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.