Nephrol Dial Transplant (2003) 18: 2082–2087
DOI: 10.1093/ndt/gfg355
Original Article
Prediction of time-averaged concentration of haemoglobin in
haemodialysis patients
Peter Krisper1, Franz Quehenberger2, Daniel Schneditz3, Herwig Holzer1 and
Hans Dietrich Polaschegg4
1
Division of Nephrology, Department of Internal Medicine, 2Institute for Medical Informatics, Statistics and
Documentation, 3Department of Physiology, University of Graz, Graz and 4Medical Devices Consultant,
Köstenberg, Austria
Abstract
Background. Haemoglobin (Hb) concentration is not
stable in most haemodialysis patients due to ultrafiltration-induced haemoconcentration. Pre-dialysis Hb
concentrations might therefore significantly deviate
from the time-averaged concentration (Hb-tac) which
is more likely to represent the patients ‘true’ Hb. This
study was performed to quantify these differences in
our chronic haemodialysis population and to develop
a formula for prediction of Hb-tac.
Methods. In 55 stable patients, serial blood samples
were taken over a period of 2 weeks before and
immediately after each haemodialysis as well as 30 min
post-haemodialysis to account for post-dialytic fluid
rebound. Hb-tac was calculated for every patient from
the area under the time-dependent Hb curve. We
compared the differences between Hb-tac and predialysis Hb (Hb-pre) and various prediction formulae
for Hb-tac generated by multiple linear regression
analysis which included Hb-pre and post-dialysis Hb
(Hb-post) and/or ultrafiltration rate (UFR).
Results. Mean Hb-pre after the long dialysis interval
was significantly lower than after the short interval
(11.47 vs 11.85 g/dl, P < 0.0001), both underestimating
mean Hb-tac (11.97 g/dl). More interestingly, Hb-pre
after the long interval deviated >0.5 g/dl from Hb-tac
in 50% of measurements. After the short interval,
20% still lay outside this tolerance range. The best
formula to predict Hb-tac was Hb-pre 0.5 þ Hbpost 0.38 þ 1.28 (6% outside ± 0.5 g/dl). Hb-pre þ
(Hb-post – Hb-pre)/3 may be used for quick estimation
of Hb-tac.
Conclusions. Hb-tac can be predicted from pre- and
post-dialysis blood samples after the short interval,
Correspondence and offprint requests to: Peter Krisper, MD,
Division of Nephrology, Department of Internal Medicine,
University of Graz, Auenbruggerplatz 27, A-8036 Graz, Austria.
Email: [email protected]
using a simple new formula. Because Hb-tac more
reliably reflects a ‘true’ Hb level of haemodialysis
patients, it represents a potentially useful tool for future
scientific and clinical work.
Keywords: haemodialysis; haemoglobin; post-dialysis;
prediction; target; time averaged
Introduction
Correction of anaemia in haemodialysis (HD) patients
with recombinant erythropoietin and i.v. iron is well
established and has great impact on the patients wellbeing as well as on treatment costs [1–7]. Control of
haemoglobin (Hb) in clinical practice as well as in
virtually all studies dealing with the effects of anaemia
correction in this population is usually based on predialysis blood sampling [6–9]. Also the guidelines for
anaemia management published in the last few years
by several renal associations refer to pre-dialysis
values when recommending Hb target values [10,11].
However, Hb concentration is variable in HD patients.
Pre-dialysis values vary with the time of blood sampling, e.g. they are lower after the long than after the
short interdialytic interval [12,13]. Furthermore, preand post-dialysis Hb concentrations may differ by up to
25% or 3.5 g/dl [13–15], depending on ultrafiltration,
hydration status and other effects, and they are subject
to a post-dialytic rebound. This results in a saw-toothed
pattern of Hb concentrations when seen over a whole
week (for an example, see Figure 1).
Time averaging is a common approach to characterize a variable with marked time-dependent changes.
Such a time-averaged Hb concentration (Hb-tac) could
be considered close to the ‘true functional’ Hb as
claimed by some authors [11,16]. In patients without
intradialytic haemoconcentration, pre-dialysis Hb
Nephrol Dial Transplant 18(10) ß ERA–EDTA 2003; all rights reserved
Time-averaged Hb concentration in HD patients
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Treatment
Fig. 1. Mean haemoglobin concentrations of 55 patients before,
immediately after and 30 min post-haemodialysis as a function of
time. Mean time-averaged haemoglobin (Hb-tac) was calculated
from the area under the curve divided by the observation time.
For absolute numbers and comments, see Table 1.
Treatment was performed as routinely prescribed; however,
to allow for a rebound sample taken 30 min after the end of
HD, treatment time was reduced by that amount in those who
requested it. Treatments were performed on AK 200 machines
(Gambro AB, Stockholm, Sweden) using synthetic low-flux
dialysers for HD and synthetic high-flux dialysers for haemodiafiltration (HDF) supplied by various manufacturers.
Following the routine procedures for connecting and disconnecting the blood lines, 300 ml of saline were infused
mainly at the end of each HD. The study was approved by the
local Ethics Committee, and all patients provided written
informed consent.
Blood chemistries
(Hb-pre) may be regarded as a good estimate for the
patients ‘true’ Hb and should be comparable with the
Hb of individuals not on HD. In contrast, in patients
with a high ultrafiltration rate (UFR), haemoconcentration causes a considerable increase in post-dialytic
Hb (Hb-post). Thus, Hb-pre will significantly underestimate the Hb-tac in these patients. Furthermore,
with increasing efforts to increase target Hb concentrations [4,6,8,9], it is more likely that Hb-post will reach
dangerous levels in a growing number of HD patients
[17]. Although these problems are raised from time
to time [13,15–17], studies aimed at solving this
dilemma do not exist.
It was the intention of this study to first evaluate the
magnitude of Hb variations in our dialysis population
as encountered under daily conditions. The second goal
was to determine Hb-tac and to compare this value
with pre-dialysis levels. Finally, we wanted to develop
a formula for predicting Hb-tac from easily accessible
parameters for potential routine use.
Subjects and methods
Patients
Patients were selected from our chronic out-patient HD
programme consisting of 70 patients. Only patients who had
been on HD for at least 3 months with three sessions per week
were selected. Patients who had a significant intercurrent
illness or were clinically unstable as judged by the attending
physician were excluded. Also patients with unstable Hb
during the 2-week study period were not evaluated. This was
defined as a difference in mid-week Hb-pre of >1 g/dl during
the study period or the need for red blood cell transfusions,
and was the case in two patients. All included patients were
on dry weight as clinically assessed. In a subset of 12 patients,
this was confirmed by measurement of vena cava diameter
indices [18].
Fifty-five stable patients were recruited (21 women, 34 men;
54 Caucasians, one black; mean age 58.9 ± 16.9 years;
4.2 ± 3.2 years on HD; mean body weight 68.8 ± 11.1 kg).
Causes of chronic renal failure were hypertension (n ¼ 11),
glomerulonephritis (n ¼ 7), diabetes mellitus (n ¼ 6), others
(n ¼ 14) and undetermined (n ¼ 17).
Blood samples were drawn before dialysis from the arterial
puncture site (Hb-pre), at the end of dialysis under low flow
conditions from the arterial blood line (Hb-post), and 30 min
after the end of dialysis (Hb-reb) for six consecutive HD
sessions over a period of 2 weeks. We considered 30 min as
a reasonable time span for allowing extravascular fluid to
rebound from the interstitial space [19,20]. A final Hb-pre was
drawn at the beginning of the third week. Hb was analysed
photometrically and haematocrit derived indirectly by an
automated cell counter (SysmexTM XE 2100, Toa Medical
Electronics, Kobe, Japan). The coefficient of variation in our
laboratory is 1.1% for Hb, and 1.5% for haematocrit. Only
Hb is presented in the results, because it seems to be more
comparable between laboratories [21] and Hb concentrations
are more steady in vitro over time [22] and therefore should be
used in preference to haematocrit to manage anaemia [10,11].
Analysis
For every individual patient, a Hb curve as a function of time
over the 2-week study period was constructed, connecting
Hb-pre, Hb-post and Hb-reb by straight lines (compare
Figure 1). Hb-tac was calculated from the area under this
curve divided by the duration of the observation. When data
were incomplete for the whole 2-week period, only one
complete week (e.g. Monday to Monday) was evaluated.
The capability of Hb-pre sampled on different days to
predict Hb-tac was compared with respect to the residual
standard deviation (RSD). RSD is defined as the standard
deviation of the differences between predicted and observed
values of Hb-tac (‘residuals’). The percentage of residuals
exceeding ±0.5 g/dl was used as an additional performance
criterion. This value of 0.5 g/dl was chosen as the relevant
discrepancy since most of the established guidelines use
this range to indicate Hb targets (e.g. NKF-K/DOQI:
11.5 ± 0.5 g/dl) [10].
In a second step, formulae for prediction of Hb-tac were
obtained by linear regression analysis using Hb-pre, Hb-post,
UFR or subsets of these. For these calculations, we only used
values after the short interval. We excluded the rebound
sample Hb-reb for prediction modelling because for possible
routine use it would be impracticable to draw blood samples
30 min after the end of HD. Hb-pre and Hb-post used for
prediction also contribute to Hb-tac. This can be neglected for
Hb-post but yields too optimistic results for formulae
containing Hb-pre. Therefore, for the calculation of residuals
2084
for each Hb-pre, an independent Hb-tac was also determined
by replacing this particular Hb-pre with the Hb-pre from
the successive week for samples taken on Mondays, and
switching Hb-pre concentrations from Wednesdays and
Fridays within the same week. The Tuesday, Thursday
and Saturday schedule was handled in the same way. In the
following text, Mondays or Tuesdays (after the long dialysis
interval) are also termed day 1, Wednesdays or Thursdays
day 3, and Fridays or Saturdays day 5, respectively.
The percentage of dialysis-induced haemoconcentration
(HC%) was calculated by the formula: HC% ¼ 100 – (Hbpre/Hb-post) 100.
Statistics
Unless otherwise specified, data are expressed as mean ± SD.
Mean Hb concentrations were compared by paired t-tests
using only the measurements of the first week in order to
achieve statistical independence between pairs. P-values were
multiplied by the number of comparisons to maintain the
significance level (Bonferroni correction). A P < 0.05 was
considered statistically significant.
ExcelTM (Microsoft, Seattle, WA), SPSSTM (Chicago, IL)
and SASTM (Cary, NC) were used for calculations.
Results
Complete data over the whole 2 week study period were
obtained in 41 patients; in 14 patients only 1 week could
be assessed. Mean dialysis time was 3.75 ± 0.34 h
(median 3.5), and ultrafiltration volume was 2.4 ± 1.0 l,
corresponding to a UFR of 0.64 ± 0.27 l/h. Dialysate
sodium was 137 ± 3 mmol/l (median 138), bicarbonate
P. Krisper et al.
31 ± 2 mmol/l (median 30), potassium 1.9 ± 1.1 mmol/l
(median 2.0) and glucose 1 g/l in all patients. Machine
blood flow was 296 ± 42 ml/min (median 300), and
dialysate flow 500 ml/min in HD (78% of patients) and
700 ml/min in HDF.
The Hb concentrations of the evaluated 288 HD
sessions are presented in Table 1 and Figure 1. Mean
Hb-pre after the long interval was significantly lower
than after the short interval (11.47 vs 11.85 g/dl,
P < 0.0001), while there was no significant difference
between day 3 and day 5 mean Hb-pre levels (11.80 vs
11.90 g/dl, P ¼ NS). Mean treatment-induced haemoconcentration was 6.7% after the long and 5.1% after
the short interval (P < 0.05). Mean Hb-tac (11.97 g/dl)
was significantly higher than mean Hb-pre at either day
(P < 0.001).
The differences of each individual Hb-pre value
from the patients’ Hb-tac plotted against UFR are
shown in Figure 2. As expected, there was increasing
Table 1. Mean haemoglobin concentrations (g/dl)a
Hb-pre
Hb-post
Hb-reb
Hb-tac
Day 1
Day 3
Day 5
11.47 ± 1.09b
12.30 ± 1.47
12.04 ± 1.33c
11.97 ± 1.11d
11.80 ± 1.12
12.45 ± 1.50
12.26 ± 1.35
11.97 ± 1.11d
11.90 ± 1.16
12.52 ± 1.43
12.25 ± 1.29
11.97 ± 1.11d
a
Mean values are based on all data. Only one pair of values per
patient was used in the t-test.
b
P < 0.0001 with respect to Hb-pre at days 3 and 5.
c
P < 0.01 with respect to Hb-reb at days 3 and 5.
d
P < 0.001 with respect to Hb-pre at days 1, 3 and 5.
Fig. 2. Residuals after prediction of time-averaged haemoglobin (Hb-tac) by pre-dialysis haemoglobin (Hb-pre): Hb-tac minus Hb-pre,
n ¼ 288. Residual standard deviation (RSD) is 0.51 g/dl for the whole group; it is larger after the long interval (0.66 g/dl) than after the short
interval (0.42 g/dl). Bold lines mark the ±0.5 g/dl tolerance range. At day 1, 50% of the residuals lay outside this range compared with 20%
at days 3 and 5 (P < 0.0001).
Time-averaged Hb concentration in HD patients
2085
underestimation of Hb-tac at higher UFR: the linear
regression line for Hb-tac – Hb-pre was UFR 0.61 –
0.15 (P < 0.0001, r2 ¼ 0.11). The quality when using
Hb-pre to predict Hb-tac is shown in Table 2. Overall,
30% (86/288) of Hb-pre deviated >0.5 g/dl from
Hb-tac, corresponding to an RSD of 0.51 g/dl, with a
maximum difference of 2.5 g/dl. This proportion
differed significantly between samples drawn after the
long or the short HD interval: 50% (48/96) at day 1 vs
20% (38/192) at days 3 or 5 (P < 0.0001). As prediction
of Hb-pre was better after the short interval, we decided
to include only these days in further analysis.
Table 2 shows the results of various linear
regression models. Hb-tac was best predicted by Hbpre 0.5 þ Hb-post 0.38 þ 1.28 (RSD ¼ 0.28). The
residuals after prediction with this formula are plotted
in Figure 3. Only 6% (11/192) fell outside the
mentioned ±0.5 g/dl range. The benefit is even more
pronounced if only HDs with UFR of 0.5 l/h or above
are viewed: in only 2.8% (3/108) did the predicted Hb
differ >0.5 g/dl from Hb-tac, vs 21% (23/108) if Hbpre was used. Incorporating UFR into the formula
showed no advantage.
For the potential use as a bedside estimation
of Hb-tac, simplified formulae were tested (Table 2).
Hb-pre þ (Hb-post – Hb-pre)/3 is a better approach
than using the mean of Hb-pre and Hb-post (RSD 0.32
vs 0.37).
Discussion
Table 2. Prediction of Hb-tac
Predictor
RSDa
±0.5 g/dlb
Hb-pre
Hb-pre (long interval)
Hb-pre (short interval)
Hb-pre 0.91 þ 1.16c
Hb-post 0.72 þ 2.99c
Hb-pre 0.91 þ UFR 0.47 þ 0.82c
Hb-pre 0.5 þ Hb-post 0.38 þ 1.28c
Hb-pre 0.48 þ Hb-post 0.4 –
UFR 0.12 þ 1.38c
Hb-pre þ (Hb-post – Hb-pre)/3c
(Hb-pre þ Hb-post)/2c
0.51
0.66
0.42
0.40
0.41
0.38
0.28
0.28
29.9
50.0
19.8
18.0
18.9
16.7
5.7
6.3
0.32
0.37
12.0
17.2
a
RSD: residual standard deviation (g/dl).
Percentage of results in which the difference from Hb-tac exceeded
±0.5 g/dl.
c
These formulae only refer to the short dialysis interval. Hb-pre and
Hb-post in g/dl, UFR in l/h.
b
This study attempts to determine Hb-tac in a cohort
of stable HD patients by including post-dialytic
fluid rebound in the calculations, and describes its
discrepancy to pre-dialysis values. A formula is
presented to predict Hb-tac from pre- and post-dialysis
Hb concentrations.
The mean Hb-pre of our study population was within
the recommended targets [10,11] and was significantly
lower after the long interval than after the short
interval, an expected effect [12,13] of more pronounced
overhydration at the beginning of the week (Table 1).
We observed a dialysis-induced haemoconcentration
of 5–7%, somewhat smaller than reported in other
studies, where mean intradialytic variations of haematocrit were in the range of 10% [13,14,23].
Our data confirm that in most HD patients, unlike
in the general population or patients on peritoneal
Fig. 3. Residuals after prediction of time-averaged haemoglobin (Hb-tac) by an optimized regression formula after the short interval: Hb-tac
minus (Hb-pre 0.5 þ Hb-post 0.38 þ 1.28), n ¼ 192. Residual standard deviation (RSD) is reduced to 0.28 g/dl; only 6% of the values lie
outside the ±0.5 g/dl tolerance range (bold lines).
2086
dialysis, Hb concentrations show significant shortlasting changes. Depending on sampling time or on
theoretical considerations, various Hb values can be
attributed to the same patient during 1 week. Which
one should be chosen? Our goal was to derive a
representative value for the Hb concentration in our
HD patients which should be more comparable
between them as well as with people not on HD. This
might be important for research dealing with the effects
of different Hb targets on physical or mental abilities,
on morbidity and on mortality. Lack of comparability
of individual Hb levels could play a role in the partially
disappointing results of some studies dealing with
the normalization of Hb [7,8]. Consideration of HDinduced haemoconcentration may also be prudent for
the individual patient in our daily routine as we know
that patients might live the major part of the time with
Hb levels well above those suggested in pre-dialysis
samples [15,16]. We think that Hb-tac can meet the
mentioned demands. We want to acknowledge that
there exist alternative approaches to overcome the
problem of Hb variability in patients with renal anemia.
Clyne et al. used the concept of ‘total haemoglobin’
(the body content of haemoglobin in grams), a marker
independent of the actual hydration status, and they
could show a strong relationship to physical exercise
capacity in these patients [24].
The simplest way to approximate Hb-tac, as it is
already more or less prevalent in the nephrological
community, is the use of Hb-pre after the short interval
only: for the whole group, this gives an acceptable
estimate for mean Hb-tac. Obviously, individual
deviations, which may be substantial for any particular
person, will not be detected. We could show that this
approach does not provide satisfactory results in at
least 20% of our patients.
Using our formula including a post-dialytic sample
after the short interval lowered false estimations of
Hb-tac by two-thirds to 6%. If applied in the high UFR
group (>0.5 l/h), where we expect the largest differences between Hb-pre and Hb-post, the Hb-tac will be
correctly predicted within the specified limits in 35 out
of 36 patients.
A limitation of our study is that Hb-tac cannot be
measured accurately, since portable devices analogous
to continuous blood pressure monitoring do not exist.
The Hb-tac we used as reference is a simplification: in
our model, we assumed that there is a constant decrease
or increase between times of blood sampling. This is
justifiable during dialysis and rebound as deviations
from linearity are negligible in their contribution
to Hb-tac. This may not apply for the much longer
interdialytic period. We have to suppose that a number
of patients did not follow a linear intradialytic decrease,
but to individualize this period accurately in our
patients by obtaining multiple blood samples on
interdialytic days was not practicable. Although one
study showed an almost linear decline of haematocrit
during the interdialytic period [16], recent data [13,15]
suggested a slower re-equilibration during the first 24 h
after HD. If this was really the case, Hb-tac would
P. Krisper et al.
be even higher than calculated in our model and further increase its discrepancy to Hb-pre. For obvious
reasons, the determination of Hb-tac by repeated blood
sampling over a longer period of time is impracticable
for routine use. In contrast, the formulae proposed
herein to estimate Hb-tac make use of two easily
accessible Hb measurements only: Hb-pre and Hbpost. The required post-dialytic blood count can be
collected together with the urea sample for the monthly
Kt/V, and Hb-tac can then be calculated automatically
in the laboratory. Furthermore, Hb-post may serve as a
safety measure since in the immediate post-dialytic
period Hb can reach critically high levels [17], especially
in patients in whom ‘normalization’ of Hb is the goal.
For quick estimation of Hb-tac, one can use our
simplified formula Hb-pre plus a third of the difference
between that and Hb-post.
For patients without haemoconcentration or treatment-induced haemodilution, it might not be required
to use a correction as, in those cases, ultrafiltrationinduced haemoconcentration, which is the basis of our
model, obviously plays a minor role.
The formula presented in this study is valid for
populations with comparable dialysis modes, patient
characteristics and mean Hb levels. It should only
be used in stable patients on dry weight, as chronic
hyperhydration would obviously influence Hb-tac
without any change in the patients ‘total’ Hb [24].
Whether this formula also applies to other treatment
modes, especially with regard to higher ultrafiltration
volumes and UFRs, remains to be investigated,
although our proposed formula for prediction of
Hb-tac was even more accurate at higher UFRs.
How could the determination of Hb-tac influence our
clinical dosing of erythropoietin? Optimal target values
for Hb-tac can certainly not be derived from this study,
but they are likely to be higher than the currently
recommended values for Hb-pre. Future outcome
studies that use Hb-tac as a steering parameter could
provide a definite answer to this question. Nonetheless,
Hb-tac can be used to define Hb targets in HD patients
independent of varying pre-dialysis hydration states.
As no data exist as to whether knowledge of Hb-tac
justifies an additional blood sample, we suggest making
use of this marker primarily as a scientific tool.
In conclusion, the time-averaged concentration of
haemoglobin is a new and representative marker for
anaemia management in HD patients and can be
predicted from pre- and post-dialysis blood samples
after the short interval using a simple new formula.
Because Hb-tac more reliably reflects the ‘true’ Hb
level of these patients, it is a potentially useful tool for
future scientific and clinical work.
Conflict of interest statement. None declared.
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Received for publication: 5.9.02
Accepted in revised form: 12.5.03