphosis index  113  0.162  0.033  0.161 
Flexicurve kyphosis angle ^{b} (degrees)  113  36.50  6.82  36.48 
^{a}Cobb angle in the entire study sample includes 26 cases in which the desired T4–T12 landmarks could not be used, requiring alternate landmarks (see Methods for details)
^{b}The Flexicurve kyphosis angle is an inscribed angle, which by definition will be smaller than the circumscribed angles estimated using the Cobb or Debrunner methods
Intra and interrater reliabilities of three nonradiological kyphosis assessments
Intrarater reliability (N = 113)  Interrater reliability^{a} (N = 51–54)  

Full sample  
Debrunner kyphosis angle  0.98  0.98 
Flexicurve kyphosis index  0.96  0.96 
Flexicurve kyphosis angle  0.96  0.96 
Moderate Kyphosis ^{b}  
Debrunner kyphosis angle  0.97  0.98 
Flexicurve kyphosis index  0.94  0.93 
Flexicurve kyphosis angle  0.94  0.94 
Severe Kyphosis  
Debrunner kyphosis angle  0.97  0.98 
Flexicurve kyphosis index  0.94  0.97 
Flexicurve kyphosis angle  0.94  0.95 
Values in table are intraclass correlation coefficients, defined as betweenperson variance divided by total variance
^{a}The average of the first three measurements made by the first rater was compared to one measurement performed by the second rater
^{b}Moderate kyphosis is defined as a Cobb angle of less than 53°, the sample median. Severe kyphosis is defines as a Cobb angle of greater than or equal to 53°
Validity of three nonradiological measurements of kyphosis compared to the Cobb angle criterion standard
Nonradiological kyphosis measurement and kyphosis severity  Full sample  Cobbrestricted sample^{a}  Cobb and Debrunnerrestricted samples^{b} 

Full range of Kyphosis  (N = 113; Std error = 0.094)  (N = 87; Std error = 0.107)  (N = 80;Std error = 0.112) 
Debrunner kyphosis angle  0.622  0.715  0.762 
Flexicurve kyphosis index  0.686  0.725  0.756 
Flexicurve kyphosis angle  0.686  0.721  0.758 
Moderate Kyphosis^{c}  (N = 55; Std error = 0.135)  (N = 41; Std error = 0.156)  (N = 37 ;Std error = 0.164) 
Debrunner kyphosis angle  0.275  0.354  0.405 
Flexicurve kyphosis index  0.335  0.426  0.428 
Flexicurve kyphosis angle  0.328  0.397  0.406 
Severe Kyphosis  (N = 58 ;Std error = 0.131)  (N = 46;Std error = 0.149)  (N = 43; Std error = 0.152) 
Debrunner kyphosis angle  0.447  0.602  0.641 
Flexicurve kyphosis index  0.517  0.600  0.597 
Flexicurve kyphosis angle  0.532  0.626  0.627 
Values in table are Pearson correlation coefficients for each nonradiological measure compared to the Cobb angle
^{a}Cobbrestricted sample excludes data from subjects whose Cobb angles did not span T4–T12
^{b}Cobb and Debrunnerrestricted sample excludes data from subjects whose Cobb angles did not span T4–T12 and those whose Debrunner kyphometer measures were flagged as difficult (see Methods for details)
^{c}Moderate kyphosis is defined as a Cobb angle of less than 53°, the sample median. Severe kyphosis is defines as a Cobb angle of greater than or equal to 53°
Calibration of nonradiological kyphosis measurements to theT4–T12 Cobb angle (n = 80)
Nonradiological kyphosis measurements  β coefficient  Intercept  R^{2} 

Debrunner kyphosis angle  1.067  −5.40  0.58 
Flexicurve kyphosis index  314.61  5.11  0.57 
Flexicurve kyphosis angle  1.53  0.30  0.57 
Results in table are from simple linear regression, with T4–T12 Cobb angle as outcome and each nonradiological measure as predictor. To convert a nonradiological measure to equivalent T4–T12 Cobb angle, scale by corresponding β and add intercept
Calibration was performed using a sample restricted to persons with a T4–T12 Cobb angle and a Debrunner kyphometer measurement that was not flagged as difficult (see Methods for details)
Article Categories:
Keywords: Keywords Cobb angle, Kyphosis, Reliability, Validity. 
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