Basic Statistical

8/18/2019 Basic Statistical

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Basic Statistical Concepts


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Chapter 2 Reading

instructions• 2.1 Introduction: Not very important• 2.2 Uncertainty and proaility: Read

• 2.! Bias and variaility: Read

• 2." Con#ounding and interaction: Read• 2.$ %escriptive and in#erential statistics:

Repetition

• 2.& 'ypothesis testing and p(values: Read

• 2.) Clinical signi*cance and clinical e+uivalence:Read

• 2., Reproduciility and generali-aility: Read


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Bias and variaility

Bias: Systemtic deviation #rom the true value

[ ] µ µ −ˆ E %esign Conduct /nalysis 0valuation

ots o# eamples on page "3(


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Bias and variaility

arger study does not decrease ias

ϕ µ µ +→n

ˆ 4 ∞→n

%rog 5 ( 6laceo

() ("(17 mm 'g () ("(17

%rog 5 ( 6laceo

mm 'g mm 'g

%rog 5 ( 6laceo

() ("(17

n8"7 n8277 N82777

%istriution o# sample means: 8 population mean

µ

ϕ

6opulation mean

ias


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Bias and variaility 9here is a multitude o# sources #or ias

6ulication ias

Selection ias

0posure ias

%etection ias

/nalysis ias

Interpretation

ias

6ositive results tend to e pulished hile negative o#inconclusive results tend to not to e pulished

9he outcome is correlated ith the eposure. /s aneample treatments tends to e prescried to thosethought to ene*t #rom them. Can e controlled y

randomi-ation%i;erences in eposure e.g. compliance to treatmentcould e associated ith the outcome e.g. patents

ith side e;ects stops ta


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Bias and variaility

/mount o# di;erence eteen oservations

9rue iological:

9emporal:

>easurement error:

?ariation between su@ectdue to iological #actorsAcovariates including thetreatment.?ariation over time Aand space#ten within su@ects.

Related to instruments or oserver

%esign Conduct /nalysis 0valuation


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Ra Blood pressure data

Baseline , ee


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Bias and variaility

ε β += X Y

Uneplained variation

?ariationin

oservations

80plained

variation

D


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Bias and variaility

%rug /

%rug B

utcome

Is there any di;erence eteen drug / and drug BE


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Bias and variaility

Y=μA+βx

Y=μB+βx

μA

μB

x=age

Model: ijijiij xY ε β µ ++=


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Con#ounding

Predictors

of

treatment

Predictors

of outcome

Confounder

s

9reatmentallocation

/

B

utcome


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0ampleSmoortality rateF 27.2 27.$ !$.$

Cochran Biometrics 13&,F per 1777 person(years G


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/verage age $".3 $7.$ &$.3



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/verage age $".3 $7.$ &$.3

/d@usted

mortality rateF

27.2 2&." 2".7



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Con#ounding

9he e;ect o# to or more #actors can not e separated

0ample: Compare survival #or

surgery and drug

R

i#e long treatment ith drug

Surgery at time 7

•Surgery only i# healty enough•6atients in the surgery arm may taa e

oo


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Con#ounding

Can e sometimes e handled in the design

0ample: %i;erent e;ects in males and #emales

Imalance eteen genders a;ects result

Strati#y y gender

R

/

B

Hender

>

R

R

/

/

B

B

Balance on average /lays alance


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Interaction

9he outcome on one varialedepends on the value o# anothervariale.

0ample Interaction eteen to drugs

R

/

/

B

B

Jashout

/8/K%12!"

B8/K%12!" D

Clarithromycin


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Interaction

Mean

0

1

2

3

4

5

0 4 8 12 16 20 24

Time after dose

P l a s m a c o n c e n t r a t i o n ( µ m o l / !

l i n e a r s c a l e

A"#$%&' alone

(om)ination of clarit*romcinand A"#$%&'

13.)$ ALmolFhM

!&.&2 ALmolFhM

/UC /K%12!":

/UC /K%12!" D Clarithromycin:

Ratio: 7.$$ 7.$1 7.&1O

/K%12!"

/K%12!"

0ample: %rug interaction


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Interaction

0ample: 9reatment y center interaction 9reatment di;erence in diastolic lood pressure

-25

-20

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30

Ordered center number

m m H g

/verage treatment e;ect: (".!3 (&.! (2."O mm'g

9reatment y center: p87.71

Jhat can e said aout the treatment e;ectE


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%escriptive and in#erential

statistics 9he presentation o# the results #rom a clinicaltrial can e split in three categories:

•%escriptive statistics•In#erential statistics

•0plorative statistics


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statistics%escriptive statistics aims to descrie variousaspects o# the data otained in the study.

•istings.•Summary statistics A>ean Standard %eviationP.•Hraphics.


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statisticsIn#erential statistics #orms a asis #or aconclusion regarding a prespeci*ed o@ective

addressing the underlying population.

'ypothesis Results

Con*rmatory analysis:

Conclusion


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statistics0plorative statistics aims to *nd interestingresults that

Can e used to #ormulate neo@ectivesMhypothesis #or #urther investigation in#uture studies.

Results 'ypothesis

0plorative analysis:

ConclusionE


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'ypothesis testing p(values

and con*dence intervals@ectives?ariale

%esign

Statistical >odelNull hypothesis

0stimatep(value

Con*dence interval

ResultsInterpretation


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'ypothesis testing p(

valuesStatistical model: servations ( ) nn R X X ∈= ,-X#rom a class o# distriution #unctions

{ }Θ∈=℘ θ θ : P

'ypothesis test: Set up a null hypothesis: '7: $Θ∈θ

and an alternative '1: -Θ∈θ

Re@ect '7 i# ( ) α θ θ


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Con*dence intervals

/ con*dence set is a random susetcovering the true parameter value ithproaility at least .

( ) Θ⊆XC

α −-

et ( )re/ectednot:if $

re/ected:if -,

0

$

0

$0

θ θ

θ θ θ δ

=

==

H

H X Acritical #unction

Con*dence set: ( ) ( ){ }$,: == θ δ θ XXC

9he set o# parameter values correponding tohypotheses that can not e re@ected.


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0ample

y ij 8 μ D τi D β A x ij ( x ·· D εij

?ariale: 9he change #rom aseline to end o# study in sitting %B6 Asitting SB6 ill e descried ith an /NC?/ modelith treatment as a #actor and aseline lood pressureas a covariate

Null hypoteses Asusets o# :'71: τ1 8 τ2 A%B6

'72: τ1 8 τ2 ASB6

'7!: τ2 8 τ3 A%B6

'7": τ2 8 τ3 ASB6

@ective: 9o compare sitting diastolic lood pressure A%B6 loering e;ecto# hypersartan 1& mg ith that o# hypersartan , mg

>odel:treatment e;ecti 8 12!Q1& mg , mg " mg

6arameter space:1 R

1 R

( )$23-

=++ τ τ τ


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0ample contined

Hypothesis Variable LS Mean CI (95%) p!al"e

#$ # mg !s & mg Sitting'

*+, mmHg -.+/ 0+&1 23+33#

0$ # mg !s & mg SittingS

,+ mmHg -9+0/ +#1 23+33#

*$ & mg !s . mg Sitting'

3+9 mmHg -#+&/ 3+31 3+355

. $ & mg !s . mg SittingS

0+# mmHg -*+/ 3+1 3+335 9his is a t(test here the test statistic #ollos a t(distriution

Re@ection region: ( ){ }cT >XX :

$$-4$


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6(value says nothing aoutthe si-e o# the e;ect

No. of patients per group Estimation of effect p-value

10 1.94 mmg 0.3!"

100 -0."5 mmg 0.3!#

1000 0.33 mmg 0.129

10000 0.2# mmg $0.0001

100000 0.30 mmg $0.0001

/ statistical signi*cant di;erence does N9

need to e clinically relevant

0ample: Simulated data. 9he di;erence eteen treatmentand placeo is 7.! mm'g


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Statistical and clinical

signi*cance

Statistical signi*cance:

Clinical signi*cance:

'ealth ecominical relevance:

Is there any di;erence

eteen the evaluatedtreatmentsE%oes this di;erence haveany meaning #or thepatientsEIs there any economicalene*t #or the society inusing the ne treatmentE


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Statistical and clinicalsigni*cance

/ study comparing gastropra-ole "7 mg and myglopra-ole!7 mg ith respect to healing o# erosived eosophagitis a#ter, ee

Basic Statistical

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