Burt Holland

Data and Statistics

Statistics is the field of study whose objective is the transformation of data (usually sets of numbers along with identifying characteristics) into information (usually in the form of tables, graphs, and written and verbal summaries) that can inform sound policy decisions. We give examples of applications of statistics to many fields in Chapter 1 Here we focus on the general concepts describing the collection and arrangement of the numbers themselves.

An Improved Sequentially Rejective Bonferroni Test Procedure

complexity. These procedures can be used whenever the observed levels of significance are available for all individual tests. It is shown that both the Holm and Shaffer procedures can be improved under the assumption of positive orthant dependence for the test statistics. It is noted that this assumption is met in many important practical situations and recommended that in these cases the new procedure be used in place of its predecessors whenever the required observed significance levels are available. The methodology is illustrated with a numerical example.

Cobb method or Harrison posterior tangent method: which to choose for lateral cervical radiographic analysis.

Study Design. Thirty lateral cervical radiographs were digitized twice by three examiners to compare reliability of the Cobb and posterior tangent methods. Objectives. To determine the reliability of the Cobb and Harrison posterior tangent methods and to compare and contrast these two methods. Summary of Background Data. Cobb’s method is commonly used on both anteroposterior and lateral radiographs, whereas the posterior tangent method is not widely used. Methods. A blind, repeated-measures design was used. Thirty lateral cervical radiographs were digitized twice by each of three examiners. To evaluate reliability of determining global and segmental alignment, vertebral bodies of C1–T1 were digitized. Angles created were two global two-line Cobb angles (C1–C7 and C2–C7), segmental Cobb angles from C2 to C7, and posterior tangents drawn at each posterior vertebral body margin. Cobb’s method and the posterior tangent method are compared and contrasted with these data. Results. Of 34 intraclass and interclass correlation coefficients, 28 were in the high range (>0.7), and 6 were in the good range (0.6–0.7). The Cobb method at C1–C7 overestimated the cervical curvature (−54°) and, at C2–C7 it underestimated the cervical curve (−17°), whereas the posterior tangents were the slopes along the curve (−26° from C2 to C7). The inferior vertebral endplates and posterior body margins did not meet at 90° (C2: 105° ± 5.2°, C3: 99.7° ± 5.2°, C4: 99.9° ± 5.8°, C5: 96.1 ° ± 4.5°, C6: 97.0° ± 3.8°, C7: 95.4° ± 4.1°), which caused the segmental Cobb angles to underestimate lordosis at C2–C3, C4–C5, and C6–C7. Conclusions. Although both methods are reliable with the majority of correlation coefficients in the high range (ICC > 0.7), from the literature, the posterior tangent method has a smaller standard error of measurement than four-line Cobb methods. Global Cobb angles compare only the ends of the cervical curve and cannot delineate what happens to the curve internally. Posterior tangents are the slopes along the curve and can provide an analysis of any buckled areas of the cervical curve. The posterior tangent method is part of an engineering analysis (first derivative) and more accurately depicts cervical curvature than the Cobb method.—

Radiographic analysis of lumbar lordosis: centroid, Cobb, TRALL, and Harrison posterior tangent methods.

Study Design. Delayed, repeated measures, with three examiners each twice digitizing thirty lateral lumbar radiographs. Objectives. To determine the reliability and clinical utility of the centroid, Cobb, tangential radiologic assessment of lumbar lordosis (TRALL), and Harrison posterior tangent line-drawing methods for analysis of lumbar lordosis. Background Data. Cobb’s method is commonly used for curvature analysis on lateral lumbar radiographs, whereas the centroid, TRALL, and Harrison posterior tangent methods are not widely used. Methods. Thirty lateral lumbar radiographs were digitized twice by each of three examiners. To evaluate reliability of determining global and segmental alignment, all four vertebral body corners of T12–S1 and the superior margin of the femur head were digitized. Angles created were segmental and global centroid, (two-line) Cobb angles, and intersections of posterior tangents. A global TRALL angle was determined. Means, standard deviations, mean absolute differences, interclass and intraclass correlation coefficients (ICC), and confidence intervals were calculated. Results. The interobserver and intraobserver reliabilities of measuring all segmental and global angles were in the high range (ICCs > 0.83). The mean absolute differences of observers’ measurements were small (0.6°–2.0°). Distal segmental (L4–S1) and global angles of lumbar curvature were dependent on the method of measurement. Conclusions. All four radiographic methods had high reliability and low mean absolute differences of observers’ measurements. Because it lacks a segmental analysis, the TRALL method is not recommended. The centroid, Cobb, and Harrison posterior tangent methods provide global and segmental angles. However, the centroid segmental method requires three segments and is less useful for a stability analysis.

Comparisons of lordotic cervical spine curvatures to a theoretical ideal model of the static sagittal cervical spine.

Study Design Measurements from lateral cervical radiographs of randomly selected patients are compared with two proposed ideal models. Objectives To evaluate lordotic cervical curvatures from a large population base, to provide a geometric sagittal cervical spine model, and to test the validity of the model to predict measured angles and distances. Averages of ranges and normal values for cervical lordosis under conditions of static equilibrium are sought. Summary of Background Data Seven angles and three distances were taken from 400 randomly selected lateral cervical radiographs of patients at a private clinic. Methods The radiographic measurements are compared with predicted values from our geometric sagittal cervical spine model and the Delmas ideal cervical model. Results Values were predicted successfully by the geometric model with an average error of 5% compared with the radiographic measurements. The range of lordosis, measured at the posterior of C2 and C7, was 16.5‐66°, with a mean of 34°. The average height‐to‐length ratio for the cervical spine was 0.97. Conclusions Predicted values from the geometric model were comparable with the measurements of the relative rotation angles at each vertebral interspace, absolute rotation angles from C2 to C7, and height‐to‐length ratios. A cervical lordosis of 34° and a height‐to‐length ratio of 0.97 are suggested for clinical and theoretical outcomes.

Controlling the rate of Type I error over a large set of statistical tests.

When many tests of significance are examined in a research investigation with procedures that limit the probability of making at least one Type I error--the so-called familywise techniques of control--the likelihood of detecting effects can be very low. That is, when familywise error controlling methods are adopted to assess statistical significance, the size of the critical value that must be exceeded in order to obtain statistical significance can be extremely large when the number of tests to be examined is also very large. In our investigation we examined three methods for increasing the sensitivity to detect effects when family size is large: the false discovery rate of error control presented by Benjamini and Hochberg (1995), a modified false discovery rate presented by Benjamini and Hochberg (2000) which estimates the number of true null hypotheses prior to adopting false discovery rate control, and a familywise method modified to control the probability of committing two or more Type I errors in the family of tests examined--not one, as is the case with the usual familywise techniques. Our results indicated that the level of significance for the two or more familywise method of Type I error control varied with the testing scenario and needed to be set on occasion at values in excess of 0.15 in order to control the two or more rate at a reasonable value of 0.01. In addition, the false discovery rate methods typically resulted in substantially greater power to detect non-null effects even though their levels of significance were set at the standard 0.05 value. Accordingly, we recommend the Benjamini and Hochberg (1995, 2000) methods of Type I error control when the number of tests in the family is large.

Modeling of the Sagittal Cervical Spine as a Method to Discriminate Hypolordosis: Results of Elliptical and Circular Modeling in 72 Asymptomatic Subjects, 52 Acute Neck Pain Subjects, and 70 Chronic Neck Pain Subjects

Study Design. Computer analysis of digitized vertebral body corners on lateral cervical radiographs. Objectives. Using elliptical and circular modeling, the geometric shape of the path of the posterior bodies of C2–C7 was sought in normal, acute pain, and chronic pain subjects. To determine the least squares error per point for paths of geometric shapes, minor axis to major axis elliptical ratios (b/a), Cobb angles, sagittal balance of C2 above C7, and posterior tangent segmental and global angles. Summary of Background Data. When restricted to cervical lordotic configurations, normal, acute pain, and chronic pain subjects have not been compared for similarities or differences of these parameters. Conventional Cobb angles provide only a comparison of the endplates of the distal vertebrae, while geometric modeling provides the shape of the entire sagittal curves, the orientation of the spine, and segmental angles. Methods. Radiographs of 72 normal subjects, 52 acute neck pain subjects, and 70 chronic neck pain subjects were digitized. For normal subjects, the inclusion criteria were no kyphotic cervical segments, no cranial-cervical symptoms, and less than ± 10 mm horizontal displacement of C2 above C7. In pain subjects, inclusion criteria were no kyphotic cervical segments and less than 25 mm of horizontal displacement of C2 above C7. Measurements included segmental angles, global angles of lordosis (C1–C7 and C2–C7), height-to-length ratios, anterior weight bearing, and from modeling, circular center, and radius of curvature. Results. In the normal group, a family of ellipses wasfound to closely approximate the posterior body margins of C2–C7 with a least squares error of less than 1 mm per vertebral body point. The only ellipse/circle found to include T1, with a least squares error of less than 1 mm, was a circle. Compared with the normal group, the pain group’s mean radiographic angles were reduced and the radius of curvature was larger. For normal, acute, and chronic pain groups, the mean angles between posterior tangents on C2–C7 were 34.5°, 28.6°, and 22.0°, C2–C7Cobb angles were 26.8°, 16.5°, and 12.7°, and radius of curvature were r = 132.8 mm, r = 179 mm, and r = 245.4 mm, respectively. Conclusions. The mean cervical lordosis for all groups could be closely modeled with a circle. Pain groups had hypolordosis and larger radiuses of curvature compared with the normal group. Circular modeling may be a valuable tool in the discrimination between normal lordosis and hypolordosis in normal and pain subjects.

Reliability of Centroid, Cobb, and Harrison Posterior Tangent Methods: Which to Choose for Analysis of Thoracic Kyphosis

Study Design. Thirty lateral thoracic radiographs were digitized twice by each of the three examiners. Objectives. To determine the reliability of the centroid, Cobb, and Harrison posterior tangent methods when applied to analysis of thoracic kyphosis. Background Data. Reliability studies on measurements of thoracic kyphosis are rare. Methods. Blind, repeated-measures design was used. Thirty lateral thoracic radiographs were digitized twice by each of three examiners. To evaluate reliability of determining global and segmental alignment, vertebral bodies of T1–T12 were digitized. Centroids at the intersection of vertebral body diagonals and tangents to posterior vertebral bodies were constructed by computer. Also the computer constructed global and segmental centroid angles, Cobb angles (two-line method), and posterior tangent intersection angles from T1 to T12. Interclass and Intraclass correlation coefficients for these data were calculated and interpreted. Results. From the points selected by examiners, all three methods have similar high ICC values for the global angles (> 0.94). For the segmental angles, the interobserver and intraobserver reliability is also very similar for all three methods, with ICCs in the good and excellent ranges (0.59–0.75 and 0.75–1.0, respectively). The mean absolute differences of observers’ measurements are low, similar, and in the range of 0.9° to 2.5°. Conclusions. The centroid, two-line Cobb, and Harrison posterior tangent methods, when applied to measurements of kyphosis, are all reliable and have similar small error ranges. The centroid method does not give an accurate segmental analysis, uses more points and more time in clinical applications, and results in smaller angles of total kyphosis than the Cobb or posterior tangent methods. The posterior tangents are the slopes along the curve.

Intermittent calf and foot compression increases lower extremity blood flow.

PURPOSE Although foot compression increases foot skin perfusion and calf compression increases popliteal artery blood flow, these compression techniques have not been evaluated in combination. The purpose of this study was to evaluate whether calf and foot compression applied separately and simultaneously increase popliteal artery blood flow and/or foot skin perfusion, and to assess the relative merits of compression in patients with superficial femoral artery occlusion. METHODS Twenty-two legs from 12 normal volunteers with ankle/brachial indices (ABIs) > 0.96, and 10 legs from 7 claudicator patients with angiographically documented superficial femoral artery (SFA) occlusion and patent popliteal arteries with ABIs < 0.8 were studied in the sitting position. Calf and foot cuffs connected to a rapidly inflating and deflating timed-pressure pump (Art-Assist-AA 1000; ACI Medical Inc., San Marcos, California) were applied to the subject in the sitting position. Skin blood flow of the great toe was measured with a laser doppler (Laserflo model BPM 403A; TSI Inc., St. Paul, Minnesota), and popliteal artery blood flow was measured using duplex ultrasonography (ATL-Ultramark 9; Advanced Tech Laboratory, Bothell, Washington). Foot and calf compression was applied separately and simultaneously at 120 mm Hg pressure, with a 10-second inflation and 20-second deflation cycle. Popliteal artery blood flow and foot skin perfusion were recorded and the mean of 6 cycles calculated. RESULTS Precompression popliteal artery blood flow (mL/min) for volunteers was 38.86 +/- 3.94, and for patients was 86.30 +/- 14.55 (P = 0.001). Precompression foot skin perfusion (mL/min/ 100/g tissue) for volunteers was 1.67 +/- 0.29, and for patients was 4.00 +/- 0.92 (P = 0.01). With the application of calf, foot, and simultaneous calf and foot compression, the popliteal artery blood flow increased in volunteers by 124%, 54%, and 173%, respectively, and in patients by 76%, 13%, and 50%. Foot skin perfusion increased in volunteers by 260%, 500%, and 328%, respectively, and in patients by 116%, 246%, and 188%. Relative increases in popliteal artery blood flow and foot skin perfusion were higher in volunteers compared with patients during compression; however, the absolute values for foot skin perfusion and popliteal artery blood flow were consistently higher in patients. CONCLUSIONS Measured in the sitting position, the resting popliteal artery blood flow and foot skin perfusion are greater in patients with SFA occlusion compared with normal volunteers. Following compression, popliteal artery blood flow and foot skin perfusion increased in both groups, but relatively more in volunteers. Increases in popliteal artery blood flow are significantly higher with calf compression than with foot compression for both groups. A patent SFA allows for additive increases in popliteal artery blood flow with simultaneous foot and calf compression in normal persons, whereas this is not observed in patients. However, the increases in foot skin perfusion in patients with an occluded SFA parallel the increases shown in normal volunteers, with separate and simultaneous foot and calf compression.

Increasing the cervical lordosis with chiropractic biophysics seated combined extension-compression and transverse load cervical traction with cervical manipulation: nonrandomized clinical control trial

BACKGROUND Cervical lordosis has been shown to be an important outcome of care; however, few conservative methods of rehabilitating sagittal cervical alignment have been reported. OBJECTIVE To study whether a seated, retracted, extended, and compressed position would cause tension in the anterior cervical ligament, anterior disk, and muscle structures, and thereby restore cervical lordosis or increase the curvature in patients with loss of the cervical lordosis. STUDY DESIGN Nonrandomized, prospective, clinical control trial. METHODS Thirty preselected patients, after diagnostic screening for tolerance to cervical extension with compression, were treated for the first 3 weeks of care using cervical manipulation and a new type of cervical extension-compression traction (vertical weight applied to the subjects forehead in the sitting position with a transverse load at the area of kyphosis). Pretreatment and posttreatment Visual Analogue Scale (VAS) pain ratings were compared along with pretreatment and posttreatment lateral cervical radiographs analyzed with the posterior tangent method for changes in alignment. Results are compared to a control group of 33 subjects receiving no treatment and matched for age, sex, weight, height, and pain. RESULTS Control subjects reported no change in VAS pain ratings and had no statistical significant change in segmental or global cervical alignment on comparative lateral cervical radiographs (difference in all angle mean values < 1.3 degrees ) repeated an average of 8.5 months later. For the traction group, VAS ratings were 4.1 pretreatment and 1.1 posttreatment. On comparative lateral cervical radiographs repeated after an average of 38 visits over 14.6 weeks, 10 angles and 2 distances showed statistically significant improvements, including anterior head weight bearing (mean improvement of 11 mm), Cobb angle at C2-C7 (mean improvement of -13.6 degrees ), and the angle of intersection of the posterior tangents at C2-C7 (mean improvement of 17.9 degrees ). Twenty-one (70%) of the treatment group subjects were followed for an additional 14 months; improvements in cervical lordosis and anterior weight bearing were maintained. CONCLUSIONS Chiropractic biophysics (CBP) techniques extension-compression 2-way cervical traction combined with spinal manipulation decreased chronic neck pain intensity and improved cervical lordosis in 38 visits over 14.6 weeks, as indicated by increases in segmental and global cervical alignment. Anterior head weight-bearing was reduced by 11 mm; Cobb angles averaged an increase of 13 degrees to 14 degrees; and the angle of intersection of posterior tangents on C2 and C7 averaged 17.9 degrees of improvement.