Evaluating sequential values using time-adjusted biological variation.
One can compare the difference between two sequential values with the biological variation. Biological variation is a measure of the random disturbances of an analyte's value, measured at different times. When the difference > Z square root 2 SD(BV) then the difference is due to an underlying disease process or physiologic change. A Z value of 1.96 yields a 95% confidence limit. When using multiple sequential values or time periods exceeding that for the empirically derived biological variance, a random walk model allows one to estimate the spread of the variance. For a difference, (delta) to be significant, delta > Z square root 2n SD(BV), where n is the ratio of time reflecting the longer time period divided by the shorter time period. Not all variances grow to this degree over time, because restoring forces diminish the extent of random disturbances. The relationship between a biological variance measured over a longer time period to the one measured over a shorter period can be expressed in terms of this restoring force as SD2 BV,n = SD2 BV,1 sigma(n) j=1 e(-2)(j-1)phi, where n is the ratio of time periods. One can calculate phi using this formula and a spreadsheet. From phi one can calculate the biological variance for any time period, within experimental limits, and compare the difference in sequential values with it. Test intervals can be calculated based on these biological variances.
Kroll
Martin H
MH
Dallas VA Medical Center, TX 75216, USA. Martin.Kroll@med.va.gov
D000704:Analysis of Variance; D000818:Animals; D019295:Computational Biology / Q000379:methods; D006801:Humans; D015233:Models, Statistical; D011897:Random Allocation; D012107:Research Design; D013995:Time