Notes on the use and interpretation of radiostereometric analysis.

Derbyshire B, Prescott RJ, Porter ML - Acta Orthop (2009)

Related In: Results  -  Collection

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Figure 0004: (a) The mean direction cannot be determined as the mean of the vector angles from the positive x-axis; here, this would be 100 degrees, but the mean direction should be in the bottom right quadrant. (b) If the angle is measured in positive and negative (clockwise) directions with respect to the positive x-axis, the mean can still not be determined; here, it would be zero degrees, which is incorrect.
Mentions: Some papers (Kiss et al. 1995, 1996, Alfaro-Adrian et al. 1999, 2001, Catani et al. 2005) have included diagrams of a hip stem as viewed from different directions, and a resultant translation vector has been drawn at each of the measurement landmarks. The direction of the resultant has been determined from the mean (or median: Catani et al. 2005) displacement vector component in each of 2 axis directions. Thus, in the x–y plane, when mean values were used, the angle to the x-axis was found by tan-1(mean y / mean x). In addition, the standard errors of the mean x and mean y (or the upper and lower quartiles) have been represented as the major and minor axes of an ellipse drawn at the end of each resultant vector (Figure 2). This method might not provide a good estimate of a representative direction of translation. It would place heavier weight on those prostheses with the largest scalar changes. For example, in Figure 3, the 6-mm vector dominates the direction of the resultant, reducing it to less than 30° to the x-axis. The true mean direction is 40°, i.e. (25 + 50 + 75 + 10) / 4, and the mean scalar magnitude is 3 mm, i.e. (2 + 2 + 2 + 6) / 4. The whole concept of calculating the mean direction has to be used with caution, however. It cannot be used in this simple way when the vectors are spread over a 360° range. The following examples show why this is so. In Figure 4a, 3 vectors are at 10°, 50°, and 240° to the positive x-axis. The mean angle would therefore be 300° / 3, i.e. 100°. This is incorrect; the mean should be in the bottom right quadrant. If the angle of the vector at 240° is calculated in the negative, clockwise direction, i.e. –120°, the mean angle would be –60° / 3, i.e. –20°, which appears to be correct. However, using positive and negative directions like this does not work: the mean angle of the 2 vectors in Figure 4b would be zero, which is clearly incorrect.

Bottom Line: With increasing numbers of research groups carrying out radiostereometric analysis (RSA), it is important to reach a consensus on how the main aspects of the technique should be carried out and how the results should be presented in an appropriate and consistent way.In this collection of guidelines, we identify a number of methodological and reporting issues including: measurement error and precision, migration and migration direction data, and the use of RSA as a screening technique.Alternatives are proposed, and a statistical analysis is presented, from which a sample size of 50 is recommended for screening of newly introduced prostheses.

View Article: PubMed Central - PubMed

Affiliation: Centre for Hip Surgery, Wrightington Hospital, Appley Bridge, UK. Brian.Derbyshire@wwl.nhs.uk

ABSTRACT
With increasing numbers of research groups carrying out radiostereometric analysis (RSA), it is important to reach a consensus on how the main aspects of the technique should be carried out and how the results should be presented in an appropriate and consistent way. In this collection of guidelines, we identify a number of methodological and reporting issues including: measurement error and precision, migration and migration direction data, and the use of RSA as a screening technique. Alternatives are proposed, and a statistical analysis is presented, from which a sample size of 50 is recommended for screening of newly introduced prostheses.

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