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