## Getting coefficient of variation and the power in the Box-Cox transformation

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# Getting coefficient of variation and the power in the Box-Cox transformation

[ Edited ]

This is slightly more in the realm of math questions than SAS, but maybe someone can help me figure out how to use SAS to compute it:

The CDC publishes US infant growth charts for weight and length -- complete with percentile, z-scores, and "LMS parameters: the median (M), the generalized coefficient of variation (S), and the power in the Box-Cox transformation (L)" to allow us to calculate our own percentiles from weight and length. The chart starts at birth.

However, I want these percentiles from BEFORE birth. The WHO just published these values for expected fetal weight at different gestational ages.

These percentiles (5th, 10th, 25th, etc.) aren't good enough for me. I need a much more granular percentile -- i.e. I need the L, M, and S values so that I can calculate my own percentile from birthweight data.

Any idea how to get those LMS values from the above table? The authors don't publish them. Do I need to contact them for raw data? That might take forever...

Thanks SO much!

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Solution
‎05-11-2018 04:46 PM
Occasional Contributor
Posts: 17

## Re: Getting coefficient of variation and the power in the Box-Cox transformation

Well, I think I found the answer to my own question:

LMS values (measures of skew, the median, and the standard deviation) were computed from the interpolated cubic splines at weekly intervals. Cole’s procedures and an iterative least squares method were used to derive the LMS parameters (L = Box-Cox power, M = median, S = coefficient of variation) from the multicentre meta-analyses for weight, head circumference and length. The LMS splines were smoothed slightly while maintaining data integrity as noted above.

Cole TJ, Green PJ: Smoothing reference centile curves: the LMS method and penalized likelihood. Stat Med. 1992, 11: 1305-1319. 10.1002/sim.4780111005.

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Solution
‎05-11-2018 04:46 PM
Occasional Contributor
Posts: 17

## Re: Getting coefficient of variation and the power in the Box-Cox transformation

Well, I think I found the answer to my own question:

LMS values (measures of skew, the median, and the standard deviation) were computed from the interpolated cubic splines at weekly intervals. Cole’s procedures and an iterative least squares method were used to derive the LMS parameters (L = Box-Cox power, M = median, S = coefficient of variation) from the multicentre meta-analyses for weight, head circumference and length. The LMS splines were smoothed slightly while maintaining data integrity as noted above.

Cole TJ, Green PJ: Smoothing reference centile curves: the LMS method and penalized likelihood. Stat Med. 1992, 11: 1305-1319. 10.1002/sim.4780111005.

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