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Brandser, Riley, Berbaum, El-Khoury, & Bennett (1996)

Reader and case sample combinations needed for 0.80 power based on the data of:

Brandser EA, Riley MA, Berbaum KS, El-Khoury GY, Bennett DL. MR imaging of anterior cruciate ligament injury: Independent value of primary and secondary signs. American Journal of Roentgenology 1996;167:121-126.

Readers: 3 musculoskeletal radiologists

Cases: 40 patients with torn ACL, 40 patients with normal ACL (80)

Truth: ACL status confirmed arthroscopically

Rating: probability of abnormality on a 5-point scale (5=definite ACL tear)

Conditions: (1) secondary signs of ACL tear visible (primary signs masked), (2) primary signs of ACL tear visible (secondary signs masked),  (3) both primary and secondary signs of ACL tear visible

ROC Model = PropROC, Parameter = AUC,

AUCs = 0.813, 0.958, 0.954, respectively.

Readers = 3, Cases = 80,

MS( Treatment*Reader ) = 0.08928400,

MS( Treatment*Case ) = 0.11532357,

MS( Treatment*Reader*Case ) = 0.04668085.

 

Given a number of readers are available, we compute the number of cases needed when treating readers and cases as random factors, when treating cases as a random factor and readers as a fixed factor, and treating readers as a random factor and cases as a fixed fracture.

 

AUC Difference = 0.03

Readers

Readers

and Cases

Random

Cases

Random

Readers

Random

3

.

673

.

4

.

605

.

5

.

564

.

6

.

537

.

7

.

518

.

8

.

503

.

9

.

492

.

10

.

483

.

11

.

476

.

12

.

469

1252

13

.

464

491

14

1817

460

305

15

1449

456

222

Note: Cells containing a period indicate that more than 2000 cases would be required.

 

AUC Difference = 0.05

Readers

Readers

and Cases

Random

Cases

Random

Readers

Random

3

.

244

.

4

.

219

.

5

.

205

.

6

950

195

624

7

480

188

196

8

366

183

116

9

311

179

83

10

279

175

65

11

258

173

53

12

242

171

45

13

231

169

39

14

222

167

35

15

214

166

31

Note: Cells containing a period indicate that more than 2000 cases would be required.

 

AUC Difference = 0.10

Readers

Readers

and Cases

Random

Cases

Random

Readers

Random

3

212

63

.

4

86

57

82

5

68

53

38

6

60

51

25

7

55

49

20

8

52

48

20

9

50

47

20

10

48

46

20

11

47

45

20

12

46

44

20

13

45

44

20

14

44

44

20

15

44

43

20

Note: Cells containing a period indicate that more than 2000 cases would be required.

 

 


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