Design adaptation methods for genetic association studies [Elektronische Ressource] / vorgelegt von André Scherag

(André Scherag)

Sujets

• Gesundheit

Informations

• Publié par: philipps-universitat_marburg
• Publié le: 01 janvier 2008
• Nombre de lectures: 25
• Poids de l'ouvrage: 2 Mo

Extrait

Aus dem Institut fur Medizinische Biometrie und Epidemiologie
des F a chb ereichs Medizin der P hilipps-U niv ersitat Ma rb urg
D irek tor: P rof. D r. rer. na t. H elmut S cha fer
Design adaptation methods for
genetic association stu dies
Ina ugura l-D isserta tion
zur Erla ngung des D ok torgra des der H uma nb iologie
(D r. rer. phy siol.)
dem F a chb ereich Medizin
der P hilipps-U niv ersitat Ma rb urg
v orgelegt v on
Andre S c h era g
a us Ba d H ersfeld
Ma rb urg, 2 0 0 8Angenommen vom Fachbereich Medizin der Philipps-Universitat Marburg am 27.02.2008
G edruckt mit G enehmigung des Fachbereichs.
Dekan: Prof. Dr. M. R othmund
R eferent: Prof. Dr. H. Schafer
1 . K orreferent: Prof. Dr. K .-H. G rzeschikContents
1 Introd u ction 9
2 G enetic m ap p ing of com p lex traits 1 3
2.1 Biological background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.1 Genetic linkage analysis . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.2 L inkage diseq uilibrium mapping - genetic association analysis . . 16
2.2 Statistical methods for genetic association analysis . . . . . . . . . . . . . 20
3 M ath em atical b ackg rou nd 2 5
3.1 Adaptive designs and adaptive design methods . . . . . . . . . . . . . . . 26
3.1.1 General framew ork . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.1.2 Adaptive designs . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.3 Methods for design adaptation . . . . . . . . . . . . . . . . . . . . 34
3.2 Point and interval estimates of genetic e ects . . . . . . . . . . . . . . . 36
3.2.1 C ase-control design . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2.2 Family-based trio design . . . . . . . . . . . . . . . . . . . . . . . 37
4 S am p le size m od i cations for cand id ate g ene stu d ies 4 9
4 .1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 9
4 .2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 0
4 .2.1 Fix ed sample, group seq uential and data adaptive plans . . . . . . 5 0
4 .2.2 Approx imation of the T DT by a Brow nian motion process - group
seq uential T DT . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1
4 .2.3 Interim analysis and sample size adaptation . . . . . . . . . . . . 5 3
3Contents
4.3 Simulation studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.3.1 Comparison of FS, GS, and AS designs . . . . . . . . . . . . . . . 55
4.3.2 Comparison with adaptive designs . . . . . . . . . . . . . . . . . . 56
4.3.3 Modifying the rule for interim sample size reassessments . . . . . 62
4.4 Real data application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5 Flexible two-stage designs for genomewide association studies 71
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.2.1 N otation for a case-control genomewide association study . . . . . 73
5.2.2 The exible two-stage procedure . . . . . . . . . . . . . . . . . . . 75
5.3 Simulation studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.4 Real data application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6 General discussion 8 7
6.1 Design adaptation methods for genomewide association studies . . . . . . 88
6.2 Design adaptation methods for candidate gene investigations . . . . . . . 90
6.3 Limits and prospects of gene characterization using estimates of genetic
eects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7 Summary 95
8 Z usammenfassung 97
R eferences 99
L ebenslauf 114
V erzeichnis akademischer L ehrer 118
D anksagung 119
4Contents
Ehrenwortliche Erklarung 121
A ppendix 122
5Summary of commonly used notation
and abbreviations
Variables
; signicance levels of a statistical test
c critical value of a level test
F denotes the (1 )-quantile of the central F-k1;k2;(1 )
distribution with (k1,k2) df
(in chapter 5, F is used to denote a
cumulative distribution function)
i; j; k index variables
K ; U ; X random variables
(bold letters for vectors, small letters for their
realizations)
n ; N variable and random variable for sample size
p p-value
(not to be confused with the allele frequency
abbreviation)
t information time variable
1 (in chapter 5, t is the (1 )-quantile of the
cumulative distribution function of a test statistic)
T test statistic
Z N(0; 1)-distributed random variable
z (1 )-quantile of a standard normal distribution1
2 (1 )-quantile of a chi-squaredk;1
distribution with k df
6Parameters
LD measure
2; Brownian motion process drift and variance
f = (f ;f ;f ) penetrance vector0 1 2
proportion of sample size
proportion of cases relative to total sample size
; genotype relative risk parameters1 2
p;q allele frequency of D and M
recombination fraction
# parameter of a random distribution
w = (w ;w ;w ) weights for CA Trend Test0 1 2
Distributions, Measures, F unctions, Pro cesses, and sets
N(0; 1) standard normal distribution
U(0; 1) uniform distribution
() conditional (type I) error function
E() expected value
’(), () decision functions
Ifg indicator function
m infg minimum function (and arg m in is for the argument
of the minimum)
m axfg maximum function
inffg inmum function
Pr() probability measure
() cumulative distribution of a standard normal distribution
1 () quantile function of the standard normal distribution
V ar() variance
fB(t);t 0g standard Brownian motion stochastic process
fX(t);t 0g stochastic process
I;J;H ;M ;M ;M sets of SNP markers1 2
(with small letters denoting the cardinality of the set)
B Borel sets