Skip to main content

Table 4 Average estimates of haplotype frequencies for a 32 loci case

From: An EM algorithm based on an internal list for estimating haplotype distributions of rare variants from pooled genotype data

   

k=2

  

k=4

Position of ‘1’

TRUE

 

CDMLE

EML

EM- CDL

EM-ATCDL

EM-TCDL

 

CDMLE

EM-CDL

EM-ATCDL

EM-TCDL

      

(a) n=100

      

None

0.7995

 

0.7979

0.8248

0.8250

0.7981

0.8009

 

0.7990

0.8451

0.7970

0.8040

   

(0.0150)

(0.0117)

(0.0117)

(0.0148)

(0.0132)

 

(0.0154)

(0.0086)

(0.0133)

(0.0125)

1

0.0509

 

0.0514

0.0433

0.0433

0.0492

0.0503

 

0.0502

0.0387

0.0462

0.0507

   

(0.0103)

(0.0082)

(0.0082)

(0.0089)

(0.0088)

 

(0.0121)

(0.0069)

(0.0077)

(0.0080)

2

0.0034

 

0.0035

0.0020

0.0020

0.0033

0.0031

 

0.0037

0.0011

0.0030

0.0024

   

(0.0032)

(0.0018)

(0.0018)

(0.0024)

(0.0026)

 

(0.0035)

(0.0011)

(0.0013)

(0.0021)

3

0.0436

 

0.0430

0.0362

0.0362

0.0435

0.0426

 

0.0441

0.0322

0.0406

0.0426

   

(0.0092)

(0.0075)

(0.0075)

(0.0082)

(0.0074)

 

(0.0105)

(0.0054)

(0.0071)

(0.0065)

5

0.0034

 

0.0033

0.0018

0.0018

0.0032

0.0028

 

0.0034

0.0011

0.0030

0.0023

   

(0.0028)

(0.0016)

(0.0016)

(0.0020)

(0.0023)

 

(0.0035)

(0.0011)

(0.0013)

(0.0021)

6

0.0034

 

0.0038

0.0023

0.0023

0.0033

0.0031

 

0.0033

0.0014

0.0028

0.0022

   

(0.0031)

(0.0019)

(0.0020)

(0.0021)

(0.0025)

 

(0.0035)

(0.0013)

(0.0014)

(0.0019)

9

0.0073

 

0.0080

0.0054

0.0054

0.0079

0.0088

 

0.0081

0.0036

0.0070

0.0092

   

(0.0038)

(0.0026)

(0.0026)

(0.0032)

(0.0037)

 

(0.0043)

(0.0019)

(0.0026)

(0.0031)

11

0.0034

 

0.0032

0.0018

0.0018

0.0030

0.0027

 

0.0032

0.0010

0.0029

0.0023

   

(0.0026)

(0.0016)

(0.0016)

(0.0022)

(0.0024)

 

(0.0031)

(0.0011)

(0.0015)

(0.0021)

15

0.0034

 

0.0035

0.0019

0.0019

0.0030

0.0028

 

0.0038

0.0012

0.0031

0.0028

   

(0.0033)

(0.0018)

(0.0018)

(0.0023)

(0.0025)

 

(0.0031)

(0.0010)

(0.0015)

(0.0021)

19

0.0068

 

0.0063

0.0039

0.0039

0.0062

0.0061

 

0.0066

0.0026

0.0056

0.0057

   

(0.0039)

(0.0025)

(0.0025)

(0.0029)

(0.0034)

 

(0.0041)

(0.0015)

(0.0018)

(0.0026)

20

0.0068

 

0.0068

0.0042

0.0042

0.0062

0.0063

 

0.0063

0.0026

0.0054

0.0059

   

(0.0039)

(0.0025)

(0.0025)

(0.0028)

(0.0030)

 

(0.0038)

(0.0015)

(0.0022)

(0.0026)

21

0.0034

 

0.0038

0.0022

0.0022

0.0035

0.0032

 

0.0037

0.0012

0.0031

0.0025

   

(0.0035)

(0.0020)

(0.0020)

(0.0023)

(0.0026)

 

(0.0034)

(0.0011)

(0.0015)

(0.0021)

22

0.0102

 

0.0105

0.0071

0.0071

0.0097

0.0103

 

0.0112

0.0052

0.0086

0.0098

   

(0.0058)

(0.0037)

(0.0037)

(0.0041)

(0.0041)

 

(0.0052)

(0.0022)

(0.0030)

(0.0029)

23

0.0034

 

0.0039

0.0022

0.0022

0.0031

0.0030

 

0.0035

0.0011

0.0030

0.0025

   

(0.0027)

(0.0015)

(0.0016)

(0.0021)

(0.0022)

 

(0.0030)

(0.0010)

(0.0015)

(0.0021)

24

0.0102

 

0.0105

0.0069

0.0069

0.0107

0.0114

 

0.0106

0.0049

0.0088

0.0115

   

(0.0050)

(0.0033)

(0.0033)

(0.0043)

(0.0042)

 

(0.0059)

(0.0023)

(0.0036)

(0.0043)

1, 3

0.0040

 

0.0046

0.0037

0.0037

0.0041

0.0040

 

0.0052

0.0041

0.0049

0.0047

   

(0.0041)

(0.0032)

(0.0032)

(0.0033)

(0.0034)

 

(0.0048)

(0.0029)

(0.0030)

(0.0031)

1, 9

0.0029

 

0.0036

0.0026

0.0026

0.0030

0.0022

 

0.0030

0.0018

0.0027

0.0010

   

(0.0027)

(0.0019)

(0.0019)

(0.0026)

(0.0028)

 

(0.0031)

(0.0015)

(0.0022)

(0.0020)

6, 7

0.0204

 

0.0191

0.0148

0.0146

0.0215

0.0199

 

0.0206

0.0124

0.0212

0.0223

   

(0.0067)

(0.0048)

(0.0047)

(0.0056)

(0.0054)

 

(0.0073)

(0.0037)

(0.0048)

(0.0046)

3, 14

0.0034

 

0.0030

0.0019

0.0019

0.0020

0.0027

 

0.0036

0.0015

0.0025

0.0029

   

(0.0029)

(0.0018)

(0.0018)

(0.0026)

(0.0025)

 

(0.0026)

(0.0011)

(0.0020)

(0.0018)

3, 6, 7

0.0034

 

0.0039

0.0029

0.0029

0.0021

0.0027

 

0.0038

0.0025

0.0024

0.0019

   

(0.0035)

(0.0025)

(0.0025)

(0.0029)

(0.0031)

 

(0.0041)

(0.0022)

(0.0028)

(0.0029)

1, 6, 7, 24

0.0034

 

0.0039

0.0028

0.0028

0.0007

0.0006

 

0.0039

0.0020

0.0002

0.0000

   

(0.0025)

(0.0019)

(0.0019)

(0.0019)

(0.0018)

 

(0.0026)

(0.0014)

(0.0009)

(0.0002)

1, 12, 13, 22, 25

0.0034

 

0.0035

0.0025

0.0024

0.0027

0.0032

 

0.0033

0.0017

0.0004

0.0031

   

(0.0022)

(0.0016)

(0.0017)

(0.0023)

(0.0023)

 

(0.0026)

(0.0013)

(0.0014)

(0.0020)

Sum of remaining

 

0.0340

0.0227

0.0227

0.0102

0.0074

 

0.0703

0.0310

0.0255

0.0076

haplotype probabilities

           

Sum of probabilities

 

0.0103

0.0097

0.0100

0.0132

0.0173

 

0.0131

0.0118

0.0111

0.0200

of missed haplotypes

           

Sum of squared errors

 

0.00077

0.00125

0.00126

0.00059

0.00054

 

0.00101

0.00281

0.00055

0.00048

Length of list

 

39.65

152.30

39.65

22.08

19.63

 

71.24

71.24

29.29

19.81

SD of length

 

(3.90)

(71.65)

(3.90)

(4.20)

(3.70)

 

(5.02)

(5.02)

(5.82)

(5.22)

      

(b) n=200

      

None

0.7113

 

0.7108

0.7674

0.7677

0.7115

0.7219

 

0.7110

0.8075

0.7109

0.7374

   

(0.0202)

(0.0132)

(0.0132)

(0.0197)

(0.0161)

 

(0.0232)

(0.0119)

(0.0192)

(0.0147)

1

0.0034

 

0.0031

0.0013

0.0013

0.0032

0.0022

 

0.0034

0.0005

0.0031

0.0012

   

(0.0032)

(0.0014)

(0.0014)

(0.0022)

(0.0025)

 

(0.0054)

(0.0007)

(0.0015)

(0.0018)

3

0.0034

 

0.0039

0.0016

0.0016

0.0032

0.0028

 

0.0036

0.0005

0.0030

0.0017

   

(0.0034)

(0.0014)

(0.0014)

(0.0022)

(0.0025)

 

(0.0047)

(0.0007)

(0.0014)

(0.0022)

5

0.0034

 

0.0037

0.0016

0.0016

0.0035

0.0029

 

0.0036

0.0006

0.0032

0.0017

   

(0.0035)

(0.0015)

(0.0015)

(0.0022)

(0.0027)

 

(0.0049)

(0.0007)

(0.0013)

(0.0022)

7

0.0068

 

0.0066

0.0038

0.0041

0.0061

0.0064

 

0.0065

0.0027

0.0058

0.0061

   

(0.0048)

(0.0024)

(0.0028)

(0.0030)

(0.0040)

 

(0.0070)

(0.0024)

(0.0024)

(0.0053)

9

0.0034

 

0.0037

0.0015

0.0015

0.0034

0.0029

 

0.0038

0.0006

0.0031

0.0016

   

(0.0038)

(0.0016)

(0.0016)

(0.0024)

(0.0029)

 

(0.0049)

(0.0008)

(0.0015)

(0.0022)

10

0.0102

 

0.0098

0.0050

0.0050

0.0087

0.0093

 

0.0103

0.0026

0.0088

0.0085

   

(0.0059)

(0.0029)

(0.0030)

(0.0035)

(0.0035)

 

(0.0072)

(0.0017)

(0.0026)

(0.0042)

11

0.0034

 

0.0038

0.0016

0.0016

0.0032

0.0029

 

0.0027

0.0004

0.0031

0.0010

   

(0.0030)

(0.0013)

(0.0013)

(0.0023)

(0.0026)

 

(0.0044)

(0.0007)

(0.0014)

(0.0019)

14

0.0034

 

0.0034

0.0014

0.0014

0.0031

0.0023

 

0.0030

0.0004

0.0029

0.0013

   

(0.0037)

(0.0016)

(0.0016)

(0.0022)

(0.0027)

 

(0.0048)

(0.0007)

(0.0015)

(0.0021)

17

0.0034

 

0.0033

0.0014

0.0014

0.0029

0.0023

 

0.0031

0.0005

0.0028

0.0014

   

(0.0035)

(0.0014)

(0.0014)

(0.0021)

(0.0024)

 

(0.0047)

(0.0008)

(0.0015)

(0.0021)

20

0.0034

 

0.0037

0.0015

0.0015

0.0030

0.0025

 

0.0028

0.0004

0.0029

0.0014

   

(0.0035)

(0.0014)

(0.0014)

(0.0019)

(0.0025)

 

(0.0042)

(0.0006)

(0.0014)

(0.0021)

21

0.0264

 

0.0251

0.0164

0.0164

0.0252

0.0252

 

0.0266

0.0117

0.0257

0.0260

   

(0.0089)

(0.0051)

(0.0051)

(0.0064)

(0.0063)

 

(0.0135)

(0.0040)

(0.0055)

(0.0056)

22

0.0068

 

0.0074

0.0040

0.0040

0.0095

0.0099

 

0.0067

0.0016

0.0089

0.0074

   

(0.0055)

(0.0029)

(0.0029)

(0.0040)

(0.0051)

 

(0.0067)

(0.0017)

(0.0038)

(0.0062)

24

0.0306

 

0.0307

0.0223

0.0234

0.0289

0.0295

 

0.0297

0.0194

0.0273

0.0291

   

(0.0096)

(0.0066)

(0.0066)

(0.0070)

(0.0074)

 

(0.0146)

(0.0049)

(0.0058)

(0.0061)

25

0.0136

 

0.0138

0.0075

0.0075

0.0129

0.0129

 

0.0155

0.0047

0.0139

0.0125

   

(0.0072)

(0.0036)

(0.0036)

(0.0040)

(0.0036)

 

(0.0100)

(0.0029)

(0.0042)

(0.0051)

26

0.0034

 

0.0033

0.0013

0.0013

0.0029

0.0023

 

0.0037

0.0005

0.0031

0.0014

   

(0.0035)

(0.0014)

(0.0014)

(0.0024)

(0.0026)

 

(0.0052)

(0.0007)

(0.0014)

(0.0021)

28

0.0675

 

0.0661

0.0487

0.0488

0.0615

0.0640

 

0.0668

0.0390

0.0614

0.0629

   

(0.0136)

(0.0089)

(0.0089)

(0.0107)

(0.0105)

 

(0.0162)

(0.0075)

(0.0090)

(0.0086)

30

0.0036

 

0.0032

0.0017

0.0017

0.0070

0.0064

 

0.0043

0.0009

0.0077

0.0060

   

(0.0029)

(0.0015)

(0.0015)

(0.0039)

(0.0056)

 

(0.0053)

(0.0011)

(0.0040)

(0.0067)

31

0.0034

 

0.0037

0.0016

0.0016

0.0031

0.0025

 

0.0031

0.0004

0.0030

0.0014

   

(0.0037)

(0.0016)

(0.0016)

(0.0021)

(0.0025)

 

(0.0044)

(0.0006)

(0.0013)

(0.0020)

32

0.0038

 

0.0034

0.0016

0.0016

0.0045

0.0041

 

0.0041

0.0007

0.0042

0.0029

   

(0.0032)

(0.0015)

(0.0016)

(0.0029)

(0.0037)

 

(0.0060)

(0.0010)

(0.0021)

(0.0038)

2, 25

0.0034

 

0.0034

0.0015

0.0015

0.0021

0.0026

 

0.0036

0.0006

0.0013

0.0018

   

(0.0033)

(0.0015)

(0.0015)

(0.0029)

(0.0028)

 

(0.0048)

(0.0008)

(0.0020)

(0.0023)

7, 24

0.0510

 

0.0507

0.0403

0.0386

0.0525

0.0530

 

0.0523

0.0319

0.0524

0.0519

   

(0.0120)

(0.0079)

(0.0078)

(0.0094)

(0.0084)

 

(0.0139)

(0.0063)

(0.0089)

(0.0064)

12, 13

0.0034

 

0.0031

0.0013

0.0013

0.0016

0.0023

 

0.0029

0.0005

0.0011

0.0014

   

(0.0033)

(0.0015)

(0.0015)

(0.0025)

(0.0026)

 

(0.0049)

(0.0009)

(0.0020)

(0.0022)

21, 23

0.0034

 

0.0031

0.0015

0.0015

0.0018

0.0023

 

0.0035

0.0007

0.0016

0.0019

   

(0.0035)

(0.0016)

(0.0016)

(0.0027)

(0.0026)

 

(0.0042)

(0.0009)

(0.0023)

(0.0023)

21, 28

0.0009

 

0.0031

0.0021

0.0021

0.0022

0.0019

 

0.0035

0.0016

0.0015

0.0010

   

(0.0038)

(0.0022)

(0.0022)

(0.0027)

(0.0030)

 

(0.0050)

(0.0017)

(0.0023)

(0.0027)

21, 30

0.0033

 

0.0035

0.0018

0.0018

0.0022

0.0018

 

0.0035

0.0008

0.0016

0.0012

   

(0.0033)

(0.0016)

(0.0016)

(0.0027)

(0.0027)

 

(0.0044)

(0.0010)

(0.0024)

(0.0023)

22, 30

0.0034

 

0.0029

0.0014

0.0013

0.0017

0.0017

 

0.0037

0.0007

0.0014

0.0014

   

(0.0031)

(0.0015)

(0.0015)

(0.0024)

(0.0027)

 

(0.0051)

(0.0009)

(0.0021)

(0.0022)

24, 28

0.0034

 

0.0042

0.0034

0.0033

0.0036

0.0035

 

0.0064

0.0036

0.0037

0.0040

   

(0.0048)

(0.0030)

(0.0030)

(0.0032)

(0.0034)

 

(0.0072)

(0.0028)

(0.0029)

(0.0036)

28, 32

0.0030

 

0.0034

0.0019

0.0019

0.0022

0.0019

 

0.0033

0.0011

0.0018

0.0018

   

(0.0033)

(0.0018)

(0.0019)

(0.0028)

(0.0028)

 

(0.0037)

(0.0011)

(0.0021)

(0.0026)

4, 7, 24

0.0034

 

0.0028

0.0015

0.0016

0.0013

0.0024

 

0.0028

0.0008

0.0008

0.0019

   

(0.0025)

(0.0014)

(0.0014)

(0.0022)

(0.0022)

 

(0.0027)

(0.0008)

(0.0016)

(0.0019)

7, 22, 24

0.0034

 

0.0042

0.0025

0.0026

0.0019

0.0011

 

0.0029

0.0015

0.0018

0.0012

   

(0.0036)

(0.0022)

(0.0021)

(0.0028)

(0.0024)

 

(0.0034)

(0.0013)

(0.0024)

(0.0025)

7, 24, 30

0.0034

 

0.0034

0.0023

0.0023

0.0019

0.0018

 

0.0033

0.0014

0.0018

0.0018

   

(0.0032)

(0.0022)

(0.0022)

(0.0031)

(0.0031)

 

(0.0035)

(0.0013)

(0.0024)

(0.0029)

Sum of remaining

 

0.0828

0.0454

0.0453

0.0178

0.0083

 

0.2194

0.0592

0.0243

0.0160

haplotype probabilities

           

Sum of probabilities

 

0.0278

0.0265

0.0271

0.0263

0.0384

 

0.0474

0.0462

0.0222

0.0553

of missed haplotypes

           

Sum of squared errors

 

0.00161

0.00451

0.00456

0.00103

0.00100

 

0.00334

0.01152

0.00092

0.00152

Length of list

 

62.39

159.68

62.39

30.60

23.57

 

106.91

106.91

36.11

21.92

SD of length

 

(4.88)

(27.84)

(4.88)

(6.04)

(4.22)

 

(6.41)

(6.41)

(7.12)

(5.11)

  1. Average estimates of haplotype frequencies for a 32 loci case based on 100 simulations of n pools of k individuals each using CDMLE (collapsed data MLE), EML (EM with combinatorially determined list), EM-CDL (EM with CD list), EM-ATCDL (augmented and trimmed CD list) and EM-TCDL (CD list with trimming and no augmentation), with standard errors in parentheses.
Back to article page

BMC Genomic Data

ISSN: 2730-6844

Contact us