Download Model for Breast Cancer Survival: Relative

(CANCER RESEARCH 48, 5565-5569, October 1. 1988]
Model for Breast Cancer Survival: Relative Prognostic Roles of Axillary Nodal
Status, TNM Stage, Estrogen Receptor Concentration, and Tumor Necrosis'
Lydia L. M. Shek and William Godolphin2
Department of Pathology; The University of British Columbia and Vancouver General Hospital, Vancouver, British Columbia, Canada V5Z 1M9
ABSTRACT
The independent prognostic effects of certain clinical and pathological
variables measured at the time of primary diagnosis were assessed with
Cox multivariate regression analysis. The 859 patients with primarybreast cancer, on which the proportional hazards model was based, had
a median follow-up of 60 months. Axillary nodal status (categorized as
No, NI.J or N4+)was the most significant and independent factor in overall
survival, but inclusion of TNM stage, estrogen receptor (ER) concentra
tion and tumor necrosis significantly improved survival predictions. Pre
dictions made with the model showed striking subset survival differences
within stage: 5-year survival from 36% (N4+, log,(ER| = 0, marked
necrosis) to 96% (No, logJER) = 6, no necrosis) in TNM I, and from 0
to 70% for the same categories in TNM IV. Results of the model were
used to classify patients into four distinct risk groups according to a
derived hazard index. An 8-fold variation in survival was seen with the
highest (>3) to lowest index values (< I ). Each hazard index level included
patients with varied combinations of the above factors, but could be
considered to denote the same degree of risk of breast cancer mortality.
A model with ER concentration, nodal status, and tumor necrosis was
found to best predict survival after disease recurrence in 369 patients,
thus confirming the enduring biological significance of these factors.
INTRODUCTION
Survival after primary breast cancer surgery has consistently
been found to be longer for patients with earlier clinical stage,
or absence of axillary nodal involvement, or ER3 positivity, or
better differentiated tumors. Although these findings are repro
ducible, the independence and relative importance of each pre
dictor is often obscured when un ivariate statistical methods are
used. Furthermore, univariate survival curves do not explain
why some patients, classified as prognostically favorable by one
of these factors, may experience early treatment failure or that
a substantial proportion of patients with axillary métastasesat
initial diagnosis remain recurrence free even 20 years later (1).
Such observations beg for improvement in identification of
subset prognostic factors.
A more comprehensive approach to survival prediction is the
formulation of risk models through multivariate regression
techniques. The Cox proportional hazards model is popular
because of its statistical sophistication and adaptability to cen
sored survival data (2). This technique facilitates the selection
of factors that independently influence survival from multiple
prognostic variables, some of which may be highly correlated.
The selection can be hierarchical, in terms of relative impor
tance, through the use of stepwise regression.
We undertook this study with objectives to derive a multivar
iate Cox model that incorporates only factors having independ
ent predictive value for risk of breast cancer mortality, to extend
the model to identify low- and high-risk groups, and to dem
onstrate the intrastudy consistency of this model. The strength
of the analysis is in the large sample size (n = 1184) with a
maximum follow-up of 10 years and availability of a relatively
extensive set of prognostic variables within the data base. Many
of these patients (n = 457) experienced a disease recurrence
which permitted investigation of an additional model specifi
cally related to postrecurrence prognosis.
MATERIALS
AND METHODS
Patients. The present series consists of women diagnosed with pri
mary breast cancer between 1975 and 1981 who were referred to the
Cancer Control Agency of British Columbia. During that time about
6000 patients were referred to the Agency. The studied group were
from a consecutive series of 1600 from which tumor was submitted for
measurement of ER. They were further selected by these criteria: valid
ER analysis on the primary tumor, known dates of diagnosis, and no
previous, concomitant, or later malignancy regardless of site (including
bilateral breast cancer) except nonmelanoma squamous cell and basal
cell carcinomas of the skin.
Postoperative follow-up of patients was regularly maintained by the
Agency or private physicians who corresponded through a standard
follow-up form. Patients were referred back to the Agency for evaluation
and therapy planning when recurrent disease was suspected or evident.
Confirmation of recurrence was obtained by histopathological diagnosis
of malignancy consistent with the primary tumor or through radiolog
ical scans. The medical records were reviewed up to the end of 1985.
The end point was death due to breast cancer as ascertained from death
certificates or autopsy reports. There were 486 deaths; 96 were not due
to breast cancer. Censored data include patients alive, with or without
evidence of disease, and dead from other causes (when the primary
cause of death as stated on death certificates or autopsy reports was
not breast cancer). Patients were considered lost to follow-up if there
was cessation of letter correspondence with the patients and if their
physicians had no contact with them for a long period of time. The
status of "lost to follow-up" was subsequently assigned when patient
contact was unsuccessful, even after information was sought from
known relatives, city or telephone directories, or vital statistics. In this
study approximately 3% of all patients not known to be dead at the
date of last contact were considered lost to follow-up; these data were
also censored.
Variables. The following patient and tumor characteristics were
tested in the Cox analysis.
Clinical TNM stage was assigned according to Union Internationale
Contre le Cancer criteria, based on complete information on size of
breast lump with or without fixation to underlying pectoralis muscle or
chest wall, palpability of axillary lymph nodes, and presence or absence
of distant spread as verified by metastatic work-up.
The number of axillary node métastasesfor patients who had an
axillary dissection was taken from the original pathology report and
was categorized as none (No), 1 to 3 nodes positive (Ni-j), and 4 or
more nodes positive (N4+). It was not possible to determine the mini
Received 1/29/88; revised 5/27/88; accepted 7/1/88.
mum number of nodes examined in each case; this information was not
The costs of publication of this article were defrayed in part by the payment
always recorded in a standard manner. However, the classification of
of page charges. This article must therefore be hereby marked advertisement in
negative nodes was made with confidence and an axillary dissection of
accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
' This research was supported by grants from the British Columbia Health
an average of 10 nodes was the usual practice among local surgeons.
Care Research Foundation and the British Columbia Cancer Foundation.
Microscopic examination of available nodal sections was routine.
2To whom requests for reprints should be addressed.
Tumors were analyzed for ER in a single laboratory by an established
3The abbreviations used are: ER, estrogen receptor; N0, 0 axillary nodes with
radioactive ligand binding method described in detail elsewhere (3-5).
cancer; NI_J, 1-3 axillary nodes with cancer; N«»,
4 or more axillary nodes with
Receptor concentration was uniformly expressed as fmol of bound
cancer.
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SURVIVAL MODEL FOR BREAST CANCER
estradici per mg of cytosol protein, corrected for serum protein accord
Statistical Analyses. The proportional hazards model was specified
ing to the recommendation of the European Organization for Research
by Cox (7) in the form:
on Treatment of Cancer (6). The lowest signal distinguishable from
H(t, x) = //»(r)exp (ß,x,
(A)
noise or background was about 1 fmol/mg; such results were designated
<1.
to model the effects of the ßs
upon the death (hazard) rate (//); where
The following histológica! features were assessed by the same pa
t
is
the
time
from
diagnosis,
A is a vector of prognostic variables
thologist on a section of the tumor specimen adjacent to that sent for
(covariates) x¡•
•
•
A,,and //¡>(f)
is an unknown base-line hazard function
ER assay: (a) histológica! type of the dominant growth pattern; (¿>)
when all covariates are equal to zero. The ßs
are unknown regression
degree of differentiation (well, moderate, or poor) in relation to the
coefficients estimated by maximizing the partial likelihood function
extent of tubule formation, nuclear pleomorphism, and mit otic activity;
based on conditional probability of failure. A positive coefficient de
(c) degree of confluent tumor necrosis (absent, minimal, or marked).
notes an increased risk of death with increased value of covariate; a
Tumor size as recorded in the pathology report was the largest
negative coefficient denotes the opposite effect.
diameter of the tumor.
Stepwise-up regression of all covariates selects first the single co
Age and menopausa! status were determined at the time of diagnosis.
variate
which produces the maximum likelihood, then adds the next
Patients were excluded from the regression analysis if any of the
above information was not available, resulting in 859 patients to be covariate which improves the likelihood of the preceding variable, and
proceeds in the same manner until further covariates cannot be added
studied. There was a significantly larger proportion of patients with
at a chosen significance level (e.g., 0.05).
advanced TNM stage in the excluded group (Table 1). These patients
ER data were used as the sole continuous variable after logarithmic
were most often excluded because an axillary dissection had not been
transformation. Categorical variables (Acategories) were dummy coded
done and hence pathological nodal status was unknown.
into k —1 strata (8). For example, with TNM I as a referent stratum,
The above variables were evaluated concomitantly with the effect of
SI is a dummy variable that assumes the value 1 for TNM II, 0
systemic treatment type given after relapse in a model of postrecurrence
otherwise;
S2 is another dummy variable that has a value of 1 for TNM
survival. Adjuvant systemic treatments were not considered in either
model of overall or postrecurrence survival since preliminary un ¡variate III, 0 otherwise; S3 is the final dummy variable with a value of 1 for
TNM IV and 0 otherwise. Both differentiation (0 = well or moderate,
analyses had shown they had little significant impact on survival. The
1 = poor) and necrosis (0 = absent or minimal, 1 = marked) were coded
major postrecurrence systemic treatment types for the 369 patients on
as
binary variables since preliminary analysis indicated no significant
which this model was based were: (a) cytotoxic chemotherapy if the
difference in survival between the combined subgroups.
patient had no or low ER, regardless of menopausa! status; (b) endo
The Cox proportional hazards models were generated with EPILOG
crine therapy by ovarian ablation in ER-positive premenopausal pa
(9). The predicted survival functions based on different covariate pat
tients and tamoxifen for ER-positive or ER-unknown postmenopausal
terns were obtained with the program RISK (10). Program P:2L of
patients; (c) both endocrine and cytotoxic chemotherapies given se
BMDP (11) was used to check the proportionality assumption of the
quentially.
model with stratification of covariates.
Table 1 Distribution of patients by characteristic at time of primary diagnosis
One or more data points considered for the stepwise regression analysis were
missing from the excluded group. The distribution of ER status is given in this
table: however, all statistical analyses were performed with the actual concentralion
infr»rmatir»nStudied
erouDVariableER
P"0.77
66
10456 34<0.00120
IIIIIIVNodesNoN,-JN*.Menopausal
11563517655448617833
402218
Four
riclr
COvariatCS
nf iTinrtillitv
were
shown
to be predictive
of the
Overall
anH i»Qr»h
f»r»nvpvi»H
r»rr»onnctir'
withthe from the others (Table 2). Nodal status associated
themodel
greatest likelihood value and hence was selected into
next;thefirst. TNM stage entered the regression equation
incremental coefficients reflect the detrimental effects of
increased stage at presentation. The negative coefficient
oflogf[ER]
increasingER
indicates the reduced risk associated with
concentration. The final variable selected was tumor necro
sis. Marked confluent necrosis was associated with a
greaterrisk
necrosis.Table
of mortality than minimal or no
grouDn199
status
ER positive (>10 fmol/mg)
fmol/mg)TNMI
ER negative (<10
RESULTS
0.994332250.7733670.3910
2 Final
proportionalhazards
step of stepwise regression analysis by the Cox
survivalOnly
models for overall and postrecurrence
status:PremenopausalPostmenopausalAge
included.The
cases with complete information on all studied variables were
regressioncoefficient
significance of the covariate level is indicated by a standardized
2.0corresponds
(estimated ßdivided by its standard error); a value greater than
(yr)<40
at diagnosis
roughly
(32).Variable
to P < 0.05 for a standard normal deviate
P"Overall
0«
0/SE
40-4950-5960-69a70Tumor
187238243100610249750109760851418062752%6832315511342342430701022282812712987138810221736Excluded
58718677183942453224325185413836%
182226240.5466341.0088120.5685960.09246016unique
859)Nodel
survival model (n =
statusN,-3
0.01N,*
0.47
2.65
differentiationWell
0.0001TNM
1.17
6.74
moderatePoorTumor
or
stageII
0.02III
0.41
2.31
necrosisAbsent/minimalMarkedHistological
0.0001IV
1.14
5.12
0.0001Log,
2.06
6.89
0.0001Necrosis
[ER]
-0.21
5.56
typeInfiltrative
0.001Postrecurrence
0.64
3.57
369)Log,
survival model (n =
ductalInfiltrative
<0.0001Nodal
[ER]
-0.23
6.08
lobularOthersTumor
statusN,_j
(cm)<22-5>5n582277266474952436528820625560491
size
0.005N.,»
0.52
2.83
<0.0001Necrosis
0.86
4.80
0.02" +
0.43
2.37
Estimated regression coefficient for each level of the covariate.
" xj for proportions.
Global x2 statistic that tests that all /3s = 0.
5566
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SURVIVAL MODEL FOR BREAST CANCER
Fig. 1 depicts the fitted statistical model which predicts the
probability of 5-year survival of an individual breast cancer
patient with a particular combination of the above four param
eters. The model permits prediction for any discrete time after
diagnosis. We chose the 5-year mark for illustration because
the 95% confidence intervals of estimates at this time were
relatively small, 5-year survival is of clinical interest and allows
comparison with other reports.
A counterbalance of the effects of these covariates on survival
can be seen. For example, a particular patient with TNM I,
N4+, ER = 400 fmol/mg and no tumor necrosis is predicted to
have similar survival to another with TNM I who has N0, but
ER = 1 fmol/mg and no tumor necrosis. Thus "high risk"
according to nodal status or TNM stage can be attenuated by
the presence of high ER concentration. The proportional ben
efit of high ER generally increases with increasing risk due to
other factors (Fig. 2).
A hazard index was calculated for each patient by log-linear
substitution of the obtained coefficients and covariate values.
For example a patient with NI_J, TNM II, log,.|I-'.K| = 3, and
no necrosis would have a hazard index equal to:
exp [0.47 + 0.41 + (-0.21)(3) + 0] = 1.28
Partition levels were set for even cut points after preliminary
examination of the data and four risk groups were formed. The
Kaplan-Meier plots of the observed survival represent the four
risk groups formed from the 859 patients grouped according to
a given range of hazard index (Fig. 3); the differences between
TNM II
100
r r
B
TNM III
TNM IV
"A
/VV»
ïïf
!!•
iff"/'//,"//ii;
Õ«
80
j
Õ.40
I il
20
Fig. 1. Predicted 5-year overall survival by simultaneous effects of nodal status,
TNM stage, ER concentration, and tumor necrosis. The pairs of Lines A, B, and
C designate patients with axillary' nodal status No, NT .. and N4.. respectively.
The upper of each pair designates absent or minimal tumor necrosis and the
lower designates marked tumor necrosis. Four ER concentrations (1, 7. ISO, and
400 fmol/mg), the break points on each line from lowest to highest, were
arbitrarily chosen to represent a wide range.
For example: patients with TNM I, N, . (group B), marked tumor necrosis
(the lower solid line of group B), and ER s l (lowest point on this line) would be
expected to have a 5-year survival of about 60%, which is a little less than those
patients with TNM III, N4»
(group C), minimal tumor necrosis (the upper dashed
line of group C), and ER = 400 (highest point on this line).
100
80
5«60
~ô
>
.1 40
Predicted1
20
123456789
1
l
l
l
l
l
1••
Years
Fig. 3. General model Tit: observed survival versus predicted survival as a
function of hazard index level. Each of the predicted curves represents the mean
hazard value for that category; for example, the upper curve represents a hazard
index of 0.62, which is the mean for the "<l" subgroup. The curves were
discontinued when fewer than 10 patients remained at risk in the observed survival
group.
them were highly significant (P < 0.0001). The following 5year survival was observed in each subgroup: (a) hazard index
<1 (n = 366): 91%; (*) hazard index = 1.00-1.99 (n = 256):
79%; (c) hazard index = 2.00-2.99 (n = 97): 65%; (d) hazard
index>3(/i=
140): 43%.
The goodness of fit of the model was tested graphically by
comparison of the observed survival curves defined by hazard
indices with predicted survival curves (Fig. 3). The latter curves
are Kaplan-Meier plots of the expected survival, as predicted
from the model, of any patient with a hazard index that is the
mean value of the corresponding range. If the derived model is
an accurate reflection of true survival experience of a large
group of breast cancer patients, then these predicted survival
curves (assuming the mean of a given range is its most repre
sentative value) should be reasonably close to the observed
curves. The most desirable test of this model would, of course,
be a prospective analysis of an independent group.
The basic proportionality assumption of the Cox model states
that the relationship between the underlying hazard function
and the covariates is multiplicative as shown in Equation A.
This was supported by nearly constant differences of the log
(—logsurvival) curves between strata of a covariate, specified at
the mean of the other covariates (data not shown) (12, 13).
Furthermore, interaction terms composed of the cross-products
among all terms in the model were tested when the main factors
(nodal status, TNM stage, ER, and necrosis) were in the model.
None of the interaction terms contributed significantly to the
prediction, indicating that the effect of one covariate does not
depend on the value of another.
A model consisting of only three covariates was found to best
explain variation in survival after first recurrence (Table 2).
These covariates, in order of decreasing importance, were ER
concentration in the primary tumor, pathological nodal status
at the time of primary diagnosis, and tumor necrosis (Fig. 4).
DISCUSSION
TNM I
TNM
TNM
TNM IV
Fig. 2. Relative gain in predicted 5-year survival as a consequence of high ER
concentration (400 fmol/mg) compared to negative ER (l fmol/mg), in cases
with no necrosis.
A multivariate approach was used in this study to identify
relevant and independent factors measurable at diagnosis that
could be used to model risk of breast cancer mortality. Four
such factors emerged as the best combination; in descending
order of importance they were: number of involved axillary
nodes, TNM stage, ER concentration, and extent of tumor
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SURVIVAL MODEL FOR BREAST CANCER
lOOr
N0
N13
80
60
40
20
Fig. 4. Predicted 5-year postrecurrence survival by simultaneous effects of ER
concentration, nodal status, and tumor necrosis. The upper of each pair designates
absent or minimal tumor necrosis and the lower designates marked tumor necro
sis. Four ER concentrations (1, 7, ISO, and 400 fmol/mg), the break points on
each line from lowest to highest, were arbitrarily chosen to represent a wide range.
necrosis. The incorporation of these factors in the final model
obviated the prognostic information provided by other covariates we studied, since the effect of other factors has already
been explained by one or more of the chosen covariates.
The Cox proportional hazards model has been used by others
to correlate predictive factors and survival with breast cancer.
The prognostic usefulness of ER status in addition to tumor
stage, axillary node metastasis, and histopathological grade has
been reported (14). Russo et al. (15) showed improved survival
predictions when nodal status, tumor size, and grade and ER
status were combined. Haybittle et al. (16) found that the
inclusion of tumor grade or ER status in a similar model was
mutually exclusive, such that omission of either factor in the
analysis permitted the inclusion of the other. Our prediction
model was based on a large number of patients with long followup, and we studied the quantitative effects of ER together with
its strong correlates such as tumor differentiation and tumor
necrosis. We observed that the effect of tumor differentiation
was overwhelmed when examined in this context.
There is firm agreement among studies pointing to axillary
nodal involvement as the single most important predictor (17).
In many treatment protocols métastasesin axillary nodes war
rant the institution of systemic adjuvant therapy. However,
considerable prognostic heterogeneity within nodal categories
may result in overtreatment when the sole criterion for adjuvant
therapy is the presence of lymph node métastases(18). Adjuvant
therapy is clearly indicated in patients who are considered high
risk, but there is a need to agree upon the definition of high
risk (19). It is evident from this study that high risk is a
composite of characteristics. Despite the inherent unreliability
of clinical assessment of regional lymph node involvement (20)
TNM stage was found to be independently important in con
veying the severity of this risk. There is general consensus on
the clinical importance of ER status of the primary tumor, and
we have shown that there is a quantitative relationship with
prognosis (21).
Survival predictions based on this model suggest that the
more ER present in the primary tumor, the greater the prog
nostic improvement in patients with dire features of advanced
stage disease. Therefore a high-risk patient, by the criterion of
advanced TNM stage or node positivity, may be considered to
have reduced her risk by virtue of high ER concentration in the
tumor. It is possible that there is an ER threshold beyond which
there is a weaker or no influence on survival. However, when
patients were grouped according to ER in the high range, i.e.,
>250 fmol/mg, there was clear survival advantage to the higher
ER levels. Thus if such a threshold does exist it would occur in
the very high positive range.
The positive influence of high ER concentration was also
expressed as a reduced risk of death after disease recurrence.
This favorable effect was not dependent on the mode of systemic
therapy (22), but appears to be an independent manifestation
of the generally better differentiation (23) and slower growth
rate of these tumors (24).
Although not commonly emphasized, the aggressive nature
of tumors with marked necrosis was reported by Fisher et al.
(25) some time ago. They found that the presence of necrosis
influenced treatment failure independent of pathological nodal
status, tumor size, and histológica! grade. We found that tumor
necrosis was the only histopathological feature of the primary
tumor with enduring biological influence beyond recurrence.
A hazard index is a convenient measure of the summed risk
estimate for a patient with a particular set of predictors. The
concept of one covariate compensating for the hazardous effect
of the others may be illustrated with this index. Each of the
four hazard categories in Fig. 4 is defined by a range of hazard
index values. Patients who have different patterns of the four
covariates may have the same hazard index and hence be
considered to have the same degree of risk.
We believe that the four factors identified in this study
represent different aspects of the complex interactions between
host and tumor and reflect biologically significant characteris
tics of breast cancer, although the underlying precise mecha
nisms remain speculative. The presenting TNM stage indicates
the anatomical progression of the disease, as well as signals a
permissive environment that allows full expression of tumor
invasive properties. The host may also provide facilitative con
ditions for tumor expression of metastatic properties, such as
changes in cell surface chemistry associated with loss of cell
adhesiveness (26), increased tumor cell mot ¡lily,and production
of active proteolytic enzymes that render basement membranes
defective (27). These are some features of biologically aggressive
tumors that predispose to involvement of axillary nodes. They
do not appear to be a function of time (28). Greater malignancy
of ER- tumors is consistent with their increased secretion of
autocrine and paracrine growth factors such as insulin-like
growth factor, transforming growth factors (a and ß),and a
competence factor (29). In addition, there is a link among
growth factors, steroid hormones, and their receptors and on
cogene products (30). Vascular insufficiency, as one result of
rapid tumor growth rate, is a possible cause of tumor necrosis.
This hypothesis is consistent with the significant associations
found between tumor necrosis and ploidy or the mean fraction
of cells engaged in DNA synthesis (24).
The ascertainment of pathological nodal involvement, TNM
stage, ER concentration, and tumor necrosis is feasible at
primary diagnosis. Assessment of just these four parameters
appears to enable fairly accurate prediction of the long-term
outlook for individual patients. This in turn allows the clinician
to recognize the heterogeneous prognoses of patients at any
presentation stage of disease, and may help in the selection of
specific therapies, design of overall treatment strategies (31),
and more uniform stratification for trials.
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SURVIVAL MODEL FOR BREAST CANCER
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Model for Breast Cancer Survival: Relative Prognostic Roles of
Axillary Nodal Status, TNM Stage, Estrogen Receptor
Concentration, and Tumor Necrosis
Lydia L. M. Shek and William Godolphin
Cancer Res 1988;48:5565-5569.
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