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Reassessing the accuracy and the accuracy and reproducibilityreproducibility
of Diers formetric system®of Diers formetric system®Introducing reference valuesreference values Evaluating the effect of GOTthe effect of GOT
International Academy of OsteopathyInternational Academy of Osteopathy
Ghent, October 2, 2014Ghent, October 2, 2014
The Moiré principleThe Moiré principle
IAO Research MeetingIAO Research MeetingThursday 2nd October 2014Thursday 2nd October 2014
Statistical Introduction SlidesStatistical Introduction Slides
Correlatiecoefficient : exampleCorrelatiecoefficient : exampleWhy useful ?Why useful ?
CorrelationcoefficientCorrelationcoefficient
Sample sizeSample size 1212
Correlation coefficient rCorrelation coefficient r 0,82670,8267
Significance levelSignificance level P=0,0009P=0,0009
95% Confidence interval for r95% Confidence interval for r0,4810 to 0,940,4810 to 0,949999
CorrelationcoefficientCorrelationcoefficientScatterplot with line of equalityScatterplot with line of equality
Correlationcoefficient “r”Correlationcoefficient “r”
r is free from units
r has a value in the range [-1,+1]
r is symmetric for X and Y
r expresses a linear relationship
Correlatiecoefficient “r”Correlatiecoefficient “r”
r = +1 perfect positive correlation
r = -1 perfect negative correlation
r 0 no correlation (X and Y independent)
r is a measure of linear relationship between X and Y
Positive correlationPositive correlation
yy
x
r =0.88r =0.88
Negative correlationNegative correlation
yy
x
r =-0.88r =-0.88
correlation are variables related?
Correlationcoefficient
regression dependence between variables ?
determinationcoefficient
Determinationcoefficient
Determinatiecoefficient and Linear Regression Equation
Determinationcoefficient and Linear Regression Equation
Sample sizeSample size 1212
Coefficient of determination RCoefficient of determination R22
0,68340,6834
Residual standard deviationResidual standard deviation 11,609811,6098
y = 18,9063 + 1,8239 x y = 18,9063 + 1,8239 x
ParameterParameter CoefficientCoefficient Std. ErrorStd. Error 95% CI95% CI tt PP
InterceptIntercept 18,906318,9063 6,32586,32584,8116 to 4,8116 to 33,000933,0009
2,98882,9888 0,01360,0136
SlopeSlope 1,82391,8239 0,39260,39260,9493 to 0,9493 to 2,69862,6986
4,64634,6463 0,00090,0009
Regression Equation
x
.(x ,y )
y -y (residueel)i i
.
.
..
......
. .. .
x
y
y
y - y (verklaard)i
y = bx + ai i
r2 = 0,68
68% of total variance can be explained by linear regression line y = 18,9063 + 1,8239 x
The risk that one is prepared to run to reject the nullhypothesis wrongly, is called the significance level.
Mostly this is put at 1% or 5% (P = 0.01 or P = 0.05)
If one assumes under the nullhypothesis that only chance is acting, only then one can determine which results will have just 1% or 5% chance of occurrence.
P-VALUE
⊳ ‘Probability that a result at least as extreme as that observed would occur by Chance’ (James Ware et al.)
⊳ ‘Probability of observing the data (or more extreme data) when the null hypothesis is true’ (Douglas Altman)
⊳ ‘Probability of rejecting the null hypothesis if it is true, is called the significance level of the statistical test’ (SAS manual)
P-VALUE =
e.g. p = 0.425 (NS) null hypothesis cannot be rejected.
p = 0.001 : reject null hypothesis;
p < 0.05 : conventional threshold for significance.
Bland and Altman PlotBland and Altman Plot
When evaluating two methods of measurement or when When evaluating two methods of measurement or when testing the reproducibility of two measurements it is testing the reproducibility of two measurements it is better to calculate the 95% limits of agreement than the better to calculate the 95% limits of agreement than the correlationcoefficient.correlationcoefficient.
As a first step the scatterplot has to be prepared with the As a first step the scatterplot has to be prepared with the mean of the average of the two measurements in the mean of the average of the two measurements in the horizontal axis and the difference between the two horizontal axis and the difference between the two measurements in the vertical axis. measurements in the vertical axis.
95% limits of agreement = 95% limits of agreement = mean of the differences +/- 1.96 x Standard Deviationmean of the differences +/- 1.96 x Standard Deviation
Bland JM, Altman DG (1986). "Statistical methods for assessing agreement between Bland JM, Altman DG (1986). "Statistical methods for assessing agreement between two methods of clinical measurement". two methods of clinical measurement". LancetLancet 327327 (8476): 307–10 (8476): 307–10
Bland and Altman PlotBland and Altman Plot
Variationcoefficient : 1 sampleVariationcoefficient : 1 sample
All n subjects were measured once or 1 All n subjects were measured once or 1 subject was measured n times subject was measured n times
Coefficient of Variation (CV)Coefficient of Variation (CV) = (= (Standard Deviation/MeanStandard Deviation/Mean)x100 (in %))x100 (in %) Advantage : free of measurement unitsAdvantage : free of measurement units
Variationcoefficient : duplicate Variationcoefficient : duplicate measurements in the same subjectsmeasurements in the same subjects
Method of Jones for evaluation of Method of Jones for evaluation of reproducibilityreproducibility
Jones R, Payne B (1997) Clinical investigation and statistics Jones R, Payne B (1997) Clinical investigation and statistics in laboratory medicine. London: ACB Venture Publications.in laboratory medicine. London: ACB Venture Publications.
Percentile Ranking :Box and Percentile Ranking :Box and Whisker PlotsWhisker Plots
Q1 Q2 Q3
MINIMUMVALUE
MAXIMUMVALUE
INTERQUARTILERANGE
MEDIAN
25 %
Interquartile range & rangeInterquartile range & range
25 % 25 % 25 %
Toepassing statistiek op Diers metingen
Repeat measurementsRepeat measurements
Initial two groups of 19 healthy Initial two groups of 19 healthy volunteers volunteers
Learning curve !Learning curve ! Larger group volunteers more Larger group volunteers more
experienced operatorsexperienced operators
Maximal kyphoticMaximal kyphotic& lordotic angles& lordotic angles((diers formetric®)diers formetric®)
Repeat mesurements max. Repeat mesurements max. kyphotic angle kyphotic angle (box and whisker plots)(box and whisker plots)
Berekenen van verbandBerekenen van verband
Correlatiecoëfficiënt enCorrelatiecoëfficiënt en
Significantie (r en P waarden)Significantie (r en P waarden)
Max. kyphotic angle Max. kyphotic angle (correlation coefficient: r=0.49, (correlation coefficient: r=0.49, P<0.01P<0.01))
Berekenen van mate van Berekenen van mate van overeenstemmingovereenstemming
Martin Bland & Douglas AltmanMartin Bland & Douglas Altman
Max. kyphotic angle Max. kyphotic angle (Bland and Altman plot)(Bland and Altman plot)
Repeat mesurements max. Repeat mesurements max. lordotic angle lordotic angle (box and whisker plots)(box and whisker plots)
Max. lordotic angle Max. lordotic angle (correlation coefficient: r=0.55, (correlation coefficient: r=0.55, P<0.01P<0.01))
Max. lordotic angle Max. lordotic angle (Bland and Altman plot)(Bland and Altman plot)
Trunk torsion Trunk torsion (Bland and Altman plot; (Bland and Altman plot; P>0.1P>0.1))
Learning curveLearning curve
?
Coefficient of variation (angles)Coefficient of variation (angles)
Initial groups: Initial groups: 12.9% to 14.3%12.9% to 14.3% Learning curve! Change ! Change
Careful positioning and techniqueCareful positioning and technique New population: 116 persons, New population: 116 persons,
CV: CV: 6.4% to 7.6%6.4% to 7.6% (r-values > 0.80)
Nog wat statistiek….Nog wat statistiek….
Cumulative Frequency DistributionCumulative Frequency Distribution
Frequency distribution histogramFrequency distribution histogramSample sizeSample size 3030
Lowest valueLowest value 19,0000
Highest valueHighest value 120,0000
Arithmetic meanArithmetic mean 70,033370,0333
95% CI for the mean95% CI for the mean 59,9700 to 80,096759,9700 to 80,0967
MedianMedian 69,500069,5000
95% CI for the median95% CI for the median 57,3500 to 83,650057,3500 to 83,6500
VarianceVariance 726,3092726,3092
Standard deviationStandard deviation 26,950126,9501
Relative standard deviationRelative standard deviation 0,3848 (38,48%)0,3848 (38,48%)
Standard error of the meanStandard error of the mean 4,92044,9204
Coefficient of SkewnessCoefficient of Skewness -0,01942 (P=0,9615)-0,01942 (P=0,9615)
Coefficient of KurtosisCoefficient of Kurtosis -0,6896 (P=0,3609)-0,6896 (P=0,3609)
D'Agostino-Pearson testD'Agostino-Pearson testfor Normal distributionfor Normal distribution
accept Normality (P=0,6580)accept Normality (P=0,6580)
CHARACTERISTICS OF NORMAL OR GAUSSIAN DISTRIBUTIONS
CHARACTERISTICS OF NORMAL OR GAUSSIAN DISTRIBUTIONS
68.27% of the data falls between X ± 1 SD
95.45% of the data falls between X ± 2 SD
99.73% of the data falls between X ± 3 SD
1. If the size of the random sample is less or equal to 2000 : the Shapiro-Wilk test.
2. If the random sample counts more than 2000 observations : the Kolomogorov-Smirnov test.
How to investigate if the random sample has a ‘normal’ spreaded distribution?
Cumulative Frequency DistributionCumulative Frequency Distribution
Q1 Q2 Q3
MINIMUMVALUE
MAXIMUMVALUE
INTERQUARTILERANGE
MEDIAN
25 %
Interquartile range & rangeInterquartile range & range
25 % 25 % 25 %
Cumulatieve Frequentie Distributie : Cumulatieve Frequentie Distributie : Percentile RankingPercentile Ranking
PercentilesPercentiles 95% Confidence Interval95% Confidence Interval
2,52,5 20,000020,0000
55 23,000023,0000
1010 34,500034,5000
2525 49,000049,0000 34,6490 to 64,512834,6490 to 64,5128
7575 89,000089,0000 76,3248 to 106,754876,3248 to 106,7548
9090 107,5000107,5000
9595 115,0000115,0000
97,597,5 118,7500118,7500
Cumulative Frequency DistributionCumulative Frequency Distribution
Toepassing statistiek op Diers metingen
Percentile rankingPercentile ranking
Importance of gender and BMIImportance of gender and BMI
Cumulative frequency distributionCumulative frequency distribution (curve of normal distribution)(curve of normal distribution)
85 90 95 100 105 110 115
100
80
60
40
20
0
low_NA1breed2=24
Rel
ativ
e fr
eque
ncy
(%)
98
84
32
Comparison percentile rank of same Norberg (hip)-angle Comparison percentile rank of same Norberg (hip)-angle
in 2 breedsin 2 breeds (conventional reference value =105°)(conventional reference value =105°)
8080 8585 9090 9595 100100 105105 110110 115115 120120
100100
8080
6060
4040
2020
00
Low NALow NA
Rel
ativ
e fr
eque
ncy
(%)
Rel
ativ
e fr
eque
ncy
(%)
DobermannDobermannBorder collieBorder collie
Gender difference max.Gender difference max.kyphotic angle kyphotic angle
Gender difference Gender difference max. lordotic angle max. lordotic angle
Body Mass Index (BMI)Body Mass Index (BMI)Quetelet, 1835
Weight (kg) divided by height squaredWeight (kg) divided by height squared19-25: optimal group 019-25: optimal group 0
25-30: overweight group 125-30: overweight group 1>30: obese group 2>30: obese group 2
SagittalSagittalimbalanceimbalance
BMI versus Sagittal ImbalanceBMI versus Sagittal Imbalance
BMI versus Sagittal ImbalanceBMI versus Sagittal Imbalance
4°
BMI versus Sagittal ImbalanceBMI versus Sagittal Imbalance(best-fitting curves of Gaussian distribution)(best-fitting curves of Gaussian distribution)
GOT trial: static assessmentGOT trial: static assessment
113 persons before and after general 113 persons before and after general osteopathic treatmentosteopathic treatment
Paired student’s t-test: two-sided and one-Paired student’s t-test: two-sided and one-sided, cumulative frequency distribution sided, cumulative frequency distribution curve, ROCcurve curve, ROCcurve
General Osteopathic TreatmentGeneral Osteopathic Treatment
GOT GOT reduces Sagittal Imbalance reduces Sagittal Imbalance (ROC curve analysis)(ROC curve analysis)
GOT GOT
Sagittal imbalance (two-sided) significant Sagittal imbalance (two-sided) significant decreased: decreased: P=0.034
Lordotic angulation and apical deviation Lordotic angulation and apical deviation (one-sided) significant decreased: P=0.028; (one-sided) significant decreased: P=0.028; 0.0340.034
Low Back PainLow Back Pain
BMI BMI Sagittal Sagittal ImbalanceImbalance
GOTGOT
????
????
Reseach into: Reseach into: comparative effectiveness, , cost-benefit ratio, and different models of cost-benefit ratio, and different models of
CAM health care integration CAM health care integration
Qualitative Spine Profile (QSP)Qualitative Spine Profile (QSP)
Individuele rug-configuratie-kaartIndividuele rug-configuratie-kaart
in vergelijking met personen van het zelfde in vergelijking met personen van het zelfde geslacht en met de zelfde BMI geslacht en met de zelfde BMI