A simple technique to estimate best and worst case survival in patients
with metastatic colo-rectal cancer treated with chemotherapy
M. Williams1, R. A. Singer2, A. Lerner3
An original research article
Corresponding Author & Guarantor: Dr. M. Williams1
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Affiliations:
1: Department of Clinical Oncology, Charing Cross Hospital, Imperial College Healthcare NHS Trust, London, UK.
2: Department of Clinical Oncology, Kent and Canterbury Hospital, Canterbury, UK.
3: Dept. of Clinical Oncology, The Royal Surrey County Hospital, Guildford, UK.
Abstract:
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 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 colo-rectal 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 overall survival (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 overall survival give reasonable estimates of the times at which different survival levels are reached in patients with metastatic colo-rectal 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.
Running title: Simple estimates of survival in metastatic colo-rectal cancer
Key words: Survival; Prognosis; Metastatic colo-rectal cancer; Review
Key Message: In patients with metastatic colorectal cancer, simple multiples of the median overall survival predict the time to the 90%, 75%, 25% and 10% survival levels. This is consistent with findings from other disease sites (metastatic breast, lung and prostate cancer). Clinicians can use this information to inform discussions with patients.
Clinical Trial Number: N/A
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).
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 health-care utilisation rates (7), and their decisions around medical care are influenced by their perception of prognosis (8).
Kiely has presented a method (9) 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 overall survival 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 (10,11) and prostate (12) but not colo-rectal cancer.
In this study we have systematically reviewed recent phase III randomised trials of chemotherapy in metastatic colo-rectal cancer, to see whether simple multiples of the median overall survival time can estimate the time points at which different survival levels (90%, 75%, 25%, 10%) are reached.
Methods:
We identified randomised clinical trials of first-line palliative chemotherapy in patients with metastatic colo-rectal cancer published between 2000 and 2011 and indexed in MEDLINE (Appendix 1). 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 2 different chemotherapy regimens, were given as first line treatment for metastatic colo-rectal cancer, included at least 100 patients per treatment arm, included censored curves of overall survival, were published in English and where, in at least one treatment arm, at least 75% of patients had died at the time of 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 overall survival (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 (Fig. 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 (9,11,13), we considered the agreement between the two to be acceptable if the estimate lay within 0.75 to 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.
Results:
We identified 139 trials, of which 46 met our inclusion criteria (references in Appendix 2, 3a - 3e), yielding a total of 96 Kaplan-Meier curves (Fig. 2). Studies had varying length of follow-up and we were able to measure 96 data points for 90%, 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; Fig. 3a). The median time to 90% overall survival level was 4.6 months (IQR: 3.7 – 6), to the 75% level was 9.5 months (8 – 11), to the 25% level was 27.7 (24 – 32.2) and to the 10% survival level was 39.3 months (34.9 – 44.4) (Figs. 3b – 3e; Supplementary material). 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 (Fig. 3 b-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 Tau = 0.35; p = 0.001) (Fig. 4).
Discussion:
In this analysis of 46 trials enrolling 29 011 patients receiving first-line chemotherapy for metastatic colo-rectal cancer, simple multiples (0.25, 0.5, 2, and 3) of the median overall survival time can be used to estimate survival centiles (90%, 75%, 25% and 10%). Despite the variation in median overall survival 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 (9,10), 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. Firstly, 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 to 88% overall. This pattern is in keeping with previous studies. Secondly, the data to support this approach comes from randomised trials, which may not include a representative population (e.g. European patients with colo-rectal 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 (14). Although we used 0.75 – 1.33 as a definition of agreement, in fact most data is more tightly grouped than this, 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 approximately 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 (17). Given the data presented here, we can expect that for patients with metastatic colo-rectal 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), and few will live longer than 40 months (10% survival level). Metastatic colo-rectal 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 (16), 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 overall survival in metastatic colo-rectal 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 over-estimate prognosis (1,14) and we hope that this study and others will provide more objective estimates on which to base discussions with patients and their families.
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 colo-rectal 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.
An earlier version of the work was presented at the NCRI conference, UK, 2012.
No funding was received for this work.
The authors have declared no conflicts of interest.
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