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Articles |
Departments of
1
Medical Gastroenterology S and
2
Clinical Chemistry, Odense University Hospital, Denmark.
3
Department of Cardiology A, Århus Amtssygehus, 8000
Århus C, Denmark.
4
Department of Clinical Chemistry, Vejle County Hospital,
Denmark.
a Address correspondence to this author, at the Århus Amtssygehus. Fax +45 89 49 76 19.
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Abstract |
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 Top Abstract IntroductionMaterials and MethodsResultsDiscussionAppendix 1References |
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Introduction |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionAppendix 1References |
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It is therefore reasonable to assume that INR values, even from patients on stable OAT, fluctuate for a given intensity of anticoagulation. Extremes of such fluctuation occurring on the day of venipuncture could give values that interfere with adjustment of coumarin therapy. We recently estimated that the intraindividual variation of INR during treatment (the "in-treatment within-subject variation") was 10.1% (6). No studies so far have considered the impact of this intraindividual variation, which reflects both biological and analytical components, on measured INR and on therapeutic control in patients in OAT.
In daily clinical practice it is difficult to obtain a sufficient number of INR measurements from individual patients within a reasonable timespan to address the problem. We therefore decided to illustrate the problem by computer simulations, as has been done elsewhere to address various problems in clinical situations (7)(8)(9)(10). The aims of our study were (a) to develop an educational tool with the scatterplot, which would allow the effect of the in-treatment within-subject variation on consecutive INR measurements to be visualized, and (b) to investigate to what extent in-treatment within-subject variation alone, or with assumed in-treatment setpoints selected above and below the mid-interval setpoint, could explain values outside the intended therapeutic intervals and critical differences in patients in stable OAT. Further, the effects of analytical bias and imprecision were investigated. The results are presented in relation to a graphical model with difference plots that incorporate the therapeutic interval and limits for critical differences (11)
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Materials and Methods |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionAppendix 1References |
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1) INR values for a patient on continuous, constant OAT would be
gaussian-distributed around an assumed in-treatment setpoint, µ, with
an assumed in-treatment standard deviation, 
/.
2) The simulations reflected steady-state conditions, e.g., a patient receiving a constant dose of vitamin K antagonist.
3) Consecutive measured INR values were independent of each other.
To mimic already established therapeutic intervals and targets for
in-treatment setpoints for OAT, we chose the assumed in-treatment
setpoints as being within the interval INR 2.0–3.0 (5).
The total CV—the in-treatment within-subject variation—of 10.1%, was
based on our previous study in patients in stable OAT (6).
Given the assumed in-treatment setpoint, µ, and the in-treatment
within-subject variation, CV, we calculated / as follows:
 | (1) |
The critical difference for the 95% range of differences was
calculated as
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/values were calculated with the
above equation for in-treatment within-subject variations of 10.1% and
15%. The arrays of generated INR values were regarded as consecutive
measurements within single patients and the differences between
consecutive measurements were calculated. To control the simulation
procedure, we calculated the estimated in-treatment setpoint,
, and the estimated in-treatment standard deviation,
s, from the values produced. To incorporate information about the
degree of anticoagulation in relation to the therapeutic interval and
in relation to the last measured value, we recently proposed the use of
difference plots. According to this model, the difference between the
last measured INR value and the previous value,
INRi-INRi-1, should be
plotted against INRi [11].
calculation of number of observations exceeding therapeutic
intervals
The fraction of INR observations observed outside the therapeutic
interval was calculated from the gaussian-distributed simulated data
for the assumed in-treatment setpoints µ = 2.1, 2.3, 2.5, 2.7, and
2.9, according to different assumed in-treatment within-subject CVs
(7.5%, 10%, 15%, and 20%). For this purpose we used the gaussian
distribution as available in the computer software Statistix 4.0
(13).
introduction of analytical bias
Analytical bias will impose a systematic error on the measured INR
values. We investigated the effect of analytical bias, i.e., from -0.4
to 0.4, on the number of INR measurements falling outside the
therapeutic interval INR 2.0–3.0 when the clinician's target is INR
2.5. The percentage of true INR values falling outside the therapeutic
interval was estimated by the use of the gaussian-distributed data. In
the model of analytical bias, the "true" patient value is
Xi = µ + wi, where µ
signifies the steady-state value and wi the
within-subject variation (analytical and biological variation). The
measured value will therefore be Yi = µ +
wi + B, where B is the analytical bias.
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Results |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionAppendix 1References |
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, top). For the assumed in-treatment setpoint µ = 2.5 within
the therapeutic intervals 2.0–3.0 and the assumed in-treatment
within-subject variations CV = 10.1%, ~5% of the simulated
results were below or above the vertical lines that represent the
therapeutic interval. Because the random array of INR values generated
and the lines representing the critical differences are based on the
same CV, ~5% of the observations in Fig. 1
(top) were found outside
the lines representing the critical difference. The fact that more
observations are below the lower line for the critical difference than
above the upper line for the critical difference merely reflects
regression towards the mean and the choice of simulated / and
percentage for critical differences.
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effect of other assumed in-treatment setpoints
If different assumed in-treatment setpoints for INR were applied
within the therapeutic interval 2.0–3.0, the ellipsoid cluster would
be centered according to the assumed in-treatment setpoints. For µ =
2.1 and 2.9, e.g., this resulted in a considerable number of
observations below or above the therapeutic interval, respectively, as
shown in Fig. 1
(middle and bottom). However, the total number
exceeding the critical differences will be unchanged, for this is
calculated according to the setpoint. Table 1
summarizes the number of INR measurements that fall outside the
therapeutic interval for different assumed in-treatment setpoints, µ,
calculated by the use of the gaussian distribution.
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effect of increasing values for the in-treatment within-subject cv
Too intense or inadequate anticoagulation poses considerable risks
for complications in patients receiving OAT. The effect of increasing
the assumed in-treatment within-subject CV to 15% is illustrated in
Fig. 2
. The percentage of observed INR values above or below the
therapeutic interval was calculated according to the
gaussian-distributed data, and is presented separately and combined
with the total percentage exceeding the limits for the therapeutic
interval for various assumed in-treatment setpoints in Fig. 3
(top). In Fig. 3
(bottom), the corresponding calculations for
various assumed in-treatment setpoints and increasing in-treatment
within-subject variation are presented.
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Differences in serial measurements of INR (
INR) that fall outside
the lines for critical difference reflect a considerable change between
serial INR measurements, and changes in dose of anticoagulants should
be considered. If the in-treatment within-subject variation is lower or
higher than 10.1%, then theoretically the 95% coverage intervals
should be changed accordingly. However, the coverage intervals in
individual patients will in most instances not be known. If the
coverage interval based on our previous estimate of the in-treatment
within-subject variation of 10.1% is used with various assumed values
for within-subject variation, the number of INR results determined by
the use of computer simulation to be outside the coverage interval will
be distributed according to Fig. 4
.
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consequence of analytical bias
The size of the assumed in-treatment setpoint and the in-treatment
within-subject variation will determine the number of INR values
outside therapeutic intervals. Clinical decisions, such as a change in
OAT dose, based on INR values accidentally outside the therapeutic
interval will lead to fluctuating INR measurements (i.e., a
"ping-pong" effect: too intensive anticoagulation alternating with
insufficient anticoagulation (11)). Analytical bias giving
rise to a shift in the setpoint (and often not apparent to the
clinician) also poses a risk for misinterpretation of INR values
obtained and may lead to too little or too much anticoagulation.
The effect of increased CV is easy to grasp but the effect of
analytical bias may need further explanation. If a laboratory has an
analytical bias of +0.4 INR, then all measured values are 0.4 INR too
high. This will lead the clinician to compensate by changing the target
to a measured 2.5 INR, the mid-point in the interval 2.0–3.0—which,
however, in the patient corresponds to 2.1 INR. If the patient's CV is
~7.5%, then the clinician will expect virtually no measured values
(Yi) to be outside the interval; but
the patient will be monitored at a lower INR, with the result that
~25% of the "true" values (Xi)
will be <2.0. Most likely, this will not be observed by the clinician.
Consequently, an analytical bias will lead to mistreatment of all
patients as long as it persists. The effect may be acceptable for bias
between -0.2 and +0.2 INR, but greater bias may have significant
consequences for the patients. The effect of introducing analytical
bias and increasing CVs is presented as function of analytical bias in
Fig. 5
, which shows the number of "true" values,
Xi, outside the therapeutic interval.
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Discussion |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionAppendix 1References |
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When treatment with OAT is initiated in a patient, a therapeutic interval and a target for in-treatment setpoint are selected according to the indication for treatment and individual risk factors. During initiation of therapy and in steady-state, all INR values will be compared with this setpoint or therapeutic interval and doses adjusted accordingly. The intensity of anticoagulation actually achieved, the steady-state in-treatment setpoint, in terms of the INR value, is, however, affected by several factors that may lead to poor therapeutic control. As is obvious from controlled trials, where therapeutic control must be assumed to be more optimal than in daily clinical practice, a substantial number of INR measurements fall outside the intended therapeutic interval (poor therapeutic control). The reason for this is unclear, but spontaneous variation, in part due to biological variation of the prothrombin time and thus INR, could contribute. This variation might lead to frequent changes in the dosing and introduce "ping-pong" effects with regard to dosing with vitamin K antagonist (11).
To address some of the problems when monitoring OAT patients, we
performed this computer simulation study as an extension of our
previous study. Thus, the computer simulations were based on the
assumption of a gaussian distribution of consecutive INR values around
assumed in-treatment setpoints, and on our previous estimate of the
in-treatment within-subject variation of INR measurements in patients
in stable OAT (6). Computer simulation is not necessary to
obtain information about the number of INR measurements that fall
outside the therapeutic interval; this information may also be obtained
with software that provides a cumulative gaussian distribution or with
use of statistical tables. Regarding the number of observed differences
falling outside the critical differences, however, the theoretical
calculations are much more complicated (with simulation of / but
calculation of critical differences based on constant CVs), so here the
computer simulations provide a simple solution.
With a mean in-treatment setpoint of 2.5 and in-treatment within-subject variation of 10.1%, only 5% of INR measurements will be <2.0 or >3.0, a generally accepted therapeutic interval for the treatment of deep venous thromboembolism and pulmonary embolism (1). However, even a small change in the assumed in-treatment setpoints substantially influences the fraction of INR values observed outside the therapeutic interval.
The fact that as many as 30% of INR measurements are outside
therapeutic intervals in major studies of anticoagulation could reflect
a combination of higher CVs and deviating setpoints. The simulation
study suggests that the intraindividual variation is actually >10.1%,
so for the optimal setpoint of 2.5 an intraindividual variation as
great as 18% is likely (Fig. 3
, bottom). In a prospective study of
patients receiving OAT, we found a total within-subject CV (analytical
and biological variation) of 14.1% (14).
We have previously suggested a graphical method that uses difference
plots for presenting consecutive INR measurements
(6)(11). This model incorporates lines that
reflect the critical differences (expressed as 95% coverage intervals
of difference) and the therapeutic interval and is a clinically
relevant approach. This method, however, gives rise to regression
towards the mean, given the mathematical relationship between the
difference INR and INRi,
INRi contributing to both of the variables that
are plotted. Plotting INR against 1/2(INRi +
INRi-1) would correct
these findings but would be less relevant when the results are applied
to the clinical situation (15). Using coverage intervals
that are based on results from a retrospective study may not be
sufficient for individual patients' results if the intraindividual
variation exceeds 10.1% (14). Serial changes are likely
to be considered significant if the intraindividual variation is
>10.1%, as shown in Fig. 4
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Selection of the patients that were used for calculation of the in-treatment within-subject variation may have influenced the estimated CV. The CV value we used was based on retrospective data from patients in whom sufficient consecutive INR measurements were available and where no change in OAT had taken place during the study period—thereby lumping together preanalytical, analytical, biological factors, and interactions with extraneous factors. All patients with unstable or poor therapeutic control, whatever the reason, were excluded. This may have lead to an underestimation of the in-treatment within-subject variation (11).
Use of biological variation obtained from healthy individuals would have been meaningless for this computer simulation because the quantity in question, the prothrombin time (INR), is dependent on the dosage of vitamin K antagonist. Furthermore, the intraindividual biological CV is generally accepted as being higher in the diseased state than in health. In consequence, intraindividual variation of INR must be assessed in patients receiving vitamin K antagonists when they are in steady-state of OAT; that evaluation is probably a realistic estimate of the minimal variation that can be expected during OAT.
Estimating the in-treatment within-subject variation and the use of
consecutive INR values in the computer simulation studies provides
information about the probability, under standardized conditions, of
obtaining INR values outside a therapeutic interval. Knowledge
regarding the size of this variation could perhaps lead to improved
dose adjustments in patients receiving vitamin K antagonists; this
information also would allow the clinician, in selected cases, to
perform optimal treatment with oral anticoagulants for other targets
and intervals. The differences in results of simulation performed with
setpoints deviating from mid-interval (Fig. 1
, middle and bottom)
stress that the therapeutic interval must be selected accordingly.
Estimating the total CV for individual patients in whom anticoagulation
is in a steady-state may be worthwhile, if lifelong treatment is
planned. Using difference plots with therapeutic interval and the
critical differences could perhaps reduce the risk of changing the dose
of anticoagulant when no significant change has actually taken place,
even though the value for INR may be outside the therapeutic interval
(11). Such an approach can reduce the risk of a
"ping-pong" effect.
In the majority of laboratories the imprecision is well below 5% and
will have only negligible effect on the biological in-treatment CV,
which usually exceeds 10% (16). The influence of
analytical bias, unknown to the clinician, should also be considered in
assessment of quality of treatment with oral anticoagulants. The
present study suggests that analytical bias will lead to mistreatment
of patients if it exceeds ±0.2 INR (Fig. 5
). Estimation of the
analytical bias for individual institutions requires analysis of
externally provided samples. This was illustrated in a Nordic external
assessment of analytical quality, where an analytical bias accounted
for a between-laboratory CV of 10.5% without use of a common
ISI-calibrator. This between-laboratory imprecision was reduced to
3.9% by use of a common ISI-calibrator, emphasizing the need for
proper international calibration (17).
Simulation studies of clinical situations, as performed in this study, are inexpensive and do not entail health risks. They allow ethical evaluation of hypotheses according to various assumed conditions—optimal as well as extreme (unacceptable to patients and others). Thus, computer simulation may be an important tool for performance testing of clinical strategies before their introduction. The simulation procedure allows as many measurements as required, but caution is required when positive results are obtained and when the results are transferred to the clinical situations that initiated the simulation. Nevertheless, a simulation study may disclose the limits for what is possible. Data from the present study seem to suggest that some of the INR values measured outside therapeutic intervals in patients during stable OAT may be attributable to spontaneous fluctuations. Given that the in-treatment within-subject variation probably is higher than suggested in the previous retrospective study, this spontaneous variation may be even more important. The impact of higher than expected within-subject variation may be aggravated by a tendency in controlled clinical trials to aim at a lower target for in-treatment setpoints than the central value within the therapeutic interval (3) (reflecting a concern over severe hemorrhagic complications (5)). Systematic analytical bias, a laboratory problem that usually is not apparent to the clinician who is treating the patient and who is reacting to the INR measurement, will substantially increase the number of INR values that fall outside the therapeutic interval but without the clinician's knowledge. Therefore, analytical bias will probably be reflected only in the number of patients experiencing side-effects to the treatment, e.g., thromboembolic complications and hemorrhagic events.
In conclusion, the simulations suggest that therapeutic intervals can be chosen to be unrealistically narrow when related to the steady-state in-treatment within-subject variation. Attempts to decrease the total variation by better education of the patients could perhaps help solve this problem. Many of the factors affecting the effectiveness of anticoagulation, however, cannot be corrected. The therapeutic interval should be considered more as a target for optimal treatment than a standard for rigorous decision limits for changing dosage. Otherwise, the ping-pong effect will dominate the clinical performance (11). If a setpoint of 2.5 mean INR is chosen and the total CV is 10.1%, it will be impossible to obtain 100% of INR measurements within the INR interval 2.0–3.0, even if the patient is in steady-state during the total period of observation. Either one has to be satisfied with a quality of anticoagulation in which ~80% of the INR measurements are within the therapeutic interval, or the therapeutic interval should encompass INR 2.5 ± 3 s (target ± 3 times the standard deviation). The effect of analytical imprecision may be negligible because it is usually <5%, which is less than one-half of the CV of in-treatment variation, but the effect of analytical bias may be considerable if it exceeds ±0.2 INR.
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Appendix 1 |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionAppendix 1References |
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In-treatment within-subject variation: the CV of INR measurements for patients in steady-state OAT.
Assumed in-treatment setpoint: the setpoint applied in computer simulation.
Assumed in-treatment variation/standard deviation: the CV and /
assumed for a patient in the computer simulations performed.
Estimated in-treatment setpoint: the calculated setpoint achieved by performing the computer simulations.
Estimated in-treatment variation/standard deviation: the calculated CV and s achieved by computer simulation.
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Acknowledgments |
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References |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionAppendix 1References |
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The following articles in journals at HighWire Press have cited this article:
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  J. Horsti, H. Uppa, and J. A Vilpo Poor Agreement among Prothrombin Time International Normalized Ratio Methods: Comparison of Seven Commercial Reagents Clin. Chem., March 1, 2005; 51(3): 553 - 560. [Abstract] [Full Text] [PDF]
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