Abstract
Background
This study aimed to determine the differences arising form indexing a measured physiological variable by using different body surface area (BSA) estimation formulae.
Methods
The studied variables were the overall measured peritoneal creatinine clearance plus residual renal clearances (MeasCtCl) of 19 men and 23 women in a stable condition who were undergoing peritoneal dialysis and were a mean 55.7 ± 15.8 and 55.1 ± 14.1 years of age, respectively. The patients had comparable body mass indexes (BMIs; 25.01 ± 4.14 in men and 24.5 ± 3.46 in women). The MeasCtCls were indexed to 1.73 m2 using 5 formulae: by Du Bois, Boyd, Mosteller, Livingston and Yu. The numerical and percentage differences between the MeasCtCl values and each approach to indexation were calculated, as well as the differences between the indexations. Paired t-test and similarity percentage test were used to evaluate the significance of the differences.
Results
The impossibility of adequately comparing data indexed according to different BSA estimation formulae was shown, documenting a high risk of erroneous evaluations and conclusions.
Conclusions
Some methods to avoid these errors in clinical applications are suggested, as well as the possibility of indexing only to height.
Introduction
Studies reported in the literature (1–9) have demonstrated the problems due to the use of body surface area (BSA) in indexing many physiological functions. BSA has been used to index the glomerular filtration rate (GFR) since 1928 (10), and at present, weekly peritoneal dialysis schedules. Recently BSA has been proposed for rescaling extracorporeal dialysis (11, 12).
This model of indexation may induce methodological mistakes, and as a result, erroneous conclusions may occur on the actual significance of the differences between data when the indexations have been based on different formulae for the estimation of BSA. Errors can result even with formulae based on the same structure, such as BSA = constant × heightA × weightB, which is the most common form of these equations, and even when the heights and weights are similar among the populations compared, as has been theoretically analyzed and demonstrated in previous papers (5–7, 9). The aim of this study was to determine if significant differences can result between the indexations of the same measured values of creatinine clearance in real populations, in applying to their heights and weights different formulae for BSA estimation.
Methods
This study was based on the registered data of 42 patients who were undergoing peritoneal dialysis (23 women and 19 men). These patients were selected out of 75 patients because they were in a more stable and satisfactory condition at the time of data registration, compared with the remaining 33 subjects. The following baseline data were obtained: age, height, weight, overall measured peritoneal creatinine clearance plus residual renal clearances (MeasCtCl), and the derived variable of MeasCtCl per height in centimeters. The descriptive statistics for the variables are shown in Table I. No significant differences were observed between the men and women regarding age (mean 55.7 ± 15.8 years vs. 55.1 ± 14.1 years, t = 0.13, p = 0.900) and body mass index (BMI; 25.01 ± 4.14 vs. 24.5 ± 3.46, t = 0.41, p = 0.684). A comparison of MeasCtCl values between the 2 sexes resulted in a significant difference, as expected (86.6 ± 9.8 L/week vs. 63.1 ± 4.3 L/week, t = −27, 13%, p = 0.000); however, indexing these values to height (MeasCtCl/cm), the difference in the means (-21.4%) was not statistically significant (0.504 ± 0.234 L/cm in men vs. 0.396 ± 0.126 L/cm in women, t = 1.80, p = 0.083). Therefore, men and women had similar MeasCtCl based on height. The indexation of the MeasCtCl values to BMI for men and women showed similar results; however, the p value was very close to be of no significant value (t = −2.04, p = 0.052). This seems to indicate that the creatinine generation rate and clearance rate were more correlated to the height than to the body mass.
Baseline data
BMI = body mass index; CV = coefficient of variation; MeasCtCl = overall measured peritoneal creatinine clearance plus residual renal clearances; SD = standard deviation; SEM = standard error of the mean.
Formulae for BSA estimation
MeasCtCl values were indexed to 1.73 m2 according to 5 formulae for BSA estimation based on height and weight. The formulae were selected because of their frequent use according to the literature: (i) Du Bois and Du Bois, from 1916 (13): the first formula based on measured BSA and on a mathematical BSA estimation. This formula is still widely used, even though proposed 97 years ago. Formula: 0.007184 × height0.725 × weight0.425, (ii) Boyd, from 1935 (14): formula: 0.01787 × height0.5 × weight0.4938. (iii) Mosteller, 1987 (15): formula: [(height × weight)/3,600]0.5, where height is in centimeters and weight in kilograms, (iv) Livingston and Lee, 2001 (16): formula: 0.0495 × height0.2061 × weight0.6046, (v) Yu et al, 2010 (17): formula: 0.00713989 × height0.7437 × weight0.4040. All of these formulae result in a BSA estimate expressed in meters squared. Table II shows the MeasCtCl values and the 5 indexations according to the BSA estimation formulae.
Measured CtCl/week values and measured CtCl/week values indexed for 1.73 m2 based on different formulae
CtCl = creatinine clearance; CV = coefficient of variation; SD = standard deviation.
Analysis of the differences
A statistical analysis of the numerical and percentage differences between MeasCtCl values and IndexCtCl values was performed for the men and women. Additionally a statistical analysis of the differences between the 5 indexations was performed.
A t-test for paired data: the normal distribution of the differences was determined using the Anderson-Darling test.
A similarity percentage test was used to compare the similarity between IndexCtCl values. Assuming A as the base value, and B as the value compared with A, the similarity between A and B was evaluated according to: {[(A + B)/2]/A} × 100, and appreciated in terms of percentage value. With 100% as the full similarity between the items of 2 compared IndexCtCl or between their percentage differences, the mean size of the differences can also be evaluated by the degree of their dissimilarity, whose value is 100 minus the mean of the similarities of all of the considered items.
The statistical graphical test empirical cumulative distribution function (empirical CDF) was used to evaluate the reciprocal agreement of the 5 IndexCtCl values. This test is applied to each sample, plotting the value of each observation versus the percentage of the remaining ones having the same or lower values, therefore fitting a cumulative distribution of the values, each value having a corresponding percentile value. Assuming a reference percentile point (generally the 87th percentile by default or a different one selected by the researcher), it is possible to ascertain if the samples should present or not the same values at the 87th percentile of their distribution, and consequently the existence of differences and their size.
The calculations and statistical analysis of the data were performed using the statistical software MINITAB 15 (Minitab Statistical Software; MINITAB Inc., State College, PA, USA).
Results
Table III shows the statistics of the numerical and percentage differences between MeasCtCl and each indexation.
Numerical and percentage differences between MeasCtCl and each indexation approach
CV = coefficient of variation; MeasCtCl = overall measured peritoneal creatinine clearance plus residual renal clearances; SD = standard deviation.
Table IV shows the results of the comparison of each MeasCtCl indexation with each of the other indexations according to the formula used. The last column on the right side shows the values of the average dissimilarity between the items of the indexations. These data were found to be highly correlated with t-test values, with a negative correlation, the lower the dissimilarity, the greater the t-test value, according to their sign (+ or -). A linear regression of paired t-test values on 100% minus the mean of the similarities (men: R = 0.841, R 2 = 0.708, p = 0.0023, correlation = −0.841; women: R = 0.883, R 2 = 0.779, p = 0.000, correlation = −0.883.
Comparison of each MeasCtCl indexation with each of the other indexations according to the formula used
MeasCtCl = overall measured peritoneal creatinine clearance plus residual renal clearances; SD = standard deviation.
The results in Tables IV and V show that the only comparable indexations in men are those from Du Bois versus Yu, and Mosteller versus Yu, and that where a significant difference was not attained, the dissimilarity level suggests the unsuitability of using any of the 2 indexations. The results for the women show a full heterogeneity within the 5 indexations and even the levels of the dissimilarity do not attain values greater than 5%, having 100 – average similarities quite low (-0.93, 2.87; see Tab. V).
Comparison of percentage differences between MeasCtCl and each indexation by each indexation versus others
MeasCtCl = overall measured peritoneal creatinine clearance plus residual renal clearances; SD = standard deviation.
Empirical CDF test
The figures show the results obtained applying the empirical CDF to the percentage differences between each pair of indexations. It is possible to note in the graphical representations for men as well as for women (Figs. 1 and 2) that the values corresponding to the 87th percentile are different each other, with the only exception those for women in the pair Du Bois versus Mosteller (value of 101) and Du Bois versus Yu (value of 103), corresponding to their low levels of dissimilarities in the tables above.
Empirical cumulative distribution function test for men, of the similarities between the percentage differences of measured creatinine clearance (CtCl) and the indexed CtCl, according to the different indexations used.
Empirical cumulative distribution function test for women, of the similarities between the percentage differences of measured creatinine clearance (CtCl) and the indexed CtCl, according to the different indexations used.
The differences within the indexations have so far been analyzed comparing the data concerning all patients (men, n = 19; women, n = 23). A different method can be followed, by analyzing the differences of the indexations concerning each single patient, by calculating for each patient, the overall basic statistics of his/her different IndexCtCl: mean, standard deviation, coefficient of variation, minimum and maximum values, their percentage differences and the skewness. The data obtained are shown in Table VI.
Data of individual patients
In Table VI it can be noted that: (i) The coefficient of variation within the indexations had high values: 1.73–4.64 for men and 1.82–4.18 for women, with a mean overall for the patients of 2.42 and 2.58, respectively, (ii) The overall mean of the differences is 5.42% ± 2.34% for men, and 5.57% ± 1.257% are larger than 4.5% in 14/19 men and in 19/23 women. These differences show that to use either indifferently indexation is problematic, something that is also shown by the high coefficient of variation within the different indexations, assuming that the coefficient of variation is considered to have moderate value when between 0.05 and 0.15.
Discussion
The results of the study clearly show that the values of CtCl/week indexed according to different formulae for BSA estimation are quite different from each other, possibly resulting in clinical and scientifically misconstrued appreciation of the actual differences. These errors will be more significant and more frequent when the weights are out of proportion to the height, while the differences among the different indexations will be negligible when the weights are in the normal range with respect to the corresponding heights of the populations studied. Fluid retention, abnormally increased fat mass and/or loss of muscle mass is very frequent in renal patients undergoing dialytic treatment as well as in patients affected by renal diseases even with normal GFR. Consequently this kind of error will be frequent in clinical nephrology due to disproportionate weight.
One way to overcome these errors is that any paper or database showing indexed data should report the formula by which indexation was performed. From this, different researchers could correctly compare their data, simply by indexing them with the formula used by the other researcher. At present only a very few publications report the BSA formula used to index the published data. Indeed, the researchers should let the others know their measured not their indexed data – a collaboration that is possible but not always available. A second way is to use the measure of fractional urea clearance (Kt/V) instead of creatinine clearance, because Kt/V avoids the need for indexation. This measure is at present often assumed to evaluate the extent and adequacy of peritoneal dialysis treatment instead of creatinine clearance, but it also leads to an exposure to a risk of errors based on (i) the fact that estimates of total body water (TBW) are usually performed using the equations of Watson et al (17). These were determined by selecting a population of healthy volunteers and of unwell patients without any cause for, or sign of, modified hydration, whose measures of TBW by isotopes or dilution systems were regressed versus their heights and weights. Consequently the use of these equations in people who are overweight due to excess body water or fat mass or both – as in the case of patients undergoing peritoneal dialysis or who are affected by some renal disease causing edema – should be considered unsuitable because beyond the relationship of weight/height on which the equations were based, there is a resulting overestimation of water, (ii) The water prediction by the Watson formulae has to be considered of limited power (R 2 = 70.4% for males and R 2 = 73.6% for females), consequently, in any patient, the Watson TBW should be considered an approximation of the actual TBW rather than its correct measure.
The variable to use for indexing measurements of dialytic treatments or of GFR should not show significant changes over time, and it should have a rational correlation with the lean body mass (muscle mass), a correlation absent using BSA and present using Kt/V if a correct measure of V is used. These characteristics are peculiar to height, which changes very slowly over the years by a few centimeters from youth to old age (18). The clearances of creatinine studied in this paper were better correlated to height than to BMI. In a personal pilot study, the results of which are not yet published and at present are subjected to further evaluation on a larger population, indexation for height gave a very much better approximation to the measured data than the indexation for BSA according to 5 different BSA formulae. This means that indexation for height allows for a comparison between the measured data without significant and different modifications of their values, completely avoiding the differences shown above. Using this method, the indexed GFR or dialytic clearances are expressed in milliliters or liters per minute per height in centimeters. The proposed method could be considered for indexing renal functions or dialysis measures or other physiological functions at present indexed for BSA.
The similarity percentage test better reveals the relevance of the differences between different indexations than the results of paired t-tests. The similarity test weighs the equality of each couple of indexations by comparing their sizes in percentage terms, and a difference greater than 5% should suggest that any of the compared indexations should not be used. The differences as such are better represented and more easily perceptible by the empirical CDF. The significant inverse correlations of the dissimilarity values with the t-test values emphasize these results, given that the similarity test is able to predict the significance of the statistical comparison between 2 groups of data. Further confirmation is obtained by the analysis of the 5 indexed CtCl according to each patient (Tab. VI). The main implication in the clinic is that the indexations will be different even when the formulae have been applied to the same subjects, – i.e., based on the same heights and weights. It was stressed that the use of Kt/V instead of creatinine clearance avoids the indexations but not other forms of errors, and that Watson's formulae can be applied only in subjects with a normal body composition. The comparison of data indexed by different formulae was possible in any case using their reindexation, but this method does not allow any kind of comparison. The choice of a new method of indexation would have grounds for interest, but its application would need new normality ranges for each physiological function previously indexed to 1.73 BSA, a problem that the scientific community prefers to consider negligible by ignoring the many published alerts about the errors generated by the indexation to BSA.
Conclusions
This study showed that the differences existing between indexations based on different formulae for BSA estimation even applied to the same subjects attained statistical significance and large numerical sizes as highlighted by the similarity percentage test. Comparison of the data for 2 populations with different distributions of height and weight and indexed on the basis of 2 different formulae will attain greater risks of misconstruction depending on the differences in anthropometric measures of the populations on which the formulae have been built and of the populations to be compared. Indexing all of the original measured data on the same formula could decrease the risk of error, possibly, using a formula based on ranges of height and weight, the closest possible to the same ranges of the populations undergoing the comparison. Some ways to avoid these errors when comparing data indexed using different formulae are suggested, but the best solution is certainly to select a different variable to index, which is not subjected to change over time and not causing differences between the indexations. In this paper, it was suggested that this might possibly be patients' height.
Footnotes
Abbreviations and statistics definitions
No grants or funding have been received for this study.
Conflict of interest: The author has no financial interest related to this study to disclose.