Clinical Chemistry 46: 939-949, 2000;
(Clinical Chemistry. 2000;46:939-949.)
© 2000 American Association for Clinical Chemistry, Inc.
Progression Criteria for Cancer Antigen 15.3 and Carcinoembryonic Antigen in Metastatic Breast Cancer Compared by Computer Simulation of Marker Data
György Sölétormos1,2,3,a,
Per Hyltoft Petersen4 and
Per Dombernowsky2
Departments of
1
Clinical Biochemistry and
2
Oncology, Herlev Hospital, University of Copenhagen, 2720 Copenhagen, Denmark.
3
Department of Clinical Biochemistry, Hillerød Hospital,
DK 3400 Hillerød, Denmark.
4
Department of Clinical Biochemistry, Odense University
Hospital, 5000 Odense, Denmark.
a Address correspondence to this author at: Department of Clinical Biochemistry, Hillerød Hospital, Helsevej 2, DK 3400 Hillerød, Denmark. Fax 45-48-24-00-67; E-mail geso{at}fa.dk
 |
Abstract
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Background: We investigated the utility of computer simulation
models for performance comparisons of different tumor marker assessment
criteria to define progression or nonprogression of metastatic breast
cancer.
Methods: Clinically relevant values for progressive cancer
antigen 15.3 and carcinoembryonic antigen concentrations were combined
with representative values for background variations in a computer
simulation model. Fifteen criteria for assessment of longitudinal tumor
marker data were obtained from the literature and computerized.
Altogether, 7200 different patients, each based on 50 measurements,
were simulated. With a sampling interval of 4 weeks, the monitoring
period for each event was ~3.8 years.
Results: Modulation of the background variation, the starting
concentrations, and the cutoffs enabled identification of criteria that
were robust against false-positive signals of progression.
Conclusions: The computer simulation model is a fast, effective,
and inexpensive approach for comparing the diagnostic potential of
assessment criteria during clinically relevant conditions of
steady-state and progressive disease. The model systems can be used to
generate tumor marker assessment criteria for a variety of malignancies
and to compare and optimize their diagnostic performance.
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Introduction
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The potential roles of the serological tumor markers cancer
antigen 15.3 (CA
15.3)1
and carcinoembryonic antigen (CEA) in monitoring patients with
metastatic breast cancer have been the subject of several studies
(1)(2)(3). Their usefulness depends on their ability to
identify, predict, and exclude tumor growth before the changes are
detectable by other methods. The exact clinical applications, however,
are still unclear because of uncertainty in the interpretation of
sequential concentrations (4). However, recent studies have
suggested that the magnitude of any changes in concentration as well as
the upper reference limits or other cutoff values should be integrated
into tumor marker-based decision limits (5). The purpose of
the present study was to investigate whether computer simulation of CA
15.3 and CEA data could be used to compare the diagnostic performance
of different criteria in terms of progression. Descriptive parameters
of patient-related marker data were integrated into the simulation
procedure according to the desired clinical and laboratory situation.
Software programs for monitoring of tumor marker increments in breast
cancer were developed on the basis of previously published assessment
criteria. The criteria were compared in a variety of simulated
conditions of steady-state and progressive disease.
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Materials and Methods
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design of the database
The Corel Quattro Pro 8.0 software package was used for data
generation and calculations. The first step was to generate four data
sections with steady-state data. Each section comprised simulations of
100 different patients, each with 50 measurements. The data in all four
sections were characterized by the same variability in terms of the
total CV (CVT), although the generated numbers
differed among the simulated patients. In the next step, the
steady-state data in three of the sections were combined with
increasing values representing tumor growth.
criteria for monitoring sequential tumor marker concentrations
The algorithms were computerized and classified according to their
characteristics as shown in
Figs. 1–4
(5)(6)(7)(8)(9)(10)(11)(12)(13). The criteria were based on at least two or
three measurements; however, the maximum number of measurements and/or
the maximum considered time span remained unreported. The increments
associated with metastatic growth fulfilled criteria for progression
among patients within ~6 months after exceeding the baseline value
(5)(14). For the sake of comparison, the
observation window for each criterion used in the simulation model was
therefore set to ~6 months (28 weeks). The tested concentration,
which represented either the latest or the second latest determination,
was compared with a maximum of seven or six previous concentrations,
respectively. The observation window then moved to the next
measurement, which now became the latest, and the first measurement
from the previous observation period was disregarded. The procedure was
repeated until all 50 marker determinations were scanned for
progression by the respective criteria.
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Figure 1. Criteria based on at least two measurements to assess
sequential tumor marker concentrations that start below cutoff.
Points connected by dashed lines indicate measurements
that are not necessarily consecutive. Points connected by solid
lines indicate consecutive measurements. CD,
required critical difference. *, recommended cutoff; **,
recommended cutoff x 3.8 (Table 1
). (A),
the criterion is based on at least two measurements. The latest
concentration, which is below or above the recommended cutoff, is at
least 25% higher than any previous concentration below cutoff
[Dnistrian et al. (6)]. (B), the
criterion is based on two consecutive measurements. The latest
concentration is above and the second latest is below the recommended
cutoff without requirements for the magnitude of the difference in
concentrations [Barak et al. (7)].
(C), the criterion is based on at least two
measurements. The latest concentration is above the recommended cutoff
and at least 25% higher than any previous concentration below cutoff
[Tondini et al. (8)]. (D), the
criterion is based on at least two measurements. The latest
concentration is above the recommended cutoff and is twice that of any
previous concentration below cutoff [Sölétormos et al.
(5)]. (E), the criterion is based
on at least two measurements. The latest concentration is 3.8 x
above the recommended cutoff and significantly higher than any previous
concentration below cutoff [Sölétormos et al.
(5)].
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Figure 2. Criteria based on at least three measurements to assess
sequential tumor marker concentrations that start below cutoff.
Solid lines between points indicate consecutive
measurements. Points connected by dashed lines indicate
measurements that are not necessarily consecutive. CD,
critical difference between concentrations; *, recommended cutoff;
**, recommended cutoff x 2 (Table 1
).
(A), the criterion is based on three consecutive
measurements and two consecutive increments without requirement for the
magnitude of the difference in concentrations. The third latest
concentration is below the recommended cutoff. The second latest and
the latest concentrations are below, above, or on different sides of
the recommended cutoff [Bonfrer (9)].
(B), the criterion is based on at least three
measurements. The latest concentration is higher than the second latest
concentration without requirements for the magnitude of the difference.
The second latest concentration is at least 25% higher than any
previous concentration below the recommended cutoff. The second latest
and the latest concentrations are below, above, or on different sides
of the recommended cutoff [Bonfrer (9)].
(C), the criterion is based on three consecutive
measurements and two consecutive increments. The latest concentration
is at least 12% higher than the second latest concentration. The
second latest concentration is at least 12% higher than the third
latest concentration. The third latest concentration is below the
recommended cutoff. The second latest and the latest concentrations are
below, above, or on different sides of the recommended cutoff [Mughal
et al. (10)]. (D), the criterion
is based on three consecutive measurements. The latest and the second
latest concentrations are above and the third latest concentration is
below the recommended cutoff. The latest concentration is at least 30%
higher than the second latest concentration. There is no requirement
for the magnitude of the difference between the second and the third
latest concentrations [Nicolini et al. (11)].
(E), the criterion is based on three consecutive
measurements. The latest and second latest concentrations are above and
the third latest concentration is below two times the recommended
cutoff. The latest concentration may be higher, equal to, or lower than
the second latest concentration. There is no requirement for the
magnitude of the difference between the second and the third latest
concentrations [Molina et al. (12)].
(F), the criterion is based on at least three
consecutive measurements. The latest and the second latest
concentrations are above the recommended cutoff. The latest
concentration is higher than the second latest concentration, and the
second latest concentration is higher than the third latest
concentration. There is no requirement for the magnitude of the
difference between the latest and the second latest concentrations. The
second latest concentration is significantly higher than the third
latest or any previous concentration below cutoff
[Sölétormos et al. (5)].
(G), the criterion is based on three consecutive
measurements. The latest and second latest concentrations are above and
the third latest concentration is below the recommended cutoff. The
latest concentration may be higher, equal to, or lower than the second
latest concentration. There is no requirement for the magnitude of the
difference between the second and the third latest concentrations
[Chan et al. (13)].
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Figure 3. Criteria based on at least two measurements to assess
sequential tumor marker concentrations that start above cutoff.
Points connected by dashed lines indicate measurements
that are not necessarily consecutive. CD, required
critical difference between concentrations. *, recommended cutoff
(see Table 1
). (A), the criterion is based on
at least two measurements. The latest concentration is at least 25%
higher than any previous concentration above the recommended cutoff
[Dnistrian et al. (6)]. (B), the
criterion is based on at least two measurements. The latest
concentration is significantly higher than any previous concentration
above the recommended cutoff [Sölétormos et al.
(5)]. (C), the criterion is based
on at least two measurements. The latest concentration is twice that of
any previous concentration above the recommended cutoff
[Sölétormos et al. (5)].
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Figure 4. Criteria based on at least three measurements to assess
sequential tumor marker concentrations that start above cutoff.
Solid lines between points indicate consecutive
measurements. Points connected by dashed lines indicate
measurements that are not necessarily consecutive. CD,
required critical difference between concentrations. *, recommended
cutoff (see Table 1
). (A), the criterion is
based on three consecutive measurements and two consecutive increments
above the recommended cutoff without requirements for the magnitude of
the difference in concentrations [Bonfrer (9)].
(B), the criterion is based on at least three
measurements. The latest concentration is higher than the second latest
concentration without requirements for the magnitude of the difference.
The second latest concentration is at least 25% higher than any
previous concentration above the recommended cutoff [Bonfrer
(9)]. (C), the criterion is based
on three consecutive measurements and two consecutive increments above
the recommended cutoff. The latest concentration is at least 12%
higher than the second latest concentration. The second latest
concentration is at least 12% higher than the third latest
concentration [Mughal et al. (10)].
(D), the criterion is based on at least three
consecutive measurements. The latest concentration is higher than the
second latest concentration, and the second latest concentration is
higher than the third latest concentration. There is no requirement for
the magnitude of the difference between the latest and the second
latest concentrations and between the second and the third latest
concentrations. The latest concentration is significantly higher than
the third latest or any previous concentration above the recommended
cutoff [Sölétormos et al. (5)].
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The criteria developed by Sölétormos et al. (5)
differed from the others because the assessment procedure
(a) involved two sets of criteria for CA 15.3 and CEA
concentrations, one set to identify slow rise and another to identify
fast rise kinetics; (b) considered whether concentrations
started below or above the cutoff value; (c) integrated the
cutoff value in the procedure for assessment of below-cutoff
concentrations; and (d) ensured that an increment was
significant before it was interpreted as indicative of progression.
Accordingly, a change was significant if the difference, expressed as a
percentage of the mean value, exceeded
2 · Z · CVT
(15), where 2 is a constant (for two measurements) and
the Z-statistic depends on the probability selected for
significance and on whether the expected change is uni- or
bidirectional. A unidirectional change (increment) was expected if
concentrations were increased at a steady state or were below the
cutoff value; Z = 1.65 for P <0.05.
CVT was equal to the average within-subject total
variation determined among healthy females and comprised the analytical
imprecision and the within-subject biological variation,
~13% for CA 15.3 and CEA (16).
simulation of cutoffs and starting concentrations
The performance of criteria at different concentrations and
cutoffs was investigated by changing the cutoff/starting concentration
ratio. The ratio standardized the number of times the cutoff value
exceeded a given starting concentration (Table 1
).
variation of steady-state concentrations
The CVTs of the generated data represented the 5th,
50th, and 95th centiles of variations observed among metastatic breast
cancer patients (14). The CVT comprised the
analytical imprecision and the within-subject biological variation and
was higher below than above the cutoff. For concentrations below the
cutoff, the steady-state CVTs for CA 15.3 and CEA were
8.5% (5th centile), 15% (50th centile), and 36% (95th centile).
Above cutoff, the CVTs were 3.1% (5th centile), 7.9%
(50th centile), and 17% (95th centile).
simulation of patients in steady state
Recent clinical studies have suggested a gaussian distribution of
steady-state tumor marker data; however, unusually large increments may
occur (16). Therefore, the generated numbers, which
represented natural logarithmic data with a mean value of zero and a
gaussian distribution, were transformed to a log-gaussian distribution.
The procedure made the steady-state concentrations unitless with a mean
of 1.0 for all individuals. Keeping a low mean value of the
gaussian-distributed numbers facilitated specification of the magnitude
of the desired fluctuations by the standard deviation of natural
logarithm values instead of the CV of concentration data because they
were nearly identical for small values (<0.15) and close for moderate
values (up to ~0.30) (17)(18). To ensure that
the first value was below the cutoff point when the lowest
cutoff/starting concentration ratio of 1.1 (Table 1
) was applied, all
values were set to start at 1.099.
rate of increase of progressive concentrations
The rates of the increases in CA 15.3 and CEA per day attributable
only to tumor growth, without contribution from background variation,
that are characteristic for metastatic breast cancer have been provided
as natural logarithm-transformed data (14). The rate
constants were 0.0083 (5th centile), 0.0210 (50th centile), and 0.0706
(95th centile).
simulation of patients with progression
The natural logarithm-based rate constants were transformed to
exponential functions and added to the normalized steady-state
concentrations. To ensure a low starting point with a reasonable
increase for even the slowest rate constants, the starting addition of
marker from the tumor was set to 10% of the normalized mean.
performance comparison of assessment criteria
The performance parameters of the criteria were (a) the
cumulated false-positive fraction, which denoted the cumulated number
of events with at least one increment falsely interpreted as
progression during steady state; (b) the cumulated
true-positive fraction, which denoted the cumulated number of
progressive events with at least one increment interpreted as
progression; and (c) the measurement number that
corresponded to either the cumulated false-positive or true-positive
fraction. The principles for cumulation of positive results are
illustrated in Fig. 5
.
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Figure 5. Principles for cumulation of positive signals of tumor
marker progression.
For each simulated event, the investigated algorithm was applied to the
concentration values in sequence of increasing sample number. The first
time the requirement for progression was fulfilled, the event was
considered positive at this sample number. The first positive signal of
progression was cumulated from all events. For the sake of clarity and
space, only data obtained from the first 20 measurements are shown. The
positives (%) cumulated from events with a rate constant of 0.0000
represented the false-positive signals of progression, and those
cumulated from events with rate constants of 0.0083, 0.0210, and 0.0706
represented the true-positive signals of progression. A cumulated
positive fraction of 50% means that one-half of the events were
recorded as positive at that time, and 1.0 means that all patients
fulfilled the specified criterion for progression. In the example, 23%
of steady-state events were falsely interpreted as progression. One
hundred percent of events with a rate constant of 0.0083 were
identified at the 19th measurement, and those with a rate constant of
0.0210 and 0.0706 at the 8th and 3rd measurement, respectively. Each
simulated event comprised 50 measurements. With a sampling interval of
4 weeks, the monitoring period was 196 weeks (~3.8 years).
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Results
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performance of assessment criteria when tumor marker concentrations
started in the middle of the reference interval
Performance for the CA 15.3-CEA data is shown in Table 2
. The background variation had considerable influence on the
frequency of false-positive signals because larger fluctuations pushed
the increase above the cutoff value. For the criterion in Fig. 2A
, the
susceptibility to fluctuations was independent of background variation
because the criterion considered neither a critical difference nor a
cutoff value. The ability to detect true-positive signals of
progression depended on the rate of marker increase, the required
critical difference, and the applied cutoff value. Progressive
concentrations with a slow rate of increase were detected earlier if
the required difference was small and the cutoff value was low. At
medium and fast rate constants, the increments were so large that any
of the required changes were reached early. The background variation
had little influence on the frequency of true-positive signals because
almost all criteria identified 100% of progressions irrespective of
the CVT. The background variation, however,
influenced the time of detection of marker progression, especially for
slow rate constants. Marker kinetics with faster rate constants were
influenced less by background fluctuations. The two consecutive
increments required in Fig. 2A
were mostly delayed because the
criterion derived no advantage from larger increments. The
CVT-induced smaller increments were still large
enough to meet the required change in Fig. 1A
within the accepted time
interval, whereas the change required in Fig. 2F
was not always met.
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Table 2. Diagnostic performance of assessment criteria if CA
15.3-CEA concentrations start in the middle of the reference
interval.1
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The criterion in Fig. 2D
was the only criterion where the background
variation influenced the frequency of true-positive signals. At slow
rate constants and low CVT values, none of the
progressing concentrations increased by 30%, whereas some exceeded the
critical difference at higher CVT values. At
medium rate constants and low CVT values, several
of the increments exceeded the required difference of 30%. The
frequency of true-positive signals diminished with a higher
CVT because several increments were impeded by
more fluctuations and because the CVT-induced
increments did not exceed the required change. At fast rate constants
and low CVT values, the critical difference of
30% was easily met. A few fluctuations associated with a higher
CVT were large enough to reduce the increment to
below 30%.
performance of assessment criteria when tumor marker concentrations
started high vs low in the reference interval
All criteria subjected to further investigation for robustness
against false-positive signals integrated a cutoff value in the
assessment procedure (Table 3
). Three criteria remained free of false-positive CA 15.3-CEA
signals. Assessment criteria based on higher cutoff concentrations
(Fig. 1E
and Fig. 2E
) allowed fewer false positives than those with
lower concentrations (Fig. 2
, F and G). All false progressions were
obtained when marker concentrations fluctuated in the high end of the
reference interval, and the frequency of false signals
increased with larger fluctuations. The criterion in Fig. 2D
remained
robust against false-positive information even at a low cutoff
concentration because an increase from below to above cutoff was
confirmed by a consecutive large (30%) increment. When the starting
value was lowered, the progressing concentrations rose more steeply
with smaller fluctuations when they left the reference
interval; however, detection was delayed because the time
needed to reach the cutoff was extended. The criterion in Fig. 2F
did
not detect all progressions if concentrations started high in the
reference interval because they increased too slowly after crossing the
cutoff to meet the required critical difference within the accepted
time limit. An unexpected result was that the criterion in Fig. 2F
at
high CVT signaled CA 15.3-CEA progression more
frequently for steady-state concentrations that started just below
cutoff and continuously fluctuated across the cutoff than for
concentrations with a slow rate of increase (0.0083). The progressing
concentrations had fewer below-cutoff fluctuations with fewer starting
points for tumor marker assessment when compared with the steady-state
fluctuations.
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Table 3. Diagnostic performance of assessment criteria if CA
15.3-CEA concentrations start high vs low in the reference
interval.1
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At a slow rate of CA 15.3-CEA increase, the criterion in Fig. 2D
identified more true positives at high compared with low starting
concentrations. Marker values that started high in the reference
interval fluctuated several times across the cutoff, with more set
points for starting concentrations and increased possibilities of
meeting the specifications of the criterion than marker values with low
starting concentrations that fluctuated across the recommended cutoff
within a shorter time interval. The reverse applied for medium and fast
rate constants because most of the simulated patients showed steep
tumor marker increases over consecutive increments by the time the
tumor marker reached the cutoff from low starting concentrations.
performance of assessment criteria when tumor marker concentrations
started above the reference interval
The performance for the CA 15.3-CEA data is shown in Table 4
. Background variation had a considerable effect on the
frequency of false-positive signals among criteria based on a critical
difference. The criterion in Fig. 3C
supplied fewer false positives
than the criterion in Fig. 3B
because a doubling in concentrations was
a greater requirement than a significant increment.
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Discussion
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Our data suggest a considerable potential for computer simulation
models because a large variety of clinically relevant tumor marker
kinetics can be simulated and the diagnostic ability of criteria can be
compared. The ability to identify and exclude tumor marker progression
depended on the characteristics of the individual criterion (the number
of considered measurements, the required percentage of change, and the
applied cutoff) and on the characteristics of the sequential data (the
starting concentration, the background variation, and the rate of
increase of progressing concentrations). Criteria that considered the
cutoff value and adjusted the critical difference to the background
variation of the investigated marker performed better than criteria
where these parameters were not included.
The model system was a fast approach for comparison of the diagnostic
potential of assessment criteria. It took a few months to
develop the model, but it would have taken a large multicenter study
several decades to generate the same amount of data. The model was
effective because the robustness against false-positive signals and the
ability to detect progression could be determined in detail in a
variety of situations. The computer simulation was also inexpensive:
our only investment was $250 US for a 10-gigabyte hard drive, whereas
measurements of CA 15.3 and CEA in a similar clinical trial would cost
millions of US dollars.
Computer-aided test selection and result validation will undoubtedly
become more integrated in clinical biochemistry (19).
However, in spite of the obvious advantages, this is the first tumor
marker study based on simulated data. The reason is that the
information necessary to generate clinically relevant models has only
recently become available (14)(16). All of the
criteria compared in the present report have been used for patient
monitoring (5)(6)(7)(8)(9)(10)(11)(12)(13); however, it remains unknown how they
perform under different conditions, i.e., another patient population
with different (a) starting concentrations at the initiation
of monitoring, (b) background fluctuations of the analytical
and biological variation components, and (c) rates of marker
increase during progression. Here we compared the criteria when the
above-mentioned parameters were standardized and changed according to
the simulated clinical and laboratory situations. The study that
provided the most detailed information on the diagnostic performance of
the applied criteria as well as on the time interval for detection of
progression was published by Sölétormos et al.
(5). The authors used the criteria in Fig. 1
, D and F, for
assessment of the CA 15.3-CEA concentrations that started above cutoff,
and the criteria in Fig. 3C
and Fig. 4D
for below-cutoff starting
concentrations. The date of marker progression was attributed to the
algorithm that first signaled the progression. The criteria detected
clinical progression with a median lead time of 36 days during
first-line chemotherapy for metastatic breast cancer and 76 days during
subsequent follow-up. We used the very same criteria in our simulations
as a reference against which other criteria from the same authors as
well as criteria from other authors were compared.
In reviewing the simulated below-cutoff data in Table 2
, the
performance of the criteria in Fig. 1E
[Sölétormos et al.
(5)], Fig. 2E
[Molina et al. (12)], and Fig. 2G
[Chan et al. (13)] may appear as reliable as the
criterion in Fig. 2F
, [Sölétormos et al. (5)].
All three criteria had a similar high sensitivity for progression
without any false-positive signals. However, identification of
progression was delayed for several weeks with the criteria in Fig. 1E
[Sölétormos et al. (5)] and Fig. 2E
[Molina
et al. (12)] compared with the criterion in Fig. 2F
[Sölétormos et al. (5)]. Further
investigations disclosed that the criterion in Fig. 2E
[Chan et al.
(13)] produced numerous false-positive signals even with
small fluctuations in steady-state concentrations closely below the
cutoff, whereas the criterion in Fig. 2F
[Sölétormos et
al. (5)] provided false-positive information mainly for
unusually large fluctuations (Table 3
).
In reviewing the above-cutoff data in Table 4
, the three criteria that
supplied false-positive CA 15.3-CEA concentrations less frequently were
those provided in Fig. 3C
[Sölétormos et al.
(5)], Fig. 4C
[Mughal et al. (10)], and Fig. 4D
[Sölétormos et al. (5)]. However,
identification of progression was delayed for several months with the
criterion in Fig. 4C
[Mughal et al. (10)] compared with
the criteria in Fig. 3C
and Fig. 4D
[Sölétormos et al.
(5)]. The criteria in Fig. 3C
and Fig. 4D
[Sölétormos et al. (5)] provided
false-positive information mainly for unusually large fluctuations.
Overall, the criteria developed by Sölétormos et al.
(5), as shown in Fig. 2F
and Fig. 4D
, performed best because
signals of progression were detected early; however, sequential
concentrations with unusually large fluctuations should be interpreted
with caution. Thus, computer-simulated data should be used to
investigate whether the criteria can be further optimized without
delaying detection of early signals of tumor growth. We hypothesize
that assessment of sequential marker concentrations should be more
differentiated than hitherto recognized. It may not suffice to base
interpretation on concentrations being within or above the reference
interval. Assessment of data within the normal range should
probably depend on the baseline concentrations.
In conclusion, our results suggest that the simulation model
presented here may be applied to the development of new tumor marker
assessment criteria and to optimize already existing criteria.
Assessments of sequential data probably will benefit from a
differentiated approach where different criteria are combined depending
on the baseline concentrations. When data defining steady-state
variability and rates of increase are available, the model systems
could be applied to malignancies other than breast cancer.
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Footnotes
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1 Nonstandard abbreviations: CA 15.3, cancer antigen 15.3; CEA, carcinoembryonic antigen; and CVT, total CV, comprising the analytical imprecision and the within-subject biological variation. 
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Abstract
Introduction
