Analysis of breast cancer related gene expression using natural splines and the Cox proportional hazard model to identify prognostic associations.

Abstract

Many studies correlating gene expression data to clinical parameters assume a linear increase or decrease of the clinical parameter under investigation with the expression of a gene. We have studied genes encoding important breast cancer-related proteins using a model for survival-type data that is based on natural splines and the Cox proportional hazard model, thereby removing the linearity assumption. Expression data of 16 genes were studied in relation to metastasis-free probability in a cohort of 295 consecutive breast cancer patients treated at The Netherlands Cancer Institute. The independent predictive power for disease outcome of the 16 individual genes was tested in a multivariable model with known clinical and pathological risk factors. There is a linear relationship between increasing expression and a higher or lower hazard for distant metastasis for ESR1, ERBB4, VEGF, CCNE2, EZH2, and UPA; for ERBB2, ERBB3, CCND1, CCNE1, EED, CXCR4, CCR7, SDF1, and PAI1 there is no clear increase or decrease; and for EGFR there seems to be a non-linear relation. Multivariable analysis showed that the 70-gene prognosis profile outperforms all the other variables in the model (hazard-rate 5.4, 95% CI 2.5-11.7; P = 0.000018). EGFR-expression seems to have a non-linear relation with disease outcome, indicating that lower but also higher expression of EGFR are associated with worse outcome compared to intermediate expression levels; the other genes show no or a linear relation.

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PRECLINICAL STUDY
Analysis of breast cancer related gene expression using natural
splines and the Cox proportional hazard model to identify
prognostic associations
Bas Kreike•Guus Hart•Harry Bartelink•
Marc J. van de Vijver
Received: 15 September 2009/Accepted: 8 October 2009/Published online: 27 October 2009
? Springer Science+Business Media, LLC. 2009
Abstract
to clinical parameters assume a linear increase or decrease
of the clinical parameter under investigation with the
expression of a gene. We have studied genes encoding
important breast cancer-related proteins using a model for
survival-type data that is based on natural splines and the
Cox proportional hazard model, thereby removing the
linearity assumption. Expression data of 16 genes were
studied in relation to metastasis-free probability in a cohort
of 295 consecutive breast cancer patients treated at The
Netherlands Cancer Institute. The independent predictive
power for disease outcome of the 16 individual genes was
tested in a multivariable model with known clinical and
pathological risk factors. There is a linear relationship
between increasing expression and a higher or lower haz-
ard for distant metastasis for ESR1, ERBB4, VEGF,
CCNE2, EZH2, and UPA; for ERBB2, ERBB3, CCND1,
CCNE1, EED, CXCR4, CCR7, SDF1, and PAI1 there is no
clear increase or decrease; and for EGFR there seems to be
a non-linear relation. Multivariable analysis showed that
the 70-gene prognosis profile outperforms all the other
variables in the model (hazard-rate 5.4, 95% CI 2.5–11.7;
Many studies correlating gene expression data
P = 0.000018). EGFR-expression seems to have a non-
linear relation with disease outcome, indicating that lower
but also higher expression of EGFR are associated with
worse outcome compared to intermediate expression lev-
els; the other genes show no or a linear relation.
Keywords
data ? Natural spline analysis ? Cox proportional hazard
analysis ? Distant metastasis-free probability
Breast cancer ? Microarray gene expression
Introduction
Gene expression profiling by microarray analysis in human
cancer has proven to be a powerful tool to identify novel
prognostic and predictive factors. Several studies have used
microarray analysis to generate expression profiles pre-
dicting disease outcome, using unsupervised hierarchical
clustering and supervised methods of analysis [1–10]. Until
now, little attention is given to the exact nature of the
relation between expression levels and outcome such as
cancer recurrence. Often, implicitly or explicitly it is
assumed that the outcome measure increases or decreases
in a linear fashion with the gene expression level.
Prior to the emergence of microarray analysis, many
studies of the prognostic significance of the expression
level of single genes or proteins have been performed in
breast cancer. A problem when analyzing gene expression
levels in relation to breast cancer survival is the catego-
rization of patients. The categorization is usually based on
subjectively chosen cut-off points in the distribution of
the expression levels. It is often not stated how these
choices were made and this may lead to non-optimal
categories resulting in loss of statistical power and
precision.
Electronic supplementary material
article (doi:10.1007/s10549-009-0588-6) contains supplementary
material, which is available to authorized users.
The online version of this
B. Kreike ? G. Hart ? H. Bartelink
Divisions of Radiation Oncology and Experimental Therapy,
The Netherlands Cancer Institute, Plesmanlaan 121,
Amsterdam 1066 CX, The Netherlands
M. J. van de Vijver (&)
Department of Pathology, Academic Medical Center,
Meibergdreef 9, Amsterdam 1105 AZ, The Netherlands
e-mail: m.j.vandevijver@amc.uva.nl
123
Breast Cancer Res Treat (2010) 122:711–720
DOI 10.1007/s10549-009-0588-6

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In this study we use an alternative approach to the anal-
ysis of the relation between microarray results and breast
cancer survival data. Our model is based on natural splines
[11] and the Cox proportional hazard model. The basic
model of Cox assumes a linear relation between the loga-
rithm of the hazard rate and the expression level of a marker
or gene. In our approach we use the natural spline to model
this relation more flexibly. A spline has to pass through a
certain number of points (‘‘knots’’) not lying on a straight
line. Guidelines have been formulated for the number and
position of the knots in regression analyses such as the
proportional hazard analysis [11]. Furthermore the natural
spline approach avoids categorization of expression levels
or patients. Therefore, the natural spline technique is a
powerful tool in the statistical analysis of microarray data.
We used the natural spline technique to analyze the
association of the expression of 16 (breast) cancer-relevant
genes, measured using microarray analysis, with disease
outcome. We studied estrogen receptor alpha (ESR1),
genes encoding for proteins of the ERBB-family (EGFR,
ERBB2, ERBB3, and ERBB4), cyclin-family members
(CCND1, CCNE1, and CCNE2), Polycomb-group family
members (EZH2, EED) and several genes that are thought
to play a role in the development of distant metastases
(VEGF, CXCR4, CCR7, SDF1, PAI1, and UPA). We also
adjusted their individual prognostic power for confounding
by other known clinical prognostic factors (e.g., clinical
tumor stage, age, pathologic tumor characteristics, etc.) and
the 70-genes prognostic profile previously identified by our
group [1, 12].
Materials and methods
Detailed patient information has been described previously
[12]. Briefly, tumors from 295 women with breast cancer
treatedbetween1984and1995wereselectedfromthefresh-
frozen-tissue bank of The Netherlands Cancer Institute
according to the following criteria: primary invasive breast
carcinoma,\5 cm in diameter at pathological examination;
ageatdiagnosisB52 years; andnegativehistoryofprevious
cancer except non-melanoma skin cancers. All patients
received modified radical mastectomy or breast-conserving
treatment, including dissection of the axillary lymph nodes
and radiotherapy if indicated. Among the 295 patients,
151 had lymph-node-negative disease and 144 had lymph-
node-positive disease. Ten of the 151 patients with
lymph-node-negative disease and 120 of the 144 who had
lymph-node-positive disease had received adjuvant che-
motherapy (n = 90), hormonal therapy (n = 20), or both
(n = 20). Patients were assessed at least annually after
completion of therapy. Median duration of follow-up was
7.8 years (range, 0.05–18.3) for the 207 patients without
metastasis as first event and 2.7 years (range, 0.3–14.0) for
the 88 patients with metastasis as first event. The median
follow-up among all 295 patients was 6.7 years (range,
0.05–18.3).
Details on RNA isolation, labeling of complementary
RNA, competitive hybridization of each tumor cRNA with
pooled reference cRNA from all samples to 24,500 element
oligonucleotide microarrays, and measurement of expres-
sion ratios were previously described [1]; and wherever
possible we adhered to reporting Recommendations for
Tumor Marker Prognostic Studies (REMARK) [13].
Expression levels were quantified as log10(R), where R is
the ratio of the intensities of test and reference sample and
log10 denotes the logarithm with base 10.
Statistical analysis
Natural splines and the Cox proportional hazard model were
used to study the relation of gene expression levels and
distant metastasis free probability (DMFP). Concisely,
natural splines consist of connected piecewise cubic poly-
nomials, each defined on a separate range of the expression
level. The boundaries between the ranges are called knots.
Guidelines have been given for the choice of the number
and position of the knots. We used five knots at the positions
advocated by Harrell [11]: 5, 25, 50, 75, and 95% quantiles
of the expression level. More detailed information on these
calculations are given in Supplementary material 1.
Table 1 displays the P values of: the natural spline
analysis; non-linearity test, and linear test. The ‘‘non-line-
arity’’ and ‘‘linear relation’’ P values are independent from
each other; however, the ‘‘natural spline’’ P value depends
on both. We used the ‘‘linear relation’’ P value for the
relation between the expression level and DMFP unless the
‘‘non-linearity’’ P value is\0.01; for these cases the ‘‘nat-
ural spline’’ P value was used. This summarizing P value is
given in Table 1 under the heading ‘‘overall’’.
By definition, a single hazard ratio can only be given in
the linear model. Hazard ratios per unit expression level
based on the linear model are given in Table 2 including
the 95% confidence interval (CI).
The relation between the gene expression level and
DMFP was visualized in graphs of the hazard rate as a
function of the gene expression ratio; the units in which
they are expressed, ln(hazard ratio) per unit expression
level, may be difficult to interpret intuitively. Therefore,
we also created survival-type curves, but these curves
necessitate categorization of the expression level. We used
a categorization scheme intended to reflect the shape of the
hazard rate function as clearly as possible by creating a
possibly large number of categories, where the number and
widths of the categories depended on the shape of hazard
rate function (see the thin vertical lines in Figs. 1a–4a). In
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the next step, adjacent categories were concatenated in a
stepwise manner until further concatenation would result in
a loss of information as measured by the Akaike Infor-
mation Criterion (AIC) [14]. The complete process was
performed in an automated way.
The remaining categories are shown by the thick vertical
lines in the ln(hazard ratio) plots and the resulting survival
curves are shown in Figs. 1b–4b. Nominal P values for the
differences between the curves are given under the heading
‘‘categorization’’ in Table 1. These P values are calculated
from the log-rank test, without taking into account the
ordering of the categories (‘‘nominal scale’’). A large dif-
ference between the log-rank and overall P value indicates
that differences in prognosis are overestimated by the
Kaplan–Meier curves. Five- and 10-year metastasis-free
percentages are given in Table 2.
In order to get an impression of the variability of the
categorization process described above, 100 bootstrap
samples of size 295 were created from the original data and
the full process of categorization was repeated 100 times.
Normal probability-plots were used to identify outliers.
The appearance of humps in the normal plot may indicate
the existence of subpopulations.
Conclusions were generally formulated in terms of the
strength of evidence. These are mainly based on P values
from the linear or spline models using the following cate-
gorization:P[0.05 = ‘‘noevidence’’;0.05\P\0.01 =
‘‘not much evidence’’; 0.01\P\0.001 = ‘‘some evi-
dence’’; 0.001\P\0.0001 = ‘‘evidence’’; P\0.0001 =
‘‘proof’’.
We tested the individual prognostic power of the
selected genes in relation to known clinical and patholog-
ical risk factors for DMFP in a multivariable analysis. The
16 selected genes were tested in one model together with
use of chemotherapy, hormonal therapy, type of surgery
(mastectomy versus breast conserving surgery), tumor
diameter; number of tumor involved lymphnodes; tumor
grade, presence of vascular invasion, age, estrogen receptor
status, and prognostic class assignment based on the
70-gene prognosis signature [1]. The use of systemic
Table 1 Rate of metastases and
gene expression: P values using
different models/hypotheses
Gene Natural splineNon-linearity Linear relationOverall Categorization
ESR10.0120.550.00080.0008 0.0007
EGFR
0.00650.00390.69 0.0065 0.0013
ERBB2
0.02 0.05 0.0450.045 0.0008
ERBB3
0.460.7 0.150.15 0.052
ERBB4
0.00630.280.0011
\0.0001
0.97
0.0011
\0.0001
0.97
0.0004
\0.0001
0.073
VEGF
0.0006 0.44
CCND1
0.60.42
CCNE1
0.016 0.0840.02
\0.0001
0.0005
0.02
\0.0001
0.0005
0.0046
CCNE2
0.00140.59 0.0001
EZH2
0.00740.590.0002
EED
0.150.0830.220.220.0094
CXCR4
0.210.150.570.570.0035
CCR7
1.001.00 1.001.00 1.00
SDF1
0.0180.030.0790.0790.0016
PAI1
0.0290.110.022 0.0220.0012
\0.0001
UPA
0.00070.015 0.0053 0.0053
Recurrence free survival
05 10 15
0
20
40
60
80
100
Gene expression ratio
ln(hazard ratio)
-1.5-1.0-0.5 0.00.5
-2
-1
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Years since diagnosis
BA
I II III
I
II
III
Fig. 1 ESR1 output. a Spline plot, ln(hazard ratio) and categorization for ESR1. The color-coded roman numbers indicate the groups that are
compared in (b) and correspond to the curves with the same color. b Recurrence free interval based on the categorization of the spline plot
Breast Cancer Res Treat (2010) 122:711–720713
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therapy, type of surgery, histological grade, presence of
vascular invasion, and estrogen receptor status were used
as nominal variables; all other variables were used in a
linear fashion.
Patients with missing values for the relevant variables
were omitted from the analysis. Also patients with extreme
expression levels as identified in the Normal probability
plots were excluded from analyses, which included the
relevant gene. In the case of the multivariable analysis, this
resulted in the use of 282 of the original 295 patients.
The statistical package S??(Insightful Corp, Seattle)
version 6.1–6.2 was used for the calculations and the
graphs. This package implements the natural spline through
a simple function. A user-written function for categoriza-
tion can be obtained from one of the coauthors (G. Hart).
Results
From a total of 24,500 genes we selected 16 genes for
analysis. Table 1 shows the 16 genes of interest and their
level of significance. Seven of the 16 genes show at least
some level of evidence for an association with DMFP based
on the spline model (overall P value\0.01: ESR1, EGFR,
ERBB4, VEGF, CCNE2, EZH2, and UPA). Of these 7 genes
6show a significant linear relation between gene-expression
level and hazard ratio (ESR1, ERBB4, VEGF, CCNE2,
EZH2, and UPA). Only EGFR shows some evidence of a
non-linearrelation(non-linearityPvalue = 0.0039).Forthe
other nine genes there is no or not much evidence to have
significant prognostic properties (overall P value [0.01:
ERBB2, ERBB3, CCND1, CCNE1, EED, CXCR4, CCR7,
SDF1,andPAI1).Table 2showsthehazardratio(calculated
for the linear model) for the individual genes and the cate-
gorization into groups defined by the gene-expression level
cut-offs with 5 and 10 years metastases free probability.
The normal plot for ESR1 suggests that the total popula-
tion consists of two subpopulations of sizes of about 54
(log(R)lessthan-1)and215patients(log(R)greaterthan-
0.5), respectively, with 26 patients in between (data not
shown). These groups reflect the estrogen receptor (ER)
status, the first group being the ER-negative patients and the
secondgroup the ER-positive,ashas been shownpreviously
[1, 12]. The natural spline analysis (Fig. 1a) provides evi-
dence that higher expression levels of this marker are asso-
ciated with lower rate of distant metastasis (5 year DMFP:
low expression: 56%, intermediate expression: 72%, high
expression: 81%, P = 0.0008). Figure 1a also shows a
possibleworseprognosisfortheveryhighexpressionlevels,
this is, however, not captured by the categorization. The
resulting categories roughly coincide with the subpopula-
tions indicated by the normal plot. However, the bootstrap
results indicate still considerable uncertainty about the
numberofcategoriesandthepositionoftheboundaries(data
not shown).
The natural spline analysis for EGFR (Fig. 2a) shows a
non-linear relation between gene-expression level and
DMFP. A group of 163 patients have gene-expression
ratios around zero and excellent survival rates of 84 and
75%, respectively, for 5 and 10 year DMFP. Patients with
high expression (n = 46) or low expression (n = 69) of
this gene have a poor prognosis with 5 and 10 year DMPF
of, respectively, 67 and 50% for the patients with high
expression of EGFR and 61 and 53% for the patients with
low expression of EGFR.
According to our model there is proof that the rate of
metastases increases with increasing levels of VEGF or
CCNE2, P\0.0001, with hazard rates of 4.2 and 4.5,
respectively (Table 2; Fig. 3; Supplementary material 2-
S1). There is also strong evidence suggesting that higher
EZH2 gene expression is associated with higher rates of
distant metastasis, P = 0.0005 (Supplementary material 2-
S2). The hazard rate plot suggests a rather sharp transition
from low risk at expression levels below -0.2 to high risk
at levels above 0.15. However, linearity is not ruled out,
non-linear P value = 0.59.
With a hazard ratio of 0.29 ERBB4 shows evidence
(P = 0.0011) that higher rates of distant metastases occur
when this gene is expressed at low levels (Supplementary
material 2-S3). Five year DMFP of 58 vs. 67–86% for low
levels of ERBB4 expression versus the higher levels and
10 year DMFP of, respectively, 51 vs. 60–80% (Table 2).
UPA also seems to be associated with DMFP (P =
0.0053). Especially the patients with very high expression
levels of UPA (n = 11) showed poor outcome as also
reflected by the Kaplan–Meier curves (Supplementary
material 2-S4), with 5 year DMFP of 27 vs. 73–78% for the
patients with lower expression levels of UPA and 10 year
DMFP of, respectively, 18 vs. 59–70% (Table 2).
The other nine genes (ERBB2-3, CCND1-E1, EED,
CXCR4, CCR7, SDF1, and PAI1) were not shown to be
associated with outcome based on our predefined P value
cut-off levels (Fig. 4; Supplementary material 2-S5–12).
The multivariable analysis showed that the 70-gene
prognosis profile [1] outperformed the clinical risk factors
and the individual gene expression ratios in predicting
DMFP with a HR of 5.4 (95% CI 2.5–11.7; P = 0.000018);
Table 3.
Discussion
We have used natural splines and the Cox proportional
hazard model to study the relation of gene expression levels
and disease outcome. We have developed this model of
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Table 2 Hazard ratio (95% CI)
per measurement unit for linear
model and metastases-free
percentages per category
Gene HR (95% CI) or Categories defined
by gene expression levels
N
% free from distant metastases (SE)
5-year10-year
ESR1HR: 0.54 (0.38–0.77)
-1.591/-1.159
3956% (8%)46% (10%)
-1.159/-0.203
79 72% (5%)61% (6%)
-0.203/0.596
177 81% (3%) 71% (4%)
EGFR
HR: 0.63 (0.05–8.17)
-0.388/-0.197
1080% (13%)80% (13%)
-0.197/-0.076
6961% (6%) 53% (7%)
-0.076/0.046
16384% (3%)74% (4%)
0.046/0.326
49 67% (7%)50% (10%)
ERBB2
HR: 1.57 (0.97–2.54)
-1.188/-0.7
60 65% (6%)61% (7%)
-0.7/0.361
19583% (3%)70% (4%)
0.361/0.928
4054% (8%)51% (8%)
ERBB3
HR: 0.45 (0.15–1.37)
-0.574/0.104
20772% (3%)63% (4%)
0.104/0.444
8382% (4%) 72% (6%)
ERBB4
HR: 0.29 (0.14–0.63)
-0.767/-0.228
7858% (6%)51% (7%)
-0.228/0.009
88 80% (4%)60% (7%)
0.009/0.338
10186% (3%) 80% (5%)
0.338/0.525
2667% (9%) 67% (9%)
VEGF
HR: 4.2 (2.26–7.78)
-0.65/-0.012
178 83% (3%)75% (4%)
-0.012/0.291
7567% (6%) 56% (7%)
0.291/0.89
4259% (8%) 44% (9%)
CCND1
HR: 1.01 (0.51–2)
-0.982/-0.598
2563% (10%) 45% (13%)
-0.598/1.089
27076% (3%)67% (3%)
CCNE1
HR: 7.22 (1.09–47.84)
-0.572/-0.292
1090% (9%) 90% (9%)
-0.292/0.112
24477% (3%)66% (4%)
0.112/0.467
37 55% (9%)49% (9%)
CCNE2
HR: 4.49 (2.11–9.55)
-0.835/-0.179
12287% (3%) 76% (4%)
-0.179/0.096
9973% (5%)66% (6%)
0.096/0.726
74 59% (6%) 44% (7%)
EZH2
HR: 4.68 (2.06–10.63)
-0.682/-0.124
10089% (3%) 76% (5%)
-0.124/0.132
118 71% (4%)69% (5%)
0.132/0.664
7662% (6%)46% (7%)
EED
HR: 2.33 (0.52–10.4)
-0.567/0.215
27676% (3%)67% (3%)
0.215/0.578
1753% (12%)40% (15%)
CXCR4
HR: 1.31 (0.54–3.18)
-0.753/-0.18
9282% (4%)75% (5%)
-0.18/0.145
14468% (4%)55% (5%)
0.145/0.677
5982% (5%)75% (7%)
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