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# Beyond Means and SDs - MEDLABSTATS.com

Beyond Means and SDs - MEDLABSTATS.com

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Beyond Means and SDs :Recommended Statistics forKnowledge Extraction fromAccumulated Pathology Data andyour Practice Experience`Dr Tom HartleyRoyal Hobart Hospital&University of TasmaniaHobart, Australiatom.hartley@dhhs.tas.gov.au

My message is that we should takea closer look at non-parametricstatistics.Why ?Because most of our data cannot beproved to fit the Normal ErrorCurve which is a prerequisite for allparametric statistical tests

Example 1TOTAL IRON BINDINGCAPACITY EQAPIs the Local Group performingthis assay differently from theNational Group ?Use Geometric Mean Regressionto get an objective assessment

Y on x and xon yregressionsboth suggesteither a + 8%or a -8%systematic biasdepending uponyour point ofview, local orNational.

Geometric Mean (GM) Regression FormulaeThe slope is easily calculated from the two equationswe have already got :GM Slope = SquareRoot (Slope y on x / Slope x on y )= SquareRoot ( 1.0785/0.9236) = 1.081Alternatively GM Slope = SDy / SDxGM Intercept = Mean of y data – GM Slope * Mean ofthe x data= 68.0625 – 1.0806 * 63.4375= -0.4881Geometric Mean Regression : Local = 1.081 * National - 0.4881The geometric mean regression analysis suggests that theconsensus agreement should be that the local labs are reading8% higher than the National labs.

Albumin versus Calcium – aphysiological relationshipGM Regression EquationCalcium = 0.03130 * Alb + 1.37

Example 3Rank Order CorrelationWCC versus TLC : no real physiological relationship but tend toparallel each other and have skewed histograms

Example 3Rank Order CorrelationWCC versus TLC : no real physiological relationship but tendto parallel each other and have skewed histograms

Rank Order Correlation : WCC vs TLChttp://faculty.vassar.edu/lowry/VassarStats.html

Rank Order Correlation : WCC vs TLC37 times

Example 4MULTIPLE LINEAR REGRESSIONUse this for multiparameter modelling eg Ionised Ca

MULTIPLE LINEAR REGRESSIONIonised Ca = 0.425 TCa + 0.728 – 0.00565Alb – 0.00174 Glob – 0.00445 Bic –0.00528 AG – 0.027 Phos

TOPIC 2 : BAYESIAN NETWORKANALYSISBayes TheoremMy recommendation is that will probably find Bayes Theorem easier to apply ifyou use DECISION TREES.Under those terms Bayes Theorem reads as :Probability of arriving at your Target Outcome---------------------------------------------Sum of all the Probabilities of arriving at the SAMEoutcome but by all possible routes

Decision Tree Based Upon a Fasting GlucoseReference Study

Decision Tree Based Upon a Fasting GlucoseReference StudyIf we now feed in a hypothetical Antenatal Clinic Sizeof 1534 patients into the decision tree we can see howmany cases of Gestational Diabetes they are going tohave to manage :92 + 277 + 304 = 673.This forecasting property of our analyses is perhapsone of the most useful in these times of criticalbalances between the size of clinical caseloads and thesize of the clinical facilities available to service thatcaseload.

Decision Tree Based Upon a Fasting GlucoseReference Study

What Happens When We Search for ADecision Tree in Laboratory Data ?www.bayesware.com

Can It Find Relationships We WouldExpect and Others Which AreUnexpected.We have ‘mined’ two sets of dataOne we obtained from a Vitros 950 AnalyzerOne we obtained from a Abbott Architect AnalyzerThe two datasets where obtained a year apart froma Hospital population.Could our data mining reveal differences that wecould perhaps attribute to the changeover from theVitros Analyzer to the Architect ?

The Electrolytes DatasetN = 286 Vitros results + 349 Architect results = 635Results were scored as L,N or H according to the refranges in use at the time.Raw DataTransformedData

Electrolytes Network : Na, K, HCO3,Urea, Creat

Electrolytes Network : Na, K, HCO3,Urea, CreatAnalyzer EffectAnalyzer EffectAnalyzer EffectPhysiological EffectNo Analyzer EffectNo Analyzer EffectPhysiological Effect

K : No Analyzer EffectHigh 13%Normal 80%Low 8%Low Normal High

Urea and K : No Analyzer EffectPhysiological EffectUREAHigh 26% 38% 77%Normal 59% 55% 23%Low 15% 8% 0%Low Normal HighPOTASSIUM

Bicarbonate : Analyzer EffectHighNormalLow10% Vit6% Arch78% Vit80% Arch7% Vit14% ArchLow Normal High

Sodium : Analyzer EffectHighNormalLow10% Vit2% Arch78% Vit71% Arch12% Vit27% ArchLow Normal High

Urea and Creat : Analyzer Effectand Physiological EffectHigh 0% Vit 10% Vit 74% Vit0% Arch 7% Arch 67% ArchCREATNormal39% Vit90% Arch74% Vit88% Arch20% Vit33% ArchLow61% Vit16% Vit6% Vit10% Arch5% Arch0% ArchLow Normal HighUREA

www.medlabstats.comNon-mainstream StatisticsGeometric Mean RegressionRank Order CorrelationLogistic RegressionStatistics for Small StudiesChi SquaresMann Whitney U TestStatistics for Knowledge MiningANOVARepeated Measures ANOVAMultiple Linear RegressionCHAID AnalysisBayes TheoremBayesian Analysis of Questionnaire Data using BayeswareDiscovererNow is an opportune time to expand our use of statistics in the clinicallaboratory. We have particularly stable analytical platforms so we should spendmore time on the objective examination of the very large amounts of datathese systems produce. Within these datasets is a rich resource of knowledgethat can only be appreciated after the application of robust andmultiparameter statistical tests that go beyond our usual practice.