The new teehnique was used to identify the region of interest on the heel on which to position the transducers. The transducers in the CUBA are normally in a fixed position housed within a hard plastic positioning device. To place the transducers on the new centring point previously developed the foot is positioned and immobilised with foam pads. The aim of this experiment is to measure the precision of the new technique in clinical practice and to assess whether it can be improved by removing the transducers from the plastic surrounding of the machine onto a handheld calliper device. The ultrasound transducers (12.5mm diameter) are shown on the handheld callipers in figure 9. The null hypothesis is that the precision of the BUA measurements with the transducers in the fixed position within the plastic positioning device will on average be the same as the precision of the BUA measurements with the transducers placed on a handheld calliper device.
F igure 9 U ltrasound tran sd ucers placed on handheld callipers
'aJi E â Jus
M eth o d sPaired measurements of BUA on 50 children, obtained with the transducers in the standard fixed location in the CUBA were analysed and compared to paired measurements of BUA on 50 children, obtained with the transducers placed on a handheld calliper device. The children were randomly assigned to each group and all paired measurements for each child were performed on the same day with re positioning between.
Chapter 7 The precision and accuracy o f CUBA
The precision was calculated using equation 9 on page 70 to measure the root mean square standard deviation (RMS SD) of these two sets of paired measurements. The coefficient of variation was used as a measure of relative precision error and was calculated using equation 10 (page 71). The standardised coefficient of variation was also measured by replacing the mean with the range of values as the denominator in equation 10. The null hypothesis was tested using the independent samples t test on the BUA values.
Results
The results of the mean and standard deviation of age, mean and range of BUA and precision measurements of the two groups of children are shown in table 13.
Table 13 Assessment of precision error in clinical practice Parameter measured Transducers fixed
within plastic casing of CUBA
Transducers on a handheld calliper device Mean age of group (years) 12.83 (SD 2.94) 11.37 (SD 3.05)
RMS SD (dB.MHz^) 6.05 6.02 BUA range (dB.MHz^) scan 87.00 82.60 BUA range (dB.MHz^) 2"^ scan 85.00 88.55 Mean range (dB.MHz^) 86.00 85.58 Mean BUA (dB.MHz^) & 2"^ scans together
36.23 47.21
Coefficient of variation (%) 16.70 12.75
Standardised coefficient of variation (%)
7.03 7.03
As shown in the table the RMS SD precision error was not significantly different for paired BUA measurements whether in the fixed position within the CUBA or on the handheld callipers. The relative precision error calculated using the coefficient of variation improved from 16.70% for paired measurements obtained using fixed callipers to 12.75% for paired measurements obtained using the handheld callipers. However the relative precision error calculated using the standardised coefficient of variation was 7.03% for BUA measurements obtained with transducers either fixed in position or on handheld callipers.
The mean difference of paired BUA measurements obtained with the transducers in the plastic housing was -0.29 dB.MHz'^ and when the transducers were on handheld callipers it was -2.66 dB.MHz \ The 95% confidence interval (-0.96 to +5.71) for the mean difference in dB.MHz^ of the two sets of paired BUA measurements contained zero confirming the null hypothesis (p<0.16), that there is no statistically significant difference in precision when the transducers are moved onto the handheld callipers.
Discussion
The precision of BUA when measured on the CUBA in children aged between 6 and 18 years is reported as 5% ([MUGH1996], [WILM1996], [MUGH1997]). In comparison Jaworski et al quote a precision of 1.5% for BUA in children when scanned with the Lunar Achilles [JAW01995]. Sundberg et al [SUND1998] do not quote the coefficient of variation for BUA used in their paediatric study using the Lunar Achilles. Schonau et al [SCH01994] and Lappe et al [LAPP1995] measured the speed of sound rather than the BUA in healthy children.
In this study the relative precision error of the new technique at 12.75% for CV and 7.03% for standardised CV is poor compared to previous paediatric publications using the same equipment. It was however measured systematically and precisely using the root mean square standard deviation of 50 randomly assigned paired measurements. In comparison it is not clear in each of the three CUBA papers referenced above exactly how the researchers measured the coefficient of variation in children. The authors merely state what the CV is for children aged between 6 and 18 years but do not outline the methodology used. One would assume that if the root mean square standard deviation of paired measurements had been used to calculate the coefficient of variation this would have been stated. Nor do Jaworski et al state how CV was measured in their study but they do mention that 27 children were scanned twice on one day. However the 27 children were then divided into three groups to assess the effect on CV of three different ultrasound measuring techniques. If the arithmetic mean of several CV values was used as the relative precision error in these paediatric papers this may have led to the lower CV values than are reported in this study. It is recognised that the arithmetic mean of several values of CV to calculate the overall CV of a sample will underestimate the true precision error by up
C hapter7 The precision and accuracy o f CUBA
to 25% for duplicate measurements [GLUE1995]. Also the BUA scale used in the Lunar Achilles is such that it is likely to produce a higher mean value for children, though a lower range than that obtained with the McCue CUBA. For example the dynamic range of BUA measured on the CUBA Clinical used in this research is 86 dB.MHz^ compared to the Lunar Achilles which in the paediatric study by Jaworski et al [JAW01995] has a dynamic range of only 21 dB.MHz \ The corollary being that the larger the BUA range used as the denominator in the standardised CV calculation the lower the value of standardised CV. This larger measurement range for CUBA also suggests that it has increased sensitivity compared to the Achilles because for the same time-span between scans BUA measured by CUBA will increase by a greater amount than that measured by the Achilles.
As demonstrated in the results in table 13 when the CV was calculated for the two techniques (root mean square standard deviation divided by the mean and converted to a percentage) the numerator of the CV equation was the same but the denominator was different. This made a significant impact on the resultant CV measurement. In these data this led to a higher CV for BUA measurements with the transducers fixed into the plastic housing of the CUBA leading to the erroneous conclusion that BUA is more precise when the transducers are mounted onto a handheld calliper. However when the standardised CV was measured the results demonstrate that there is no improvement in relative precision error when the callipers are removed from the plastic housing of the CUBA machine, which is confirmed with the independent samples t test.
When the RMS SD is used as a measure of the precision error the values are in absolute units rather than percentages. The RMS SD calculated in this chapter was 6.02dB.MHz'^ and it can be used as a tool to identify significant changes in BUA when the children are scanned after one year. It is particularly useful because it is not calculated as a proportion of the original BUA value which, in children, may be in single figures and therefore lead to a poor precision error measured as CV or SCV.
It is also noteworthy that the mean differences of the two sets of measurements in these data were negative, suggesting that the second scans produced higher BUA values than the first scans. This effect was amplified when the transducers were
placed on handheld callipers. On examination of these children during the procedure it was noted that the ultrasound transducers left a small imprint on both sides of the heel after the scan because of compression of overlying tissue. This effect was investigated further by performing ten sequential scans in vivo on ten volunteers. It was noted that in each subject sequential BUA values increased in magnitude, and this was associated with a reduction in heel width as overlying skin was compressed during the scan. It was therefore assumed that the greater difference in BUA measurements seen with the transducers in the handheld callipers arises because the transducers can more accurately be located over exactly the same region of interest for the second scan and therefore over the previously compressed area of subcutaneous tissue. In comparison this is more difficult to do when the transducers are located within the plastic housing of the CUBA.
It was postulated that the ability of the new technique to reproducibly position the transducers over the region of interest in the calcaneum was limited by the difficulty in precisely positioning children’s feet in relation to fixed transducers within the plastic housing of the CUBA. Therefore it was hypothesised that more precise positioning of the callipers over the region of interest on the heel would be possible by placing the transducers onto handheld callipers. Although it was physically easier for the operator to position the foot using the handheld calliper device the precision results confirm that there was no statistically significant improvement in precision error when the machine was adapted to locate the new centring point.
Conclusion
In summary a change in technique improved the accuracy of measuring the correct region of the calcaneum. Adapting the equipment to allow easier positioning of the transducers over the region of interest on the heel using the new technique appeared to improve the relative precision error from 16.70% to 12.75% when the coefficient of variation was calculated. However the relative precision error calculated using the standardised CV was 7.03% both before and after adaptation of the equipment.
These results demonstrate that if relative precision error is measured it is more appropriate to use the standardised coefficient of variation (7.03% in this study) rather than the coefficient of variation as this more accurately reflects the
Chapter 7 The precision and accuracy o f CUBA
reproducibility of the equipment and the technique. The root mean square standard deviation of paired measurements of BUA (6.02dB.MHz‘^ in this study) is an alternative useful method of reporting the precision of the ultrasound technique.
The independent samples t test confirmed the null hypothesis that there was no improvement in precision by adapting the equipment, although the operator did find the handheld callipers easier to use.