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Table 2 Simulation results

From: An EM algorithm to improve the estimation of the probability of clonal relatedness of pairs of tumors in cancer patients

   

One-step maximization

EM algorithm

EM algorithm - subset

N cases

True π

Scenario

mean

(sd)

range

N 0-1

mean

(sd)

range

N 0-1

mean

(sd)

range

N 0-1

100

0.10

1: μ=−2;σ=1.5

0.127

(0.126)

0.010-1.000

0-7

0.086

(0.036)

0.010-0.202

0-0

0.076

(0.037)

0.034-0.138

0-0

  

2: μ=−1;σ=1.0

0.105

(0.038)

0.020-0.234

0-0

0.099

(0.033)

0.020-0.212

0-0

    
  

3: μ=0.7σ=0.3

0.101

(0.031)

0.030-0.220

0-0

0.101

(0.031)

0.030-0.220

0-0

    
 

0.25

1: μ=−2;σ=1.5

0.259

(0.091)

0.079-0.729

0-0

0.214

(0.051)

0.077-0.387

0-0

    
  

2: μ=−1;σ=1.0

0.250

(0.049)

0.121-0.387

0-0

0.245

(0.047)

0.121-0.377

0-0

    
  

3: μ=0.7σ=0.3

0.252

(0.043)

0.130-0.380

0-0

0.252

(0.043)

0.130-0.380

0-0

    
 

0.50

1: μ=−2;σ=1.5

0.518

(0.113)

0.245-0.881

0-0

0.440

(0.066)

0.230-0.621

0-0

    
  

2: μ=−1;σ=1.0

0.498

(0.055)

0.325-0.640

0-0

0.490

(0.054)

0.319-0.624

0-0

    
  

3: μ=0.7σ=0.3

0.498

(0.049)

0.350-0.620

0-0

0.498

(0.049)

0.350-0.620

0-0

    
 

0.75

1: μ=−2;σ=1.5

0.756

(0.116)

0.495-1.000

0-31

0.662

(0.068)

0.477-0.924

0-0

0.758

(0.052)

0.623-0.924

0-0

  

2: μ=−1;σ=1.0

0.747

(0.050)

0.616-0.881

0-0

0.738

(0.049)

0.609-0.875

0-0

    
  

3: μ=0.7σ=0.3

0.748

(0.043)

0.630-0.850

0-0

0.748

(0.043)

0.630-0.850

0-0

    

50

0.10

1: μ=−2;σ=1.5

0.138

(0.193)

0.000-1.000

19-18

0.083

(0.049)

0.000-0.265

11-0

0.083

(0.070)

0.000-0.265

11-0

  

2: μ=−1;σ=1.0

0.113

(0.079)

0.000-1.000

4-1

0.101

(0.048)

0.000-0.272

3-0

0.038

(0.056)

0.000-0.125

3-0

  

3: μ=0.7σ=0.3

0.100

(0.042)

0.000-0.260

2-0

0.100

(0.042)

0.000-0.260

2-0

0

(0.000)

0.000-0.000

2-0

 

0.25

1: μ=−2;σ=1.5

0.270

(0.145)

0.043-1.000

0-4

0.210

(0.071)

0.043-0.456

0-0

0.194

(0.049)

0.122-0.234

0-0

  

2: μ=−1;σ=1.0

0.255

(0.076)

0.100-0.714

0-0

0.245

(0.064)

0.101-0.447

0-0

    
  

3: μ=0.7σ=0.3

0.248

(0.061)

0.100-0.440

0-0

0.248

(0.061)

0.100-0.440

0-0

    
 

0.50

1: μ=−2;σ=1.5

0.520

(0.154)

0.222-1.000

0-7

0.441

(0.091)

0.212-0.804

0-0

0.64

(0.097)

0.494-0.804

0-0

  

2: μ=−1;σ=1.0

0.501

(0.075)

0.296-0.739

0-0

0.492

(0.073)

0.293-0.713

0-0

    
  

3: μ=0.7σ=0.3

0.498

(0.069)

0.320-0.700

0-0

0.498

(0.069)

0.320-0.700

0-0

    
 

0.75

1: μ=−2;σ=1.5

0.747

(0.143)

0.480-1.000

0-52

0.659

(0.091)

0.469-0.933

0-0

0.783

(0.072)

0.650-0.933

0-0

  

2: μ=−1;σ=1.0

0.746

(0.075)

0.530-1.000

0-2

0.736

(0.071)

0.527-0.938

0-0

0.926

(0.018)

0.913-0.938

0-0

  

3: μ=0.7σ=0.3

0.746

(0.060)

0.600-0.920

0-0

0.746

(0.060)

0.600-0.920

0-0

    

25

0.10

1: μ=−2;σ=1.5

0.128

(0.197)

0.000-1.000

101-18

0.099

(0.079)

0.000-0.443

46-0

0.088

(0.112)

0.000-0.441

46-0

  

2: μ=−1;σ=1.0

0.118

(0.121)

0.000-1.000

46-4

0.103

(0.063)

0.000-0.365

26-0

0.056

(0.084)

0.000-0.365

26-0

  

3: μ=0.7σ=0.3

0.103

(0.061)

0.000-0.330

29-0

0.101

(0.056)

0.000-0.280

22-0

0.018

(0.045)

0.000-0.228

22-0

 

0.25

1: μ=−2;σ=1.5

0.276

(0.192)

0.000-1.000

6-9

0.216

(0.103)

0.039-0.543

0-0

0.222

(0.108)

0.039-0.432

0-0

  

2: μ=−1;σ=1.0

0.262

(0.110)

0.040-1.000

0-1

0.246

(0.092)

0.040-0.618

0-0

0.176

 

0.176-0.176

0-0

  

3: μ=0.7σ=0.3

0.250

(0.087)

0.040-0.520

0-0

0.249

(0.088)

0.040-0.520

0-0

    
 

0.50

1: μ=−2;σ=1.5

0.515

(0.198)

0.122-1.000

0-19

0.433

(0.124)

0.109-0.878

0-0

0.622

(0.145)

0.384-0.878

0-0

  

2: μ=−1;σ=1.0

0.505

(0.110)

0.201-1.000

0-1

0.492

(0.102)

0.201-0.846

0-0

0.490

 

0.490-0.490

0-0

  

3: μ=0.7σ=0.3

0.500

(0.096)

0.200-0.760

0-0

0.500

(0.096)

0.200-0.760

0-0

    
 

0.75

1: μ=−2;σ=1.5

0.752

(0.175)

0.358-1.000

0-82

0.665

(0.136)

0.332-1.000

0-2

0.835

(0.097)

0.614-1.000

0-2

  

2: μ=−1;σ=1.0

0.752

(0.098)

0.489-1.000

0-5

0.741

(0.094)

0.483-1.000

0-1

0.975

(0.028)

0.941-1.000

0-1

  

3: μ=0.7σ=0.3

0.749

(0.084)

0.480-0.960

0-0

0.749

(0.084)

0.480-0.960

0-0

    
  1. The EM algorithm – subset results present the estimates obtained with the EM algorithm for the datasets where the one-step maximization gave results on the boundary. N 0-1 shows the number of times the estimate was exactly 0 - number of times it was exactly 1