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Annals of Oncology 25: 2014–2019, 2014
doi:10.1093/annonc/mdu372
Published online 5 August 2014
A simple technique to estimate best- and worst-case
survival in patients with metastatic colorectal
cancer treated with chemotherapy
M. Williams1*, R. A. Singer2 & A. Lerner3
1
Department of Clinical Oncology, Charing Cross Hospital, Imperial College Healthcare NHS Trust, London; 2Department of Clinical Oncology,
Kent and Canterbury Hospital, Canterbury; 3Department of Clinical Oncology, The Royal Surrey County Hospital, Guildford, UK
Received 19 May 2014; revised 16 July 2014; accepted 27 July 2014
Background: Patients with incurable cancer usually want specific information about prognosis, and clinicians’ estimates
are often inaccurate. Studies in breast and lung cancer have suggested that simple multiples of the median overall survival
(OS) can accurately estimate the time at which 90%, 75%, 25% and 10% of patients are alive.
Patients and methods: We identified 46 phase III randomised clinical trials of chemotherapy in metastatic colorectal cancer,
representing data from 29 011 patients. We extracted data on demographics, treatment and survival from 96 patient cohorts
and assessed agreement with the estimated survival time points, calculated as 0.25, 0.5, 2 and 3 times the median OS.
Results: Median OS was 16.8 months in the trials. There were 342 assessable time points. For 301 of these, the estimated survival time was within 0.75–1.33 of the actual survival time (88% agreement). The worst agreement (76%) was at
the earliest (90%) level of survival.
Conclusions: Simple multiples of the median OS give reasonable estimates of the times at which different survival levels
are reached in patients with metastatic colorectal cancer. Taken with previous studies, these findings are likely to be valid
across a large range of patients. We would encourage clinicians to think of prognosis as a trajectory, and to consider
quoting survival ranges instead of point estimates, in discussions with patients.
Key words: survival, prognosis, metastatic colorectal cancer, review
introduction
Estimating survival in patients with incurable cancer is difficult,
and predictions made by medical staff are often inaccurate
[1, 2]. Such predictions are important for patients, and may
influence their decisions on treatment; they are also important
in planning services [3].
*Correspondence to: Dr Matt Williams, Department of Radiotherapy, Imperial College
Healthcare NHS Trust, Charing Cross Hospital, Fulham Palace Rd, Northwood, London
W6 8RF, UK. Tel: +44-203-311-8427; Fax: +44-203-311-1603; E-mail: mhw@doctors.
net.uk
When asked for prognosis, many clinicians quote the median
overall survival (OS). However, the median represents the time
by which half the patients will have died and the relevance of
this figure is not clear to patients [4, 5]. Ideally, patients should
have access to better prognostic information without the need
for complex formulae or electronic aids. There has been substantial work on estimating survival in the last few weeks of life,
often in the hospice environment (see [6] for an overview).
However, there is much less work on estimating survival in
those patients who cannot be cured but may have life expectancies measured in months and years. Such patients have high
© The Author 2014. Published by Oxford University Press on behalf of the European Society for Medical Oncology.
All rights reserved. For permissions, please email: journals.permissions@oup.com.
original articles
Annals of Oncology
health-care utilisation rates [7], and their decisions around
medical care are influenced by their perception of prognosis [8].
Kiely et al. has presented a method [9, 10] that provides estimates of survival for groups of patients having palliative chemotherapy. It generates estimates of the times at which most people
in the group will still be alive, and times to which smaller proportions of the population might be expected to live. These are
termed the ‘worst case’ (90% of patients survive at least this
long), ‘best case’ (only 10% of patients survive longer than this),
‘lower typical’ (75% of patients survive at least this long) and
‘upper typical’ (25% level). The method calculates these estimates by using simple multiples of the median OS from clinical
trials, and is based upon the fact that survival curves approximate an exponential decay pattern. This method has been evaluated in metastatic breast [9], lung [11, 12] and prostate [13] but
not colorectal cancer.
In this study, we have systematically reviewed recent phase III
randomised trials of chemotherapy in metastatic colorectal
cancer, to see whether simple multiples of the median OS time
can estimate the time points at which different survival levels
(90%, 75%, 25%, 10%) are reached.
reporting. For each trial, we obtained data from the full manuscript; where
trials had more than one publication, we used the one that contained the
most complete report of OS.
For each trial, we recorded the year of publication, number of patients enrolled in each arm, patient demographics, proportion of patients with rectal
involvement, number of treatment arms, treatment regimens used, whether
a targeted agent was used, and the median OS for each treatment arm. We
included data on all treatment arms with 100 or more patients, where survival had reached the 25% level or less.
Each survival curve was converted to JPEG format, magnified to 400%
size, and overlaid with a pixelated grid. Two authors independently measured the actual time points at which 90%, 75%, 25% and 10% levels of
survival were reached, in each arm of each study (Figure 1) . We extracted
the median OS from each arm of each study, and then calculated simple
multiples of the median OS (0.25, 0.5, 2 and 3) to estimate the time to the
90%, 75%, 25% and 10% levels of survival. We compared the actual time
taken to reach each survival level with the time estimated from the relevant
multiple of the median OS. In keeping with previous work [9, 12, 14], we
considered the agreement between the two to be acceptable if the estimate
References
(n = 156)
methods
We identified randomised clinical trials of first-line palliative chemotherapy in patients with metastatic colorectal cancer published between 2000
and 2011 and indexed in Medline (supplementary Appendix S1, available
at Annals of Oncology online). We supplemented this list with additional
references in reviews and through discussion with subject-matter experts.
Trials were screened by two authors and were eligible for inclusion if they
were phase III randomised trials, compared at least two different chemotherapy regimens, were given as first-line treatment of metastatic colorectal cancer, included at least 100 patients per treatment arm, included
censored curves of OS, were published in English and where, in at least
one treatment arm, at least 75% of patients had died at the time of
Included
trials (n = 46)
Insufficient
information
(n = 5; 3%)
Number of OS curves
(n = 101)
Not randomised
chemotherapy trials
in mCRC
(n = 52; 33%)
Curve without data for
25% centile (n = 5)
Duplicate
references for the
same study
(n = 22; 14%)
OS curves for analysis
(n = 96)
100
Not first line
(n = 18;12%)
Proportion alive
80
60
<100 patients/arm
(n = 5; 3%)
40
20
No OS curve
(n = 4; 3%)
0
0
6
12
18
36
42
48
54
60
10% of patients alive
25% alive
Median OS
75% alive
90% of patients alive
24
30
Follow-up
(months)
Figure 1. Measuring the time to different levels of survival from published
survival curves.
Volume 25 | No. 10 | October 2014
No data for 25%
percentile survival
(n = 4; 3%)
Included trials
(n = 46; 29%)
Figure 2. Flow diagram showing study and cohort inclusion.
doi:10.1093/annonc/mdu372 | 
original articles
Annals of Oncology
lay within 0.75–1.33 times of the actual time point for that survival level.
We assessed whether median OS or rates of agreement varied by trial characteristics. We used Fisher’s exact test to assess statistical significance for
rates of agreement, and Kendall’s correlation to assess correlation between
trial characteristics and median OS. We used a cut-off of P < 0.01 to
account for using multiple tests.
A
results
We identified 139 trials, of which 46 met our inclusion criteria
(references in supplementary Appendices S2 and S3a–e, available at Annals of Oncology online), yielding a total of 96
Kaplan–Meier curves (Figure 2). Studies had varying length of
follow-up and we were able to measure 96 data points for 90%,
B
Median survival
25
Time to 90% survival level
15
Frequency
Frequency
20
15
10
10
5
5
0
0
0
20
80
0
2
D
Time to 75% survival level
10
8
8
6
4
2
4
6
Time in months
8
10
Time to 25% survival level
10
Frequency
Frequency
C
60
40
Time in months
6
4
2
0
0
4
6
8
10
12
Time in months
E
14
16
15
20
25
30
Time in months
35
40
Time to 90% survival level
8
Frequency
6
4
2
0
30
40
50
Time in months
60
Figure 3. (A) Median overall survival, in months, of all patient cohorts. (B) Time in months to the 90% survival level. (C) Time in months to the 75% survival
level. (D) Time in months to 25% survival level. (E) Time in months to 10% survival level.
 | Williams et al.
Volume 25 | No. 10 | October 2014
original articles
Annals of Oncology
75% and 25% survival, and 54 points for 10% survival. This
gave a total of 342 time points at which we could assess the
agreement between the actual and estimated times.
The included trials enrolled 29 011 patients. The median OS in
the included studies was 16.8 months (IQR: 14.3–19.4; Figure 3A).
The median time to 90% OS level was 4.6 months (IQR: 3.7–6), to
the 75% level was 9.5 months (IQR: 8–11), to the 25% level was
27.7 (IQR: 24–32.2) and to the 10% survival level was 39.3
months (IQR: 34.9–44.4) (Figure 3B–E; supplementary Material,
available at Annals of Oncology online) (Table 1) . The median age
of included patients was 62 years, the median proportion of male
patients was 61%, and the median proportion of patients with
rectal cancer was 29%. Thirteen of the cohorts (14%) included at
least one biological agent (Table 2).
Of the 342 data points, 301 (88%) of the estimates were
acceptable (lay within 0.75–1.33 of the actual value). The agreement between the estimated and actual time points was worst at
the earliest (90%) survival level, where only 76% of the estimates
were acceptable. Of the 68 cohorts where we had data on all four
survival points, half agreed at all four points. There was a tendency to underestimate the time to the 90% and 75% survival
levels, and overestimate the time to the 25% and 10% survival
levels (Figure 3B–E). There was no significant variation in the
rate of agreement by trial or trial population subgroup, although
median OS increased over time (Kendall’s τ = 0.35; P = 0.001)
(Figure 4).
discussion
In this analysis of 46 trials enrolling 29 011 patients receiving
first-line chemotherapy for metastatic colorectal cancer, simple
multiples (0.25, 0.5, 2 and 3) of the median OS time can be used
to estimate survival centiles (90%, 75%, 25% and 10%). Despite
the variation in median OS between different trials, the relationship between median OS and different survival levels was
consistent. Our findings are in keeping with previous work in
breast and lung cancer [9, 11], which have widely different
median survival times. We therefore expect that this relationship
will remain true, even if the median OS were to increase in future
trials. This should allow clinicians to provide, and patients to
understand, more nuanced representations of prognosis.
There are three main weaknesses with this study. First, at the
earliest time point (90% survival), the agreement between the
estimated time to the survival level and the actual value drops to
76%, and at the other extreme (10% survival) the agreement
is 81%, compared with 88% overall. This pattern is in keeping
with previous studies. Secondly, the data to support this
approach come from randomised trials, which may not include
a representative population (e.g. European patients with colorectal cancer have a median age of 71 years; the median age in
this study was 62 years). Thirdly, the definition of agreement
(0.75–1.33) is somewhat arbitrary, although it is in keeping with
previous studies, and is more conservative than some other
authors [15]. Although we used 0.75–1.33 as a definition of
agreement, in fact most data are more tightly grouped than this,
Table 2. Trial characteristics
Characteristics
Trials
No. Percentage
Year of publication
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
No. of cohorts analysed per trial
1
2
3
4
Agents used in the 96 cohorts
Fluorouracil
Oxaliplatin
Irinotecan
Capecitabine
Bevacizumab
Cetuximab
Panitumumab
Unspecified fluoropyrimidine (capecitabine
or fluorouracil)
Vatalinib
Mitomycin C
Tegafur–uracil
Trimetrexate
Others (4 agents)
4
1
3
1
3
5
6
6
5
2
4
6
9
2
7
2
7
11
13
13
11
4
9
13
4
35
6
1
9
76
13
2
61
48
31
18
12
5
4
3
64
50
32
19
13
6
5
3
1
1
1
1
1
1
1
1
1
1
Table 1. Patient characteristics
Number of patients per cohort
Age (years)
% Male
Follow-up (months)
Rectal involvement
Volume 25 | No. 10 | October 2014
Median
Range
Number of cohorts reported
% of cohort reported
218
62
61%
31.0
29%
100–1017
58–69
38–73
17.2–61.0
14%–54%
96
88
90
64
63
100
92
94
66
66
doi:10.1093/annonc/mdu372 | 
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Annals of Oncology
suggesting a reasonable degree of homogeneity within the different trials. The low rate of agreement at the 90% survival time
point is in part due to the short timescales at this survival point:
our definition of agreement allows for ∼5 weeks difference (±)
between the actual and predicted values, which is a narrow time
window and thus more susceptible to random variation. In addition, many trials have an inclusion criterion of expected survival of more than 8 or 12 weeks. Since the median time to the
90% survival time is only 4 months, we might expect the agreement to be reduced by trial clinicians adhering to this stipulation, as it excludes patients with short survival times, and hence
explain why this approach underestimates the time to the 90%
survival level.
This approach provides a robust way of estimating the chance
of survival to different time points. It is better calibrated than
clinical opinion, and is simpler than many end-of-life scoring
systems. We hope that the greater information provided by this
approach will allow for better decision making by patients and
doctors. Initial studies suggest that this approach is acceptable
and preferred to use of median OS alone [16]. Given the data
presented here, we can expect that, for patients with metastatic
colorectal cancer having palliative chemotherapy as part of a
clinical trial, most patients will live for at least 5 months (the
90% survival level); many will live for between 10 and 28
months (between the 75% and 25% survival levels); few will
live longer than 40 months (10% survival level). Metastatic colorectal cancer may be different from other tumours, as hepatic
resection in patients with oligo-metastatic disease may alter
their prognosis. This has been documented at a population level
[17], but such patients are relatively rare and may be excluded
from clinical trials.
We can add additional information to make our estimates
more accurate. For example, there is a well-documented impact
of performance status on OS in metastatic colorectal cancer
[18, 19], with a median OS of 8.5 months in patients who are
ECOG performance status 2 [19]. In this case, we would expect
the calculated estimates to be 3, 4, 17 and 25 months. In principle, additional clinical factors (site of metastases etc.) could
also be added to a prognostic model, in order to provide better
estimates of the survival. However, the use of additional information to provide better prognostic estimates is orthogonal to
this approach, which provides a simple and accessible way to
provide more information about multiple points on the survival
curve. In both cases, the volume of data on which to base decisions is limited, and emphasises the fact that clinical information and acumen is still required, even if only to provide the
initial estimate of the median OS time point [20].
Whether we use more data to provide better estimates of
the median survival, or use our approach to calculate multiple
points on the survival curve (or both), it is important to
note that they are statistical measures that we use to communicate risk to patients. Each patient has a single, initially
unknown, prognosis and therefore data from groups of patients
can only provide an estimate of risk for individuals. We would
encourage clinicians to start considering survival in terms of a
trajectory of multiple time points. How this is discussed with
patients will vary, but terms such as ‘most’, ‘many’, ‘some’ and
‘few’ may convey the approximate survival levels, and techniques such as this allow clarification with numerical values where
useful [21]. Previous work has suggested that clinicians often
overestimate prognosis [1, 15] and we hope that this study and
others will provide more objective estimates on which to base
discussions with patients and their families.
Median overall survival
by year of trial publication
Overall survival in months
25
20
15
10
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
Year of trial reporting
Figure 4. Changes in overall survival by year of trial publication. Horizontal dark line indicates the median OS; the extent of shaded area indicates the range
from first to third quartile.
 | Williams et al.
Volume 25 | No. 10 | October 2014
Annals of Oncology
In conclusion, we have demonstrated that simple multiples of
the median OS accurately estimate the times at which different
survival levels are reached for patients with metastatic colorectal
cancer. This is in keeping with other studies in patients with
lung, prostate and breast cancer treated with palliative chemotherapy. We hope that the use of a simple formula will allow
clinicians to approximate survival at different time points, and
to use this information in discussion with their patients to give
realistic descriptions on likely survival. Although there are some
areas of clinical practice where this approach is unlikely to hold,
it seems likely that it will apply across a variety of tumour sites
where cure is unlikely.
acknowledgement
An earlier version of the work was presented at the NCRI conference, UK, 2012.
disclosure
The authors have declared no conflicts of interest.
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doi:10.1093/annonc/mdu372 | 