A step-by-step regressed pediatric kidney depth formula validated by a reasonable index

In predicting pediatric kidney depth, we are especially interested in that the errors of most estimates are within a narrow range. Therefore, this study was intended to use the proportion of estimates within a range of −5 to 5 mm (P5 mm) to evaluate the formulas and tried to regress a kidney depth formula for children. The enrolled children aged from 1 to 19 years were randomly sampled into group A and group B (75% and 25% of all recruits, respectively). Using data of the group A, the test formula was regressed by nonlinear regression and subsequently Passing & Bablok regression, and validated in group B. The Raynaud, Gordon, Tonnesen, Taylor, and the test formulas were evaluated in the 2 groups. Accuracy was evaluated by bias, absolute bias, and P5 mm; and precision was evaluated by correlation coefficient. In addition, root-mean square error was used as a mixed index for both accuracy and precision. Body weight, height, and age did not have significant differences between the 2 groups. In the nonlinear regression, coefficients of the formula (kidney depth = a × weight/height + b × age) from group A were in narrower 95% confidence intervals. After the Passing & Bablok regression, biases of left and right kidney estimates were significantly decreased. In the evaluation of formulas, the test formula was obviously better than other formulas mentioned above, and P5 mm for left and right kidneys was about 60%. Among children younger than 10 years, P5 mm was even more than 70% for left and right kidney depths. To predict pediatric kidney depth, accuracy and precision of a step-by-step regressed formula were better than the 4 “standard” formulas.