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

Brandser EA, Berbaum KS, Dorfman DD, Braksiek RJ, El-Khoury GY, Saltzman CL, Marsh JL, Clark WA. Contribution of individual projections alone and in combination for radiographic detection of ankle fractures. American Journal of Roentgenology 2000;174:1691-1697.

Conclusion: The results for interpretation of single views show a clear superiority of the lateral view over the anteroposterior and mortise views for the detection of fractures of the posterior malleolus.

Readers: 4 (2 skeletal radiologists, 2 orthopedic surgeons)

Cases: 174 ankles: 34 fractures of posterior malleolus, 140 normals.

 

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

Conditions: (1) anteroposterior view alone, (2) mortise view alone, (3) lateral view alone.

Model = CBM, Parameter = sensitivity at specificity = 0.9, sensitivities = 0.203, 0.263, 0.713, respectively.

Readers = 4, Cases = 174,

MS( Treatment*Reader ) = 1.78362961,

MS( Treatment*Case ) = 1.45560223,

MS( Treatment*Reader *Case ) = 0.84380409.

 

Sensitivity Difference = 0.05

Readers	Readers and Cases Random	Cases Random	Readers Random
3	.	.	.
4	.	.	.
5	.	.	.
6	.	1846	.
7	.	1720	.
8	.	1625	.
9	.	1552	.
10	.	1493	.
11	.	1444	.
12	.	1404	.
13	.	1370	.
14	.	1341	.
15	.	1316	.

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

 

Sensitivity Difference = 0.10

Readers	Readers and Cases Random	Cases Random	Readers Random
3	.	684	.
4	.	574	.
5	.	507	.
6	.	463	.
7	.	432	.
8	.	408	.
9	.	390	.
10	.	375	.
11	.	363	.
12	.	353	908
13	1402	344	537
14	1079	337	381
15	899	331	296

 

Sensitivity Difference = 0.20

Readers	Readers and Cases Random	Cases Random	Readers Random
3	.	173	.
4	.	145	.
5	469	129	506
6	252	118	196
7	189	110	122
8	158	104	89
9	140	99	70
10	127	96	58
11	118	93	49
12	111	90	43
13	106	88	38
14	102	86	34
15	98	85	31

 

Cautionary note:  For this data set the estimated required number of cases when only cases are treated as random sometimes considerably exceeds the required number when both cases and readers are treated as random. If the variance components were all known, this would not be possible. It happens here because we are using unbiased estimates of the variance components rather than the true unknown parameter values; in particular, it happens because the treatment-by-reader variance component estimate is negative.  In this situation a conservative approach is to rerun the program with the treatment-by-reader variance component estimate set to zero.  Alternatively, in this situation you may want to consider pooling information from several similar studies, resulting in more precise variance component estimates and hence more precise sample size estimates.  The reader is referred to the Details section of the MRMC Sample Size User's Guide for further information.