This means that the relative standard deviation of the index (i.e.

the SD divided by the mean) is reduced because some “trivial” variation is removed. We develop this principle into a strict design principle. We seek a bone index of the form A/(W a L b ), and we optimise the exponents a and b so as to minimise the Go6983 mouse mean relative SD (MRSD) of the index (the relative SD is the SD divided by the mean). This is the same as removing any linear dependency of the index on L and W. The three classical indices are used to span a triangular search area as shown in Fig. 2. Fig. 2 The triangle spanned by the three classical radiogrammetric bone indices. The W exponent increases in the horizontal direction and the L exponent in the vertical direction. The contours of the mean

relative SDs of the Sjælland study are shown. The smallest value is obtained close to the middle of the triangle, where PBI resides. The 95% this website confidence limit for the optimal index is approximately equal to the 6.66 contour Our method studies a cohort of normal children over a suitable age range, in this BAY 11-7082 solubility dmso case the Sjælland data, encompassing ages 7 through 17. The data are divided into half-year bins of bone age and into gender, and the relative SD is formed for each bin. The relative SD is averaged over all bins to form the MRSD, and the optimal index is Avelestat (AZD9668) the one with the smallest MRSD. A bone index is computed for the three middle metacarpals by computing it for each metacarpal and then averaging. Precision The precision of a bone index measurement is defined as the ability to obtain the same result on a repeated measurement. This could be determined directly by obtaining two X-rays of the hand after replacing the hand on the film cassette for a number of children. However, such a procedure would be unethical, so in this study the precision (in fact an upper limit on the true precision) is instead determined using the retrospective longitudinal

series of X-rays in the Seiiku study. Consider a triplet of measurements PBI1, PBI2 and PBI3 taken at 6-month intervals, assume that Paediatric Bone Index (PBI) grows linearly over the time span of the triplet, and define the interpolation residual e as2 $$ e = \textPB\textI_\text2 – \left( \textPB\textI_\text1 + \textPB\textI_\text3 \right)/\text2 $$ The precision error p on a single determination can then be derived from a set of observations of e as $$ p = \textrms(e)/\sqrt 1.5 $$where rms denotes the root of the mean of the squares. The assumption of linear PBI evolution over the period of the three measurements is in general not exactly true, and any deviation from linearity will add a contribution to rms(e). As a consequence, this precision estimate is an upper limit on the true precision.