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Samenvatting cursus: inleiding tot de biostatistiek

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Course
Inleiding tot de biostatistiek (C004408A)

Institution
Universiteit Gent (UGent)

(Behaalde score:15/20) Dit document bevat een beknopte samenvatting van de cursus, inclusief de extra informatie vermeld in de zelfstudie video's. Vermelding van paginanummers bij belangrijke concepten is zeer handig bij het open boek examen.

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biomedische wetenschappen
samenvatting
inleiding tot de biostatistiek

Institution
Universiteit Gent (UGent)
Education
Biomedische Wetenschappen
Course
Inleiding tot de biostatistiek (C004408A)

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Hoofdstuk 1: inleiding.............................................................................................................................9
Falsificatieprincipe van Popper...............................................................................................9
Vals positieve & vals negatieve resultaten..............................................................................9
Double blinding.......................................................................................................................9
Hoofdstuk 2: belangrijke concepten & conventies: pg. 61......................................................................9
2.1 Inleiding.......................................................................................................................................9
2.2 Variabelen : pg. 64........................................................................................................................9
Kwalitatieve variabelen...........................................................................................................9
Kwantitatieve/numerieke variabelen....................................................................................10
2.4 Toevalsveranderlijken (of toevallige veranderlijken) : pg. 66......................................................10
2.5 Beschrijven van de populatie: pg. 66..........................................................................................10
2.5.1.2 Continue toevallig veranderlijke: pg. 72............................................................................10
Normaalverdeling.................................................................................................................10
2.5.1.2.1 Cumulatieve distributie: pg. 73..................................................................................11
2.5.1.2.2 Gemiddelde en variantie (& standaardafwijking) : pg. 76..........................................11
2.5.2 Standardisatie: pg. 78..........................................................................................................11
2.5.3 Achtergrond Normale verdeling: pg. 79...............................................................................12
Een (1- α)100% referentie-interval voor een veranderlijke X................................................12
2.6 Steekproef : pg. 83......................................................................................................................12
2.8 NHANES: Lengte: pg. 84..............................................................................................................12
2.8.1 Empirische distributie : pg. 85..............................................................................................12
2.8.2 Normale benadering: pg. 88................................................................................................12
Hoofdstuk 3: Studiedesign: pg. 95........................................................................................................12
3.2 Steekproefdesigns: pg. 97...........................................................................................................12
3.3 Experimentele studies: pg. 99.....................................................................................................13
Confounding: pg. 102............................................................................................................13
Gerandomiseerd gecontroleerde studie : pg. 103.................................................................13
3.3.2 Gerandomiseerde gecontroleerde studies: pg. 105.............................................................13
Systematische allocatie = toevallige allocatie : pg. 106.........................................................13
Randomisatietechnieken: pg. 106-108..................................................................................13
3.3.3 Parallelle designs : pg. 110...................................................................................................14
3.3.4 Cross-over designs: pg. 110.................................................................................................14
3.3.5 Factoriële designs : pg. 112..................................................................................................14
3.3.6 Quasi-experimentele designs: pg. 113.................................................................................14
3.4 Observationele studies: pg. 114..................................................................................................14
*Prognostische factoren : pg. 108.........................................................................................14

1

, Simpson’s paradox: pg. 116...................................................................................................15
3.5 Prospectieve studies : pg. 118....................................................................................................15
3.6 Retrospectieve studies : pg. 118.................................................................................................15
3.7 Niet-gecontroleerde studies: pg. 121..........................................................................................15
3.7.1 Pre-test/Post-test studies: pg. 121.......................................................................................15
3.7.2 Cross-sectionele surveys......................................................................................................15
Hoofdstuk 4: Data exploratie en beschrijvende statistiek: pg. 123.......................................................16
4.2 Univariate beschrijving van de variabelen: pg. 125.....................................................................16
4.3 Samenvattingsmaten voor continue variabelen: pg. 132............................................................16
4.3.1 Maten voor de centrale ligging: pg. 133..............................................................................16
Het (rekenkundig) gemiddelde: pg. 133................................................................................16
De mediaan : pg. 134............................................................................................................16
De modus: pg. 135................................................................................................................17
Geometrisch gemiddelde: pg. 136........................................................................................17
4.3.2 Spreidingsmaten: pg. 139....................................................................................................17
Variantie van een reeks waarnemingen : pg. 141.................................................................17
(Steekproef)Standaarddeviatie of standaardafwijking s : pg. 141.........................................18
Range: pg. 142......................................................................................................................18
Interkwartielafstand: pg. 142................................................................................................18
Variatiecoëfficiënt: pg. 142...................................................................................................18
4.4 De normale benadering van gegevens: pg. 142..........................................................................18
4.4.1 QQ-plots: pg. 143.................................................................................................................18
4.5 Samenvattingsmaten voor categorische variabelen : pg. 149.....................................................20
4.5.1 Prospectieve studies en lukrake steekproeven....................................................................20
Absolute risico verschil: pg. 149............................................................................................20
Relatief risico: pg. 150...........................................................................................................20
Relatief risico verschil : pg. 151.............................................................................................20
4.5.2 Retrospectieve studies : pg. 151..........................................................................................20
De odds op een gebeurtenis : pg. 152..................................................................................20
Odds ratio op een gegeven gebeurtenis: pg. 153..................................................................21
4.5.3 Rates versus risico’s : pg. 154...............................................................................................21
4.6 Associaties tussen 2 variabelen : pg. 155....................................................................................21
4.6.1 Associatie tussen 2 kwalitatieve variabelen :pg.155............................................................21
4.6.2 Associatie tussen 1 kwalitatieve en 1 continue variabele : pg. 155......................................21
4.7 Associatie tussen 2 continue variabelen: pg. 159.......................................................................22
4.7.1 Covariantie en correlatie : pg. 165.......................................................................................22

2

, Covariantie: niet-gestandardiseerd: pg. 165.........................................................................22
Correlatie: gestandardiseerd: pg. 165...................................................................................22
4.7.2 Pearson correlatie : pg. 166.................................................................................................22
4.7.2.1 Impact van outliers : pg. 168.........................................................................................23
4.7.2.1 De pearson correlatie pikt enkel lineaire associatie op : pg. 168..................................23
4.7.3 Verschillende groottes van correlaties : pg. 170...................................................................23
4.7.4 Spearman correlatie : pg. 172..............................................................................................24
Hoofdstuk 5: Statistische besluitvorming : pg. 177...............................................................................24
5.2 Captopril voorbeeld : pg. 178.....................................................................................................24
5.2.1 Proefopzet : pg. 179.............................................................................................................24
5.3 Puntschatters: het steekproefgemiddelde: pg. 186....................................................................24
5.3.2 Het steekproefgemiddelde is onvertekend: pg. 188............................................................25
5.3.3 Imprecisie/standard error : pg. 190.....................................................................................25
Noodzaak van onafhankelijkheid: pg. 194.............................................................................25
5.3.3.1 Variantie schatter voor 𝑋̄ (steekproefgemiddelde): pg. 195........................................26
Standaarddeviatie van 𝑋̄ = STANDARD ERROR = SE: pg . 195...............................................26
5.3.3.2 Standaarddeviatie vs standard error : pg. 196..............................................................26
Gemiddelden : pg. 198..........................................................................................................26
Standaarddeviatie : pg. 199..................................................................................................27
Standaard error van het gemiddelde : pg. 200......................................................................27
5.3.3.3 Normaal verdeelde gegevens : pg. 200.........................................................................27
5.3.4 Verdeling van het steekproefgemiddelde : pg. 202..............................................................27
5.3.4.3 Niet-normaal verdeelde data: de centrale limietstelling: pg. 207 + 291........................28
5.4 Intervalschatters : pg. 216...........................................................................................................28
5.4.1 Gekende variantie op de metingen : pg. 216.......................................................................28
95% betrouwbaarheidsinterval voor het populatiegemiddelde : pg. 217.............................28
5.4.1.2 Andere betrouwbaarheidsniveaus : pg. 222.................................................................28
Een (1- α)100% betrouwbaarheidsinterval voor een populatieparameter : pg. 223.............28
5.4.2 Ongekende variantie σ2 op de metingen: pg. 223................................................................29
5.5 Principe van Hypothesetoetsen (via one sample t-test) : pg. 230...............................................29
5.5.1 Introductie d.m.v. captopril voorbeeld : pg. 230..................................................................29
5.5.1.1 Permutatietest (voor one-sample t-test) : pg. 231........................................................30
5.5.1.2 Pivot : pg. 237...............................................................................................................30
5.5.1.4 Permutatietests zijn computationeel veeleisend: pg. 239.............................................30
5.5.3 Test-statistiek T (one sample t-test/gepaarde t-test): pg. 242..............................................30
5.5.4 De p-waarde : pg. 244..........................................................................................................31

3

, Significantieniveau : pg 245..................................................................................................31
5.5.5 Kritieke waarde : pg. 246.....................................................................................................31
5.5.6 Beslissingsfouten : pg. 248...................................................................................................31
5.5.6.1 Type 1 fout : pg. 248.....................................................................................................31
5.5.6.2 Type 2 fout : pg. 251.....................................................................................................31
De kracht van een test : pg. 251............................................................................................32
5.5.7 Conclusies Captopril voorbeeld : pg. 253.............................................................................32
5.5.8 Eenzijdig of tweezijdig toetsen : pg. 255..............................................................................32
5.6 Geclusterde metingen : pg. 260..................................................................................................33
5.7 Two-sample t-test : pg. 263.........................................................................................................33
Effectgrootte : pg. 267...........................................................................................................33
Variantie op het verschil : pg. 268.........................................................................................33
Standard error : pg. 268.......................................................................................................33
Gepoolde variantieschatter Sp2: pg. 268................................................................................35
Teststatistiek T (two sampe t-test) : pg. 269..........................................................................35
5.8 Aannames !!! : pg. 271................................................................................................................35
5.8.1 Nagaan van de veronderstelling van Normaliteit : pg. 271..................................................35
5.8.2 Nagaan van homoscedasticiteit : pg. 272.............................................................................36
Welch two-sample T-test : pg. 273........................................................................................36
Hoofdstuk 6 : Enkelvoudige lineaire regressie : pg. 277........................................................................36
6.2 Lineaire regressie : pg. 283.........................................................................................................36
6.3 Parameterschatting : pg. 285......................................................................................................36
Residuen ei : pg. 286.............................................................................................................37
Schatten van β1 en β2 : pg. 287............................................................................................37
6.4 Statistische besluitvorming : pg. 288..........................................................................................37
Mean squared error = MSE : pg. 291....................................................................................37
Standard error van de parameterschatters = SEβ0 en SEβ1 : pg. 291.......................................38
Betrouwbaarheidsinterval voor de helling en toetsen: pg. 291............................................38
6.5 Nagaan van modelveronderstellingen : pg. 293..........................................................................39
6.6 Afwijkingen van modelveronderstellingen : pg. 297...................................................................39
Transformatie van de verklarende variabele (predictor X) : pg. 297.....................................40
Transformatie van de uitkomst (respons Y) : pg. 298............................................................40
Interpretatie van de modelparameters na log2 tranformatie : pg. 301.................................40
6.7 Besluitvorming over gemiddelde uitkomst : pg. 304...................................................................40
Standard error op schatter voor de gemiddelde uitkomst : pg. 304......................................40
Teststatistiek T (voor gemiddelde uitkomst) : pg. 304...........................................................41

4

, Gemiddelde uitkomst en hun 95% puntgewijze betrouwbaarheidsintervallen : pg. 306......41
6.8 Predictie-intervallen : pg. 308.....................................................................................................41
Predictie-interval : pg. 309....................................................................................................42
6.9 Kwadratensommen en Anova-tabel : pg. 313.............................................................................42
Totale kwadratensom, SSTot : pg. 313...................................................................................42
Kwadratensom van de regressie, SSR : pg. 314.....................................................................43
Kwadratensom van de fout, SSE : pg. 315.............................................................................43
6.9.1 Determinatiecoëfficiënt R2 : pg. 318....................................................................................43
6.9.2 F-testen in het enkelvoudig lineair regressiemodel : pg. 319...............................................44
MSR = gemiddelde kwadratensom v/d regressie..................................................................44
6.9.3 Anova tabel : pg. 320...........................................................................................................44
Hoofdstuk 7: Variantie analyse : pg. 329...............................................................................................44
7.1 Inleiding : pg. 329.......................................................................................................................44
7.1.1 Prostacycline voorbeeld : pg. 329........................................................................................44
7.1.2 Model : pg. 330....................................................................................................................44
7.2 Variantie-analyse : pg. 334..........................................................................................................45
7.2.1 Model voorbeeld: pg. 334....................................................................................................45
7.2.2 Kwadratensommen en Anova : pg. 337................................................................................45
Kwadratensom van de regressie SSR  SST : pg. 337...............................................................45
Gemiddelde kwadratensom MST : pg. 338...........................................................................45
Gemiddelde residuele kwadratensom MSE : pg. 340............................................................45
Totale kwadratensom SSTot : pg. 338....................................................................................46
7.2.3 Anova-test : pg. 340.............................................................................................................46
7.2.4 Anova tabel : pg. 341...........................................................................................................46
7.3 Post hoc-analyse: Meervoudig Vergelijken van Gemiddelden : pg. 341......................................46
7.3.1 Naïeve methode : pg. 341....................................................................................................46
7.3.2 Family-wise error rate : pg. 347...........................................................................................46
7.3.2.1 Bonferroni correctie : pg. 347.......................................................................................46
7.3.2.2 Methode van Tukey : pg. 350........................................................................................47
Hoofdstuk 8 : Niet-parametrische statistiek : pg. 357...........................................................................47
8.2 Vergelijken van 2 groepen : pg. 358............................................................................................47
8.2.1 Cholesterol voorbeeld : pg. 358...........................................................................................47
8.2.2 Permutatietesten (voor two-sample t-test) : pg. 359...........................................................47
8.2.2.1 Hypothesen : pg. 362....................................................................................................47
8.2.2.2 p-waarde : pg. 365........................................................................................................48
8.2.2.3 Hoe kunnen we conclusie interpreteren : pg. 367........................................................48

5

, 8.2.3 Rank Testen : pg.368............................................................................................................48
8.2.4 Wilcoxon-Mann-Whitney Test/Wilcoxon rank sum test/Mann-Withney U test : pg. 369....49
Teststatistiek T (door Wilcoxon) : pg. 370.............................................................................49
Teststatistiek S1 volstaat (door Wilcoxon) : pg. 370..............................................................49
Teststatistiek U1 (door Mann & Whitney) : pg. 372..............................................................49
Probabilistische index...........................................................................................................49
8.3 Vergelijking van g behandelingen : pg. 375.................................................................................50
8.3.1 DMH voorbeeld : pg. 376.....................................................................................................50
8.3.2 Kruskal-Wallis Rank Test : pg. 378........................................................................................50
KW teststatistiek : pg. 379.....................................................................................................50
8.3.2.1 DNA schade voorbeeld : pg. 380...................................................................................50
8.3.2.2 Posthoc Analyse : pg. 380.............................................................................................50
Hoofdstuk 9 : Categorische data analyse : pg. 383...............................................................................51
9.2 Toetsen voor proportie : pg. 383.................................................................................................51
Saksenstudie : pg 383...........................................................................................................51
Bernouilli verdeling : pg. 384................................................................................................51
9.2.1 Asymptotisch betrouwbaarheidsinterval : pg. 386...............................................................51
9.2.2 Asymptotische test : pg. 387................................................................................................51
9.2.3 Binomiale test : pg. 388.......................................................................................................52
Toevalsveranderlijke S : pg. 389............................................................................................52
Binomiale test : pg. 392 + 394...............................................................................................52
9.3 Toets voor associatie tussen 2 kwalitatieve variabelen : pg. 394................................................52
9.3.1 Gepaarde gegevens : pg. 394...............................................................................................52
9.3.1.1 Voorbeeld : pg. 394.......................................................................................................52
Absoluut risicoverschil ARV : pg. 396....................................................................................52
9.3.1.2 McNemar test : pg. 398.................................................................................................53
9.3.2 Ongepaarde gegevens : pg. 401...........................................................................................53
9.3.3 De Pearson Chi-kwadraat test voor ongepaarde gegevens : pg. 403....................................53
Voorwaarden Pearson Chi-kwadraat test:.............................................................................53
Fisher’s exact test : pg. 406...................................................................................................53
9.3.3.1 Uitbreiding naar categorische variabelen met meerdere niveaus : pg. 406..................54
Opnieuw Pearson Chi-kwadraat test : pg. 407......................................................................54
9.4 Logistische regressie : pg. 408.....................................................................................................54
Veronderstellingen: pg. 408..................................................................................................54
9.4.1 Categorische predictor : pg. 408..........................................................................................54
Globale chi-kwadraat test: pg. 410.......................................................................................55

6

, Post-hoc testen met Tukey correctie : pg. 411......................................................................55
9.4.2 Continue predictor : pg. 412................................................................................................55
Hoofdstuk 10 : Algemeen lineair model : pg. 417.................................................................................55
10.1 Inleiding: pg. 417......................................................................................................................55
10.1.1 Prostaatkanker dataset : pg. 418........................................................................................55
10.2 Het additieve meervoudig lineaire regressie model : pg. 419...................................................55
10.2.1 Statistisch model : pg. 421.................................................................................................55
10.3 Besluitvorming in regressiemodellen ~enkelvoudig lineair regressiemodel: pg. 424................56
10.4 Nagaan van modelveronderstellingen : pg. 428........................................................................56
10.5 Het niet-additieve meervoudig lineair regressiemodel : pg. 430..............................................56
10.5.1 Interactie tussen continue variabele en factor variabele : pg. 430.....................................56
10.5.2 Interactie tussen twee continue variabelen : pg. 432........................................................56
10.5.3 Interactie tussen twee factor variabelen : ZIE WERKCOLLEGE...........................................56
10.6 ANOVA tabel : pg. 437...............................................................................................................57
10.6.1 SSTot, SSR en SSE ~ enkelvoudig lineair regressiemodel : pg. 437......................................57
F-teststatistiek :pg. 438.........................................................................................................57
10.6.2 Extra kwadratensommen : pg. 439....................................................................................57
10.6.3 Type I kwadratensommen : pg. 441...................................................................................57
10.6.4 Type III kwadratensommen : pg. 442.................................................................................57
10.7 Regressiediagnostiek : pg. 443..................................................................................................57
10.7.1 Multicollineariteit : pg. 443................................................................................................57
Variantie inflatie factor of VIF : pg. 444.................................................................................58
10.7.2 Invloedrijke observaties : pg. 448.......................................................................................58
Residu’s : pg. 450..................................................................................................................58
Studentized residu’s : pg. 450...............................................................................................58
Leverage (invloed, hefboom) : pg. 450..................................................................................59
10.7.3 Cook’s distance : pg. 451....................................................................................................59
DFBETAS : pg. 453.................................................................................................................59
10.8 Contrasten : pg. 457..................................................................................................................60
10.8.1 NHANES voorbeeld : pg. 457..............................................................................................60
10.8.2 Model : pg. 457..................................................................................................................60
10.8.2.1 Transformaties : pg. 458..............................................................................................60
10.8.3 Besluitvorming : pg. 461....................................................................................................60
10.9 Factoriële proeven : pg. 465.....................................................................................................60
10.9.1 Introductie : pg. 465...........................................................................................................60
10.9.2 Data : pg. 465.....................................................................................................................60

7

,10.9.3 Model : pg. 467..................................................................................................................61
10.9.3.1 Transformaties : pg. 471..............................................................................................61
10.9.4 Inferentie : pg. 477.............................................................................................................61
10.9.4.1 Verwijderen van niet-significante interactie : pg. 477.................................................61
10.9.4.2 Niet-significante interactie term in het model weerhouden : pg. 482.........................61

8

,Samenvatting statistiek
Hoofdstuk 1: inleiding

Falsificatieprincipe van Popper
Een wetenschappelijke theorie of hypothese kan nooit bewezen worden door observatie, maar kan
wel ontkracht worden door observatie.

Vals positieve & vals negatieve resultaten

 Vals positief: nulhypothese wordt verworpen terwijl deze waar is
o Ongeacht of studie klein of groot is: kans op vals positief mooi op 5% niveau
controleren
 Vals negatief: de nulhypothese wordt niet verworpen terwijl deze onwaar is
o Kan je beïnvloeden adhv steekproefgrootte

Double blinding

 Bv.
1) ouders & kinderen weten niet of ze werden gevaccineerd of niet
2) medische staf en onderzoekers weten niet of het kind het vaccin of het placebo
kreeg

Hoofdstuk 2: belangrijke concepten & conventies: pg.
61

2.1 Inleiding

PROEFOPZET  DATA EXPLORATIE & BESCHRIJVENDE STATISTIEK  STATISTISCHE BESLUITVORMING

2.2 Variabelen : pg. 64

Kwalitatieve variabelen
1) Nominaal
 Bv. geslacht, ras, bloedgroep, kleur van ogen
2) Ordinaal: kan je ordenen
 Bv. BMI klasse, rokerstatus (nooit gerookt, ooit gerookt maar gestopt, actueel roker)

9

, Kwantitatieve/numerieke variabelen

1) Discreet: bestaat uit tellingen
 Bv. aantal partners, aantal salamanders…
2) Continu: kunnen tussen bepaalde grenzen elke mogelijke waarde aannemen
 Bv. leeftijd, gewicht, BMI…

2.4 Toevalsveranderlijken (of toevallige veranderlijken) : pg. 66

 Toevalsveranderlijke = variabele X (met hoofdletter omdat karakteristiek variabel is in
populatie!)
o Toevallige trekking van een bepaalde karakteristiek uit de studiepopulatie
o Veranderlijk: niet alle subjecten bezitten zelfde waarde voor karakteristiek
 Onbekende veranderlijke die een meting voorstelt die we plannen te verzamelen, maar nog
niet hebben verzameld

2.5 Beschrijven van de populatie: pg. 66

2.5.1.2 Continue toevallig veranderlijke: pg. 72

KANS DAT CONTINUE TOEVALLIG VERANDERLIJKE EXACT 1 WAARDE AANNEEMT = 0

 DENSITEIT/DICHTHEIDSFUNCTIE

Normaalverdeling

  = gemiddelde populatie

  = variantie populatie

  = standaardafwijking = standaarddeviatie voor de populatie = sd = SD
(= s voor steekproefstandaarddeviatie, een schatting van de standaarddeviatie voor
de populatie)

10

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