At Rikshospitalet, the working group had three members, Johan Kofstad, Ari Lahti, and Lars Mørkrid, and the tests to be assessed were calcium (Ca), potassium (K), magnesium (Mg), sodium (Na), and inorganic phosphate (Pi).

The properties of the distributions were checked by using the UNIVARIATE procedure of the SAS 8.2 program, but we run the RefVal 4.0 program in parallel, not only for comparison but also because the UNIVARIATE procedure does not seem to offer calculation of confidence intervals for nonstandard percentiles, such as 2.5 and 97.5, whereas the RefVal program readily calculates confidence intervals of desired level for any percentiles. However, because the data material is relatively large in this project (the smallest subgroup in our study was composed of 558 reference values), the statistical quality of the reference limits is not an important concern. Therefore, we will not consider confidence intervals in this presentation, but refer to the enclosed output files for more detailed description of these intervals.

In what follows, we will outline the main results obtained for each electrolyte, documented in the output files "SAS8.2_UNIVARIATE.rtf" and "RefVal4.0.rtf". The statistical analyses were carried out in the same order as the electrolytes are listed above. The variable "reskorr" (=corrected result) in the output files denotes the final, calibration-adjusted data for the electrolyte in question.

Calcium (Ca)

The distribution of S-Ca looks symmetrical but it is not gaussian according to the tests for normality. The distribution is not even transformable to a gaussian distribution by using the transformation procedure implemented in the RefVal program and described by Solberg¹. Hence, non-parametric reference limits seem to be more reliable than the parametric ones.

Assessed visually, there should be no outliers. The Dixon’s method for outlier detection, as implemented in the RefVal program, did not identify any outliers, either. This method consists of considering the distance between the two most extreme reference values and classifying the most extreme reference value as an outlier if this distance exceeds one third of the range of the reference values. However, it may fail if the two (or more) most extreme reference values lie close to each other but far from the rest of the data. Problematic cases for the Dixon’s method may also be non-gaussian distributions with very long tails, as demonstrated by data obtained for some enzymes in this project.

Recently, a robust method for outlier detection was described² that probably could be more successful than the Dixon’s method in handling such problematic situations. In this new method, the distribution is first transformed to a gaussian distribution or to a distribution close to a gaussian distribution by using the Box-Cox transformation. The distance between the 25 and the 75 percentiles is calculated (Q3-Q1), and the detection limits for outliers ("Tukey fences") are defined as the 25 percentile minus 1.5*(Q3-Q1) and the 75 percentile plus 1.5*(Q3-Q1). Because the measuring unit for the detection limits, or the distance Q3-Q1, is thereby determined using only the central part of the distribution, this method avoids the interference of the outliers themselves on the criteria to define them, which is the drawback of most of the existing methods for detection of outliers. However, because the distributions of electrolytes seemed to be rather unproblematic as far as outliers are concerned, we considered the Dixon’s method satisfactory for our purposes.

The nonparametric percentiles suggested by SAS 8.2 were as follows (mmol/L):

The RefVal program calculated exactly the same 2.5 and 97.5 percentiles, i.e. 2.17 and 2.51, respectively. Our results deviate thereby slightly from the suggestions of NORIP that are 2.16 and 2.50, respectively (www.furst.no/norip on March 20, 2003).

Suggested reference interval for serum total calcium: 2.17 – 2.51 mmol/L

Comparing the suggested reference interval with literature findings and existing reference limits for serum total Ca in Scandinavian laboratories (cf. "Existing_RIs_for_electrolytes.doc"), it seems that the suggested upper reference limit is slightly (0.1-0.15 mmol/L) lower than one is used to. This means that if the suggested upper limit were accepted as a new decision limit for hypercalcemia, the clinicians would have to consider hypercalcemic quite many patients who would be classified as normocalcemic today.

We feel us incompetent to decide whether the new upper reference limit is appropriate for a decision limit, because we cannot easily think of alterations on the population level in Ca metabolism that could explain such a decrease in the average concentrations of total S-Ca. The only thing we can say is that 97.5% of healthy adults in the Northern countries seem to have a serum total Ca today that lies below 2.51 mmol/L.

One possible explanation for the discrepancy between the results of this project and the existing reference intervals is that in this project one has strongly recommended the laboratories to take the blood samples without using the tourniquet. The tourniquet is known³ (we regret for Swedish in this reference) to be able to increase the total Ca levels up to 0.2-0.3 mmol/L. Whether this is a true explanation or not, one should obviously keep in mind, when applying the suggested reference interval, that the blood samples of patients should also preferably be taken without tourniquet.

The distribution of S-K looks symmetrical but it is not gaussian according to the tests for normality. The distribution is not transformable to a gaussian distribution by using the transformation procedure of the RefVal program. Hence, non-parametric reference limits seem to be more reliable than the parametric ones. Assessed visually, there should be no outliers, and neither did the Dixon’s method for outlier detection, as implemented in the RefVal program, identify any outliers.

The nonparametric percentiles suggested by SAS 8.2 were as follows (mmol/L):

The RefVal program calculated the same 2.5 and 97.5 percentiles, i.e. 3.60 and 4.59, respectively. Rounded to one decimal, our results are thereby equal to the suggestions of NORIP (www.furst.no/norip on March 20, 2003).

Suggested reference interval for serum potassium: 3.6 – 4.6 mmol/L

Comparing the suggested reference interval with literature findings and existing reference limits for S-K in Scandinavian laboratories (cf."Existing_RIs_for_electrolytes.doc"), it seems that the suggested upper reference limit is considerably (perhaps 0.4 mmol/L) lower than one is used to. We have no good explanation for why this should be so. Possibly has the delay between coagulation and centrifugation of the samples been shorter in this project than usually is the case, reducing leakage of potassium from red blood corpuscles. Again, we wish to remind that no matter what the clinical consequences will be, it seems to be a fact that 97.5% of healthy adults in the Northern countries have S-K levels today that lie below 4.6 mmol/L.

The distribution of S-Mg looks symmetrical but it is not gaussian according to the tests for normality. The distribution is not transformable to a gaussian distribution by using the transformation procedure of the RefVal program. Hence, non-parametric reference limits seem to be more reliable than the parametric ones. Assessed visually, there should be no outliers, and neither did the Dixon’s method for outlier detection, as implemented in the RefVal program, identify any outliers.

The nonparametric percentiles suggested by SAS 8.2 were as follows (mmol/L):

The RefVal program calculated the same 2.5 and 97.5 percentiles, i.e. 0.72 and 0.95, respectively. Our results deviate thereby slightly from the suggestions of NORIP that are 0.71 and 0.94, respectively (www.furst.no/norip on March 20, 2003).

Suggested reference interval for serum magnesium: 0.72 – 0.95 mmol/L

Comparing the suggested reference interval with literature findings and existing reference limits for S-Mg in Scandinavian laboratories (cf."Existing_RIs_for_electrolytes.doc"), it seems that the suggested reference interval is rather similar to the previous ones.

The distribution of S-Na looks symmetrical but it is not gaussian according to the tests for normality. The distribution is not transformable to a gaussian distribution by using the transformation procedure of the RefVal program. Hence, non-parametric reference limits seem to be more reliable than the parametric ones. Assessed visually, there should be no outliers, and neither did the Dixon’s method for outlier detection, as implemented in the RefVal program, identify any outliers.

The nonparametric percentiles suggested by SAS 8.2 were as follows (mmol/L):

The RefVal program calculated the same 2.5 and 97.5 percentiles, i.e. 136.94 and 145.12, respectively. Rounded to integers, our results are equal to the suggestions of NORIP (www.furst.no/norip on March 20, 2003).

Suggested reference interval for serum sodium: 137 – 145 mmol/L

Comparing the suggested reference interval with literature findings and existing reference limits for S-Na in Scandinavian laboratories (cf."Existing_RIs_for_electrolytes.doc"), it seems that the suggested reference interval is slightly narrower (1 mmol/L at both ends of the interval) than typical reference intervals for S-Na today.

The distribution of S-Pi looks symmetrical but it is not gaussian according to the tests for normality. The distribution is transformable to a gaussian distribution by using the transformation procedure of the RefVal program. Hence, parametric reference limits are available, but they are exactly the same as the non-parametric ones, as calculated by the RefVal program. Assessed visually, there should be no outliers, and neither did the Dixon’s method for outlier detection, as implemented in the RefVal program, identify any outliers.

The nonparametric percentiles suggested by SAS 8.2 were as follows (mmol/L):

The RefVal program calculated the same 2.5 and 97.5 percentiles, i.e. 0.79 and 1.51, respectively. The lower limit is the same as suggested by NORIP, but as far as the upper limit is concerned, NORIP seems to be suggesting partitioning at the age of 30 years, the upper limit being 1.63 mmol/L for those < 30 years and 1.44 mmol/L for those >= 30 years (www.furst.no/norip on March 20, 2003).

To study this issue further, we performed ordinary linear regression on the phosphate data, using the REG procedure of the SAS 8.2 program. The data points together with a first order linear regression curve are plotted in figure "Regression_pi_all.gif". Taken into consideration only these data, i.e.not observing the behavior of Pi as a correlate of age in the younger age groups, we find it hard to regard the age of 30 years as appropriate for partitioning. There seems to be a rather steady decrease of the phosphate levels with increasing age throughout the age range. The choice of a particular age for partitioning is in our opinion more or less arbitrary, and being so, we would prefer the age of 50 years because it lies roughly in the middle of the age range.

However, testing the age groups with those < 50 years and those >= 50 years against each other as possible subgroups of the phosphate data by using recently suggested proportion criteria for subgrouping⁴, saying that at least one of the proportions of the subgroups outside the reference limits of the combined distribution should exceed 4.1% to imply partitioning, we could not find any justification for partitioning (the largest percentage was 3.0%, indicating that these subgroups should preferably be combined). The square of the correlation coefficient is rather modest (R² = 0.0921) which also signifies that the decrease of phosphate level as a function of age is not dramatic enough to require division into subgroups. We also examined whether inclusion of higher terms might improve the regression model, but no substantial improvement was obtained by including the second order term (R² was increased to 0.1082, and the RMSE was equal to 0.17, i.e. almost the same as in the first order model).

Next, we ran the REG procedure separately on the phosphate data of female (0) and male (1) reference persons. "Regression_pi_female.gif" shows that the first order regression curve for females is almost horizontal, indicating that the phosphate levels keep rather constant in women as a function of age (looking at the female data, one might be inspired to try third order models, but these would hardly have any practical consequences for the project). In contrast, as seen in figure "Regression_pi_male.gif", men seem to have a strong trend of decreasing phosphate levels throughout adult age. The relatively large R² = 0.1939 also signifies that it might be worthwhile to partition the male data. Because the male data show heteroscedasticity, we performed a logarithmic transformation on these data. The transformed data are plotted in figure "Log_regression_pi_male.gif" and the studentized residuals in figure "Log_residuals_pi_male.gif".

We conclude that the decreasing trend of phosphate as a function of age, observed in the combined data, is due to the male data. These runs are documented, together with UNIVARIATE runs on the subgroups, in "SAS8.2_REG_Pi.rtf" where "lreskorr" refers to the logarithmic transformed phosphate data. We also considered a regression model involving age, gender, and their cross term as independent variables, and observed that these were all highly significant.

All of these observations seem to suggest that the phosphate data might be partitioned with respect to both gender and, within the male data, age. It turned out that both of these decisions on partitioning were indeed statistically justified (the largest proportions⁴ being 4.1% and 4.9%, respectively), leading to partitioning of the phosphate data into three subgroups: female, male < 50 years, and male >= years.

The distributions of these subgroups are visualized at the end of "SAS8.2_REG_Pi.rtf". There were no outliers, and the results obtained by the SAS 8.2 the RefVal 4.0 programs were identical. The percentiles of these distributions are shown in the following table (mmol/L).

Female: 0.85-1.49

Male < 50 years: 0.79-1.63

Male >= 50 years: 0.73-1.33

We do not know of any physiological explanations for why the phosphate level should decrease with increasing age in males, but this trend seems to be so strong that it should in our opinion preferably be accounted for in the establishment of reference intervals for phosphate.

Because partitioning of the male data at the particular age of 50 years is necessarily an arbitrary choice, we also calculated regression-based continuous reference intervals from the logarithmic transformed male data. These continuous reference intervals, together with 90% confidence intervals⁵, are shown in "Continuous_RI_phosphate_men_0.90.gif".

Calculation of such continuous reference intervals is recommendable whenever a laboratory test shows clear-cut trends as a function of a continuous variable, because arbitrary decisions on cut points for partitioning can then be avoided and reliable, age-specific reference limits can easily be obtained at any age through interpolation. However, the laboratory information systems are unfortunately not able to exploit such continuous reference intervals today, and clinicians would hardly be delighted to apply them to their decision-making, either. So far, we have to content ourselves to arbitrarily chosen cut points for partitioning, if we wish to account for trends at all, but continuous reference intervals will probably be the method-of-choice in the future.

We found treatment of the project data on calcium, magnesium, potassium, and sodium rather straightforward and unproblematic, and except a couple of suggestions for slight adjustments involving the second decimals (!) in the reference limits of calcium and magnesium, we agree fully with the preliminary project results. For inorganic phosphate, we are suggesting partitioning with respect to gender and, for males, also to age because the statistical evidence for partitioning seems rather strong although we do not know of any physiological explanations for such behavior of phosphate. We leave this issue open for further discussions.