Age- and sex-dependent reference intervals for uric acid estimated by the truncated minimum chi-square (TMC) approach, a new indirect method

TMC approach

The TMC method was described recently in detail [4]. The method first identifies an interval containing essentially non-diseased patients, the truncation interval. Then, a power normal distribution (PND) is fitted to this interval by an iterative minimum chi-square approach. This approach accounts for the fact that only a part of all values from non-diseased patients is used for parameter estimation. Assuming a PND for values of non-diseased patients is an essential component of the TMC approach. No assumption is made about the distribution of values from diseased patients. RLs are calculated from the estimated PND parameters. The prevalence of non-diseased patients in the data results from the PND and the estimated parameters: prevalence=(number of values in the truncation interval)/([probability assigned to the truncation interval by the PND] [total number of values]).

The present study uses an enhanced version of the procedure described in [4]. Now, the size of the truncation interval is automatically determined on the basis of fit criteria. The truncation interval size was formerly fixed at 70% of all values and is now automatically selected from the range 60%–80%. The selection criteria for truncation intervals are: (i) the p value for the goodness of fit must be >0.05 and (ii) the estimated prevalence must be ≥0. If these conditions hold for several truncation interval candidates, the largest interval is used for parameter estimation. To ensure condition (ii), a corresponding penalty term was added to the estimation procedure as an additional constraint.

A script based on the R programming language with automatic partitioning for age and sex, and calculation of confidence limits can be requested from the authors. The analysis is automatically stratified by age groups and sex, if the data allow so. Age groups are defined by the user. For adults, 10-year intervals are used in the present study. Five-year interval led to the same spline function, but their confidence intervals were slightly larger, as expected. Age-specific results are combined by spline functions to generate continuous relations between the patients’ age and RLs, separately for each sex. The spline function provides numerical RL estimates for all ages covered by the data. Their graphical presentation has no artificial “jumps” between different ages.

Furthermore, the programme automatically estimates the diurnal variation if the sampling times are given in the data. Instead of the sampling time, we used the time samples arrived in the laboratory assuming that the average difference between sampling and arrival time was approximately 2 h.

Differences between RLs were considered as relevant if the critical difference DC was surpassed. DC was estimated on the basis of the permissible imprecision as recently suggested [5]. It can be calculated by a software tool available free of charge on the home page of the DGKL [6].

Data selection and sources

The laboratory results of patients were selected as described earlier [7]: only first values were used if several results from the same patient were obtained during a hospital stay or during the time when the data were selected. First values were chosen to avoid ties (correlated observations from the same patient, which is against the assumptions of both direct and indirect methods).

The new proposal was used with real data obtained by routine laboratories, either of the primary health care sector (private laboratories serving mainly general practitioners) or from a large university hospital (laboratory 3) as indicated in the legends of the figures. Laboratory 1 did not receive samples of hospitalised patients and laboratory 2 only from less than 5% of hospitalised patients. Laboratory 3 excluded hospitalised patients from special wards (e.g. intensive care units and gynaecological units to minimise the number of pregnant women in the data analysed). Subpopulations of the primary health care sector usually have lower prevalence (lower percentage of diseased subjects) than hospitalised patients. Therefore, no subjects were excluded from primary health care data, in contrast to data from hospitalised patients. The laboratories which provided the measurement values were accredited according to ISO 15189 and followed the Guidelines of the German Medical Association on Quality Assurance in Medical Laboratory Examinations (RiliBAEK) [8]. The analytical methods were applied as described by the manufacturers, the uric acid concentrations were determined with a uricase/peroxidase procedure in laboratory 1 with AU 5800 (Beckman Coulter, Krefeld, Germany), in laboratories 2 and 3 with Cobas 8.000 c/02 (Roche, Basel, Switzerland). The creatine concentrations were determined with an enzymatic procedure 2 and a kinetic modification of the Jaffé procedure in the other laboratories. The cystatin C was measured with a nephelometer BN2 (Siemens, Erlangen, Germany), an enzymatic procedure in laboratory 2 and a kinetic modification of the Jaffé procedure in the other laboratories.

The time for collecting the data (data acquisition time) was either one or several years. The stability of the analytical procedure during the data acquisition time was verified by plotting the monthly medians with confidence limits as described elsewhere [6], [7].

Uric acid

The present study confirms that male subjects have higher RLs than women as also reported by others (see Table 1), and that the RLs increase with age in both genders (Figure 1). The upper RLs (97.5^th percentile) in women increased more distinctly and reached approximately the same level in the last decade studied as in men. With the TMC method, the upper RL concentration in serum or plasma determined in various laboratories varied in men between 470 and 693 μmol/L (Table 1) and in women between 363 and 758 μmol/L. Literature data varied between 473 and 568 μmol/L for men and between 330 and 472 μmol/L for women. The lower RLs were almost constant between 18 and 100 years of age.

Table 1:

TMC reference intervals (95% central interval) for the uric acid concentration in serum or plasma (μmol/L).

1. ^aInterval of the critical difference based on the RLs of laboratory No. 2. ^bReference interval (number of contributing values).

Figure 1:

Reference limits of serum uric acid (μmol/L) depending on age (years) separated by sex.

Lower lines represent the 2.5^th percentile, upper lines the 97.5^th percentile, blue lines represent men (n=24,582) and red lines women (n=24,579). The data were obtained from primary health care laboratories without exclusion of data (A: laboratory 1, n=339,192; B: laboratory 2, n=615,290), and from a university hospital (a mixture of hospitalised patients and outpatients; C: laboratory 3, n=330,589).

In laboratory 2, male subjects (18–29 years) had a TMC upper RL of 470 μmol/L. Estimation of the permissible difference on the basis of the permissible analytical imprecision was calculated as recently proposed [13]. The permissible difference limits are 445–495 for the upper RL of 470. These limits are surpassed in three laboratories in the age interval 18–29 years (marked in red in Table 1). Therefore, common RIs of the age interval 18–29 years cannot be justified.

In laboratory 3, the data could be split into non-hospitalised patients (outpatients, ambulant patients) and into hospitalised patients. The upper RLs of both groups were similar up to the age of 60 years (Table 2). In the last decade studied (80–90 years), the upper RLs increased more dramatically in the hospitalised group than in the outpatient group. This unexpected phenomenon could have several reasons: (1) a shift of the whole distribution towards higher values, (2) a critical increase of the prevalence of pathological values which cannot be tolerated by the TMC approach or (3) a broader distribution range leading to higher standard deviations (SDs) and hence to higher upper RLs.

A shift can be excluded because the modes of both distributions (80–90 year subgroups of ambulant vs. hospitalised patients) were approximately the same (Table 2). A relatively high prevalence of “pathological values” could also be excluded (Table 2). However, the range of the data distribution and the SDs of the distributions in the older group were higher in hospitalised patients than in ambulant patients (SD=115 vs. 156 with women, Table 2). One reason for a broader distribution pattern could be a lower mean glomerular filtration rate in the hospitalised group. Therefore, we prefer the last explanation as the most plausible one because the creatinine concentration was also higher in the older group of hospitalised patients (Table 3).

Furthermore, the data sets could be stratified according to the time when the samples arrived in the laboratory. If it is assumed that the transport times are approximately the same for all samples, a diurnal variation can be observed as has also been reported by others [14], [15]. This variation has a similar pattern from Monday to Friday. If the values from Monday to Friday are combined (Figure 2, not stratified by sex and age), a maximum was detected at about 7:00 am and a minimum during the night. Sennels et al. [14] reported a peak at about 5:00 am (sampling time) which corresponds to our maximum at 7:00 am for the arrival time in the laboratory if we assume an average transport time of about 2 h. The diurnal variation appeared in ambulant patients, but not in hospitalised patients. This divergence cannot be explained.

Figure 2:

Diurnal variation of the uric acid concentration in heparinised plasma (ambulant patients, laboratory 3, n=80,099).

Daily observations are calculated during 1 week and the medians from Monday to Friday are presented. The yellow areas represent the approximate 95% confidence limits based on the median absolute deviation.

Creatinine and cystatin C

RLs of men for the creatinine concentration in serum are higher than those of women confirming earlier reports (Figure 3). The limits are almost constant up to about 50 years in both genders, and then, they rise with increasing age. The gender difference is usually attributed to the lower muscle mass of women. The same pattern of age and sex dependency was observed in the other two laboratories. Cystatin C was determined in serum samples obtained from primary care patients. Age dependency was similar to creatinine (Figure 4). The upper RL was constant between the age of 18 and 50 years, and, thereafter, the concentration increases with progressing age. No significant differences exist between men and women, because the confidence limits overlap almost completely (Figure 4).

Figure 3:

Reference limits of serum creatinine (μmol/L) depending on age (years) separated by sex.

Lower lines represent the 2.5^th percentile, upper lines the 97.5^th percentile, blue lines represent men (n=386,317) and red lines women (n=460,846). The data were obtained from two primary health care laboratories (A: laboratory 1, n=327,132; B: laboratory 2, n=847,163).

Figure 4:

Reference limits of serum cystatin C (mg/L) depending on age (years) separated by sex.

Lower lines represent the 2.5^th percentile, upper lines the 97.5^th percentile, red lines represent men (n=6131) and blue lines women (n=5266). The data were obtained from a primary health care laboratory (laboratory 2).