Transcript Document

THE POWER OF AN IBS-BASED
METHOD TO INFER RELATIONSHIPS
BETWEEN PAIRS OF INDIVIDUALS
Silvano Presciuttini1, Chiara Toni1,
Simonetta Verdiani2, Lucia Casarino2, Isabella
Spinetti2, Francesco De Stefano2, Ranieri Domenici1
1Dept.
of Biomedicine, Univ. of Pisa, Italy
2Dept. Of Legal Medicine, Univ. of Genova, Italy
Five markers
(multiplex A)
0.3
0.25
0.2
0.15
0.1
0.05
0
0
1
2
3
4
5
6
7
8
9
10
Proportion of pairs
0.25
Nine markers
(multiplex A+B)
0.2
0.15
0.1
0.05
0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18
0.25
Proportion of pairs
Distribuzione del
numero di alleli
condivisi da coppie
di fratelli e di nonparenti tipizzati
rispettivamente per
5, 9 e 13 markers
Proportion of pairs
0.35
0.2
Thirteen markers
(multiplex A+B+C)
0.15
0.1
0.05
0
0
2
4
6
8
10
12
14
16
18
20
Total number of shared alleles
22
24
26
Potere di
discriminazione
di un test basato sull’IBS
e una batteria di 13 STR
• Circa il 93% delle coppie di
fratelli sono identificate con
P ~ 0.02
• L’85% con P < 0.01
• Il 73% con P < 0.002
• Il 57% con P < 0.0005
Number Simulated Unrelated H0: they are
unrelated
of shared sib pairs
pairs
alleles
(%)
(%)

1-
0
1.0000 1.0000
1
0.03 1.0000 1.0000
2
0.16 0.9997 1.0000
3
0.60 0.9981 1.0000
4
1.52 0.9921 1.0000
5
4.24 0.9769 1.0000
6
7.66 0.9345 1.0000
7
11.61 0.8579 1.0000
8
0.01
16.23 0.7418 1.0000
9
0.08
18.67 0.5794 0.9999
10
0.26
15.60 0.3927 0.9991
11
0.66
11.61 0.2367 0.9965
12
1.85
6.49 0.1206 0.9899
13
4.34
3.54 0.0557 0.9714
14
7.38
1.49 0.0203 0.9280
15
12.09
0.38 0.0054 0.8542
16
16.25
0.13 0.0016 0.7333
17
18.15
0.03 0.0003 0.5708
18
16.02
0.0000 0.3893
19
11.24
0.0000 0.2291
20
6.79
0.0000 0.1167
21
3.31
0.0000 0.0488
22
1.25
0.0000 0.0157
23
0.30
0.0000 0.0032
24
0.02
0.0000 0.0002
25
0.0000 0.0000
26
0.0000 0.0000
Total
100
100
Allele sharing in first-degree and unrelated
pairs of individuals in the Ge.F.I. AmpflSTR®
Profiler Plustm database
0.35
PARENT-CHILD
Proportion of pairs
0.3
0.25
NON-RELATIVES
FULL-SIBS
0.2
0.15
0.1
0.05
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
Total number of shared alleles
14
15
16
17
18
Inferring relationships between pairs of
individuals from locus heterozygosities (H)
1. The probabilities that two individuals share 0, 1 or both alleles
at a locus (zi), given their biological relationship, are
approximate functions of H, meaning that the likelihood ratio of
alternative relationships between any two individuals, given
their genotypes at a locus, is a function of a single parameter.
2. Application to large samples of mother-child and full-sib pairs
shows that the statistical power of this method to infer the
correct relationship is not much lower than the exact method.
3. Analysis of a large database of STR data proves that locus
heterozygosity does not vary significantly among Caucasian
populations, apart for special cases, so that the likelihood ratio
of the more common relationships between pairs of individual
may be obtained by looking at tabulated zi values.
An example of the calculations needed for a
given full-sib pair
Genotype data
Marker
CSF1PO
FGA
FES
F13A1
D19S253
F13B
LPL
TH01
D18S51
D8S1179
TPOX
VWA
D21S11
Cumulative
log(LR)
Probability
(1)chosen
Sib1
Exact calculation
Sib2
9-13
9-13
20-24.2 20-24.2
12-13
12-13
5-5
5-5
8-12
12-12
6-8
6-10
10-12
10-10
9.3-9.3 9-9.3
13-19
14-17
13-15
13-15
8-11
8-10
17-18
17-18
63-67
63-65
IBS method
Genotype
Likelihood Shared
Allele frequencies(2)
(1)
combination
ratio(3)
alleles
4
p9 = 0.044
p13 = 0.062
50.93
2
4
p20 = 0.156 p24.2 = 0.009
103.97
2
4
p12 = 0.266 p13 = 0.047
13.38
2
1
p5 = 0.184
10.32
2
2
p12 = 0.369
0.93
1
6
p6 = 0.080
1.81
1
2
p10 = 0.275
1.16
1
2
p9.3 = 0.241
1.29
1
7
0.25
0
4
p13 = 0.344 p15 = 0.116
4.82
2
6
p8 = 0.512
0.49
1
4
p17 = 0.275 p18 = 0.206
3.52
2
6
p63 = 0.244
0.76
1
6.47
>99.999%
Likelihood
ratio(4)
3.52
9.78
2.94
3.83
0.35
0.86
0.89
1.02
0.25
6.07
0.78
5.71
1.17
2.92
99.9%
Ratio
LR1/
LR2
14.5
10.6
4.6
2.7
2.7
2.1
1.3
1.3
1.0
0.8
0.6
0.6
0.6
2.21
among 7 possible alternatives; (2)calculated from sample data;
(3)FS rather than NR, computed using exact formulas; (4)FS rather than
NR, computed from tabulated values
Probabilities of zi for 18 loci and four common
relationships
PARENT-CHILD
MARKER z0
z1
z2
TPOX
0 0.632 0.368
FES
0 0.690 0.310
F13B
0 0.708 0.292
D5S818
0 0.719 0.281
CSF1PO
0 0.731 0.269
F13A1
0 0.747 0.253
D16S539
0 0.772 0.228
D13S317
0 0.786 0.214
THO1
0 0.787 0.213
D3S1358
0 0.790 0.210
D1S80
0 0.799 0.201
VWA
0 0.807 0.193
D8S1179
0 0.814 0.186
D7S820
0 0.817 0.183
D21S11
0 0.848 0.152
YNZ22
0 0.849 0.151
FGA
0 0.861 0.139
D18S51
0 0.878 0.122
FULL SIB
z0
z1
z2
0.052 0.465 0.483
0.067 0.491 0.442
0.072 0.498 0.430
0.076 0.502 0.422
0.080 0.506 0.414
0.086 0.512 0.403
0.096 0.519 0.386
0.102 0.522 0.376
0.102 0.522 0.376
0.104 0.523 0.374
0.108 0.525 0.368
0.112 0.526 0.362
0.115 0.527 0.358
0.116 0.527 0.356
0.133 0.531 0.336
0.134 0.531 0.335
0.141 0.531 0.328
0.151 0.531 0.318
SECOND DEGREE
z0
z1
z2
0.104 0.104 0.283
0.133 0.133 0.230
0.144 0.144 0.214
0.151 0.151 0.204
0.160 0.160 0.193
0.172 0.172 0.179
0.192 0.192 0.157
0.204 0.204 0.145
0.205 0.205 0.145
0.207 0.207 0.142
0.216 0.216 0.135
0.224 0.224 0.128
0.231 0.231 0.122
0.233 0.233 0.121
0.267 0.267 0.096
0.268 0.268 0.095
0.282 0.282 0.086
0.303 0.303 0.074
NON RELATIVES
z0
z1
z2
0.208 0.593 0.199
0.266 0.584 0.150
0.288 0.576 0.136
0.303 0.571 0.127
0.319 0.563 0.117
0.343 0.552 0.105
0.384 0.530 0.087
0.408 0.515 0.077
0.410 0.514 0.077
0.414 0.511 0.075
0.432 0.500 0.069
0.447 0.489 0.063
0.461 0.480 0.059
0.466 0.477 0.058
0.534 0.426 0.040
0.536 0.424 0.040
0.565 0.402 0.034
0.606 0.368 0.026
Conclusions
The IBS method presented here may be conveniently used as a
preliminary approach to investigate the relationship existing between any
pair of individuals. It can be applied by anybody using a desk calculator or
a spreadsheet.
Furthermore, the IBS method’s using of estimates of H rather than of
allele frequencies makes the IBS method particularly attractive in all those
cases where ethnicity pose a problem, since H varies less across
ethnicities.
In certain circumstances, the results of the IBS method may even be
accepted without further analyses, since the LRs are highly correlated
with those calculated by the exact method.