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Spirometer PEF (L/min)

Figure 8. The estimated standard deviation of the random within-child variation of meter PEF (when spirometer PEF is stable) over a range of possible values of spirometer PEF

This indicates that, given a stable spirometric peak flow, the within-child variability of portable meter readings increases markedly at high values of s and to a lesser extent at low values (see Figure 8 for a graphical representation). Minimum variability is estimated to occur at V = 316-8 l/min when SD = 29-8 l/min.

Given an estimated overall m:s gradient of p0 (that is, 0-386, Table IV) and given that the estimated level 2 residual for the S/S term in the ith child is v,, the true gradient in the ith child (/?,) may be estimated3'31 as = + v,- and the estimated standard error of this gradient may be obtained as

where <r2(j?0) the squared estimated standard error of the fixed coefficient for S (that is, 0-0882 = 0-0077, Table IV) and <72(v;) is the comparative variance of the relevant residual in the ith child (Goldstein, 1987, page 48).3 Comparative variance for residuals may be obtained directly in MLn30 and by selecting 'RTYPe2' (see Figure 7 step [O]) one obtains comparative variances which have been adjusted for the fact that the random parameters from which they are computed are themselves estimates.3'30 An approximate 95 per cent confidence interval (see Table V) for the estimated gradient in the ith child may then be obtained as

Figure 7 steps [O] and [P] detail the MLn code required to generate child specific gradients, standard errors and 95 per cent confidence intervals. Figure 9 plots the raw data for each child:

Table V. The estimated gradient [and 95 per cent confidence interval] for the relationship between m and s in each individual child, and the estimated magnitude of fall in true PEF that might reasonably be detected with the portable meter despite random within-child variability

Child

Estimated gradient

Mean spirometric Absolute detectable

Percentage

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