ONCOLOGY. Vol. 25 No. 1

REVIEW ARTICLE

How Long Have I Had My Cancer, Doctor?

Estimating Tumor Age via Collins’ Law

By Michael V. Patrone¹, Jessica L. Hubbs, MS²,
Janet E. Bailey, BA³, Lawrence B. Marks, MD³ | January 24, 2011

¹ University of North Carolina
² University of North Carolina School of Medicine
³ Department of Radiation Oncology, University of North Carolina School of Medicine, Chapel Hill, North Carolina

ABSTRACT: To estimate the “age” of cancers at the time of diagnosis, we reviewed data on the “time to local/regional recurrence” (LRF) following initial surgical resection for three common cancers, then applied a modified version of Collins’ law. We conducted a systematic review of English medical literature to identify studies reporting LRF rates, over time, following surgery alone for breast, lung, or colorectal cancer. Patients who received radiation/hormones/chemotherapy were excluded since these therapies may alter tumor growth kinetics after surgery. For each disease, data were considered in three ways: 1) absolute cumulative LRF rate over time; 2) percentage of LRFs manifest over time (to facilitate comparisons between studies with different absolute magnitudes of LRFs); and 3) weighted average of the percentage of LRFs manifest over time.

For breast cancer (based on data from 3043 patients from 5 studies), we found that the median time to LRF was 2.7 years. For lung cancer (based on data from 1190 patients from 4 studies), the median time to LRF was 1.5 years. For rectal cancer (based on data from 3334 patients from 10 studies), the median time to LRF was 1.5 years. Based on Collins’ law, the distribution of time to LRF suggests that the age of most of the solid tumors studied was 3 to 6 years.

“How long have I had this cancer, Doctor?” This is a question that patients frequently ask their oncologist. In many instances, the answer to the question is not particularly relevant since treatment approaches may not be influenced by the “age” of the cancer. However, in some instances the age of a cancer, which implies its natural history, may influence treatment recommendations.

In addition, the answer to this question may have helpful implications for our patients. When patients are diagnosed with cancer, they often seek to understand “why.” They search for particular events in their lives that may have “caused” the cancer to form. A better understanding of the likely age of their cancer may address misconceptions about the “causes” of their cancer and help to alleviate associated guilt (eg, “Did I cause my cancer by working too hard last month?” “No, because the cancer started to grow at least 2 years ago.”).[1-4] Also, some understanding of their cancer’s age may help to alleviate patients’ concerns regarding any delays in treatment (ie, they will be less concerned about a modest delay if they understand that the tumor has been present for a long time).

In 1955, Collins et al attempted to develop a method of measuring the growth rate of tumors. They hypothesized that if the change in tumor volume were known for a given time interval, the average growth rate could be calculated and used to estimate the time of inception for a given tumor[5]. Collins studied the interval between surgery and recurrence in patients with Wilms tumor. In a graph (see Appendix) that compared the patients’ age at diagnosis to their age at follow up, he noted that all local recurrences occurred at time intervals that were shorter than the patients’ “gestational age” (ie, their age plus 9 months) at diagnosis. This is consistent with the fact that the tumor’s “maximum age” at the time of diagnosis could be no greater than the child's age plus 9 months. Thus, a patient whose tumor is resected at the age of 3 can be considered cured when he or she reaches the age of 6 years and 9 months. This concept, known as the period of risk for recurrence, later became known as Collins’ law.[6] Other investigators have confirmed the accuracy of Collins’ law in patients with medulloblastoma and Wilms tumor.[6-10]

To address the question “how long have I had my cancer?” we used a modified version of Collins’ law. We reviewed the reported pace of local relapse following definitive local therapy as a means of estimating the age of the initial tumor at diagnosis. We hypothesize that the time of inception for various tumors might be estimated by quantifying the interval between gross total resection and time to local failure.

Methods

Assuming that the growth rate of a tumor is constant before diagnosis and after surgery (but before a local recurrence), one can use the time to local recurrence to estimate the tumor’s age. Figure 1 shows the rationale for this claim. The solid red and dotted green lines represent two scenarios. The solid line represents the situation in which only one tumor cell remains in the patient following surgery, and the dotted line represents that in which there are multiple remaining tumor cells. If more cells remain in the patient, the cancer will recur faster, thereby reducing the time to local recurrence. A group of patients who experience a local recurrence after surgery likely reflect diversity in the number of cells remaining in the post-operative tumor bed. At one extreme, the patients with the longest interval between surgery and local recurrence probably had the smallest number of residual tumor cells in the surgical bed, and their time to local failure may represent the time it takes for a small number of cancer cells to grow to a clinically evident size—which in turn might reflect the age of such cancers at diagnosis.

FIGURE 1

Idealized Graph Relating Tumor Growth Kinetics to the Clinical Appearance of a Cancer

FIGURE 2A

The Cumulative Absolute Percent of Local Recurrences as a Function of Time Following Initial Surgery, for Series of Patients with Breast Cancer

FIGURE 2B

The Percent of Local Recurrences Manifested as a Function of Time Following Initial Surgery, for Series of Patients with Breast Cancer

FIGURE 3A

The Cumulative Absolute Percent of Local Recurrences as a Function of Time Following Initial Surgery, for Series of Patients with Lung Cancer

FIGURE 3B

The Percent of Local Recurrences Manifested as a Function of Time Following Initial Surgery, for Series of Patients with Lung Cancer

For this analysis, we conducted a systematic review of the literature to identify studies that reported a time to local recurrence for various tumors. The search was conducted through several databases, including PubMed, Ovid Medline, and Elsevier, for the years 1956 to 2008, inclusive. The systematic review was focused primarily on the identification of prospective randomized controlled trials published in English in which one of the study arms was surgery alone. Prospective trials were preferred since in this type of study patients typically have regular follow-up evaluations and data collection is fairly consistent. In some instances in which there were limited prospective data, large retrospective studies were also included. In all instances, only studies that reported the rates of local failure over time were included. In some settings, the data were reported as local (+/– regional).

The systematic review involved adult patients with a clinical diagnosis of breast, lung, or rectal cancer. These cancers were chosen based on their prevalence in the population. Data were extracted from patients treated only with surgery, in order to avoid the confounding effects of radiation, hormonal therapy, or chemotherapy. These therapies may alter the growth kinetics of the tumor after initial surgery.

Data were obtained either from statistics listed in the studies or from graphs within the studies. If a graph was used to obtain data, simple measurements with a digital ruler were used to approximate data points (ie, the rates of local failure over time). After collection, the data were compiled into separate graphs for each of the tumor types. After all tumor types were graphed, the weighted average was calculated for each tumor type, with weight added to the studies with larger cohorts.

Data were considered in several ways. First, the absolute cumulative rate of LRF over time was considered. Second, in order to facilitate comparisons between studies, the data were considered as the percents of the LRFs that had manifested over time. With this approach, we were able to compare the distribution of “time to LRF” between studies even if the absolute magnitude of the LRF rate was different between studies. Third, for each disease site, the percent of the LRFs that had manifested over time was averaged from the individual studies. This average was weighted based on the total number of patients with an LRF from the study. The details are given below.

Absolute cumulative rates of LRF over time

For each article considered, the absolute cumulative rate of LRF, at various time intervals, was extracted from the report. Evaluable studies had to associate an LRF rate with a specific post-surgery time interval. In most of the studies, the LRF rates were recorded annually in the form of text, tables, or graphs. We plotted the data against time using Microsoft Excel in order to recreate the graphs from the published studies, as seen in Figures 2A, 3A, and 4A.

Computing the percent of LRFs manifest over time

The maximum reported cumulative LRF rate was noted (essentially that at the longest post-surgery time point with an associated LRF rate). At each time point, the percent of LRFs manifest by that time was calculated (ie, reported LRF rate / maximum LRF rate). This approach essentially renormalized each of the individual cumulative failure rate graphs to a maximum of 100% (Figures 2B, 3B, 4B).

Averaging data from different studies

The “percent of LRFs manifest over time” data from the multiple studies for each cancer type were averaged. The average was weighted based on the total number of patients with an LRF in each study. For a given year, the cumulative percent of LRFs for a given study was multiplied by the number of patients with an LRF in that study, and the sum of the products from the various studies was divided by the sum of all the patients with an LRF in those studies.

The articles considered for the different diseases are summarized in Tables 1-3.

Results

The absolute rates of LRF for patients with breast, lung, and rectal cancers are shown in Figures 2A, 3A, and 4A. Graphs illustrating the percent of LRFs manifest over time are shown in Figures 2B, 3B, and 4B. Note that the curves in Figures 2B, 3B, and 4B all reach 100%. The weighted averages for the data from the different diseases are shown in Figure 5.

Discussion

This analysis suggests that most LRFs for breast cancer occur in the range of 1 to 5 years post-surgery, and that the maximum time to LRF is usually in the range of 5 to 6 years. For lung and rectal cancer, most LRFs occur in the range of 1 to 3 years post-surgery, with a maximum time to LRF of ≈ 3 to 4 years. Using Collins’ law, one would then conclude that the age of most cancers at the time of diagnosis is in the range of 3 to 6 years. The LRFs occurring at shorter time intervals might result from patients with disease burdens greater than one cell after surgery.

This analysis is idealized, and several shortcomings arise from the underlying assumptions. First, it is assumed that the tumor growth rates before diagnosis and after resection are relatively similar. Based on the initial work by Collins, and subsequent work by Brown, Paulino, Sala, and others, this might be a reasonable assumption.[6-11] Nevertheless, changes in the regional physiology (eg, vasculature or immunologic status) induced by surgery might influence tumor growth.

TABLES 1–3

Summaries of Breast, Lung, and Rectal Cancer Series Contained in Systematic Reviews

FIGURE 4A

The Cumulative Absolute Percent of Local Recurrence as a Function of Time Following Initial Surgery, for Series of Patients With Rectal Cancer

FIGURE 4B

The Percent of Local Recurrences Manifested as a Function of Time Following Initial Surgery, for Series of Patients with Rectal Cancer

FIGURE 5

The Weighted Average, for All Cancer Types, of the Percent of Local Recurrences Manifested as a Function of Time Following Initial Surgery

Second, even those patients with a “relatively long” interval until local failure might have had a large number of cancer cells remaining following initial surgery. If this was the case, the observed times to local failure may underestimate the age of the cancer at diagnosis. As shown in Figure 1, the time to local failure will decrease wth increasing degrees of residual local tumor.

Third, patients with a prior diagnosis of cancer are often agressively monitored for a local recurrence (eg, with serial computed tomography scans) and might therefore present with a relatively small local/regional tumor recurrence. On the other hand, it is often difficult to detect a local recurrence on imaging since post-operative changes often limit the sensitivity of imaging. Similarly, there might have been inter-physician differences in the frequency of follow-up evaluations, and inter-patient variations in the propensity to seek medical attention, which might have influenced the reported pace of local failure. Nevertheless, the logarithmic nature of tumor growth would suggest that these effects are relatively modest. Furthermore, the preferential use of data from prospective studies was intended to minimize these variations. However, there appeared to be no systematic differences between the data from the prospective studies and those from retrospective studies with regard to the pace of the recurrences. For example, the absolute rates of reported failures were somewhat higher in the prospective series than in the retrospective series (Figures 3A and 4A); however, the pace of recurrences was similar in the prospective and retrospective series (Figures 3B and 4B). Thus, combining the data from the prospective and the retrospective series may be reasonable

Fourth, two of the studies reported local-regional recurrence, rather than “local only” recurrences. Still, the LRF data series for Forrest 1996 and Saynak 2009 used in Figures 2A, 2B, 3A, and 3B fall within the highest and lowest “local failure only” curves. Thus, the data from these studies appear very similar to data from studies that reported specifically local failures.

The information presented regarding the pace of local failure is likely not particularly relevant to treatment decisions. However, it might be helpful for patients to understand the natural history of their cancer. Patients are often very anxious to start their treatments as soon as possible. While this is understandable, the new information regarding the typical ages of cancers may help patients keep this time element in perspective.

The data presented here are from only three specific diseases and may not be applicable to other cancer types. A similar analysis could also be conducted of resected metastatic lesions. Their “time to failure” might also be indicative of their age, and one might be able to make some inferences regarding their “time of birth” relative to the treatment and diagnosis of the index primary lesion.

Conclusion

As an extension of Collins’ law, our graphs of local recurrence data suggest that the typical age of a cancer at diagnosis is approximately 5 to 6 years for breast cancer, and 3 to 4 years for lung cancer and rectal cancer.

Financial Disclosure: Dr. Marks receives research funds from the National Institutes of Health and the Lance Armstrong Foundation, and he is an unpaid advisor to Siemens. The other authors have no significant financial interests or other relationships with the manufacturers of any products or providers of any service mentioned in this article.

Acknowledgement: Thanks to Dorothy Riguera for her assistance in the preparation of this manuscript.

by Katharina Pachmann | February 16, 2011 4:59 AM EST

The question: How Long Have I Had My Cancer, Doctor? may be of more relevance than previously thought. Treatment approaches are, at present, not influenced by the "age"of the cancer.

Metastases determine the fate of the patient and their growth behaviour is most probably dependent on the growth behaviour and thus the "age" of the primary tumor. Growth behaviour of different tumors can be quite different, therefore, calculating a median time of tumor age may not be adequate.

Let us assume the story of a 65 year old patient in whom a malignant lump of 10mm size is detected in her breast. She may tell the physician: "Oh this lump has been in my breast for years and years and was always considered to be benign." Such a slow growing tumor may have a cell doubling time of about 120 days which implies that to grow from one tumor cell to 1000 tumor cells (10 doublings) has taken about three years. It takes another three years for this tumor to grow to 106 cells, a size of 1mm, which is still not detectable by the current available imaging systems. Still 3 more years pass until the tumor reaches the size of 109 cells equal to a tumor of 10mm size when it is detectable either by imaging or by the patient herself. The tumor has then been growing for 12-13 years before it is detected and most probably is removed surgically.

How about the metastases developing from this tumor: It is assumed that cells can start leaving the tumor at the 106 cells level when blood vessel formation is initiated and cell release may go on until the primary tumor is removed. Indeed, our investigations indicate that cells may start leaving the tumor already at the 100 000 cells level (1). Thus, metastasis formation can have started about 3 years before the tumor is detected and removed. If the metastases grow at the same rate as the tumor a metastasis can be expected to be detected the earliest at a size of 10mm which it has reached 6 years after the tumor has been removed.

Due to its slow growth, the tumor is not very sensitive to chemotherapy and the cells in the metastasis which had grown to 1000 until surgery of the primary tumor may be assumed to be reduced to 100. The patient will subsequently receive hormone therapy for five years reducing the cells in the metastasis to, let's say, 10 but may not completely eliminate the tumor cells.

If these cells restart growing at the same rate after hormone therapy has been stopped it will take about 27 doublings or about 9 years for the metastases to become measurable. Together with the 5 years of hormone therapy the reappearance of metastases in total has been delayed for about 15 years at what time the patient is 80 years old.

In contrast, in a young patient of the age of 40 the doubling time of the tumor cells might be assumed to be 36 days. It takes about 20 doublings, which is 2 years, for her tumor to grow to a still undetectable size of 1mm and a total of 3 years for her tumor to become detectable. Let us assume it is removed and characterized as triple negative.

At two years of growth her tumor had reached 106 cells metastases may start to grow, presumably at the same rate as the primary tumor. If untreated, overt metastases can be detectable 2 to 3 years after surgery.

However, as most breast cancer patients she is treated with adjuvant chemotherapy but no subsequent hormone therapy because the tumor is hormone insensitive (2).

The tumor in this patient, due to its rapid growth, is very sensitive to chemotherapy and the cells in the metastasis which had grown to 1000 during the last year until surgery of the primary tumor are assumed to be reduced to 1.

If this remnant cell restart growing at the same rate as before it will take about 30 doublings or about again 3-4 years for the metastases to become measurable. Chemotherapy has reduced the growth of her metastases 10 doubling times, which is about 1 year. The reappearance of metastases in total has been delayed for about 4 years at what time she is 44 years old.

This indicates that the "age" and thus the growth behaviour of the primary tumor may be extremely important for the treatment of the individual patient but it is not possible to determine from tumor size how long a cancer has been growing.

In this situation the behaviour of the circulating tumor cells and the speed of reappearance after chemotherapy might provide a tool to determine the growth activity of the tumor and to allow timely therapeutic interventions.

Camara O, Rengsberger M, Egbe A, Koch A, Gajda M, Hammer U, Jörke C, Rabenstein C, Untch M, Pachmann K. The Relevance of Circulating Epithelial Tumour Cells (CETC) for Therapy Monitoring during Neoadjuvant (Primary Systemic) Chemotherapy in Breast Cancer. Annals of Oncology 2007, 18:1484-1492
Kaplan HG, Malmgren JA, Atwood M. T1N0 triple negative breast cancer: risk of recurrence and adjuvant chemotherapy.. Breast J. 2009 5:454-60

by Frederic Grannis | February 15, 2011 3:19 PM EST

The basic concept of Collin's law is problematic. Perhaps a more accurate method of answering the patients question is, if one knows the tumor volume doubling time of the primary tumor to extrapolate backwards to the date at which there was only a single neoplastic cell. Dr. Arnie Rotter and I have crafted a tumor doubling time table for this approximation. Doing this approximation with lung cancers, the answer to the question "how long have I had this tumor?" is quite a bit longer, than the answer produced by the method of Cannon.

This method relies upon the assumption that the primary tumor will grow at a constant doubling rate until a large size is reached (Gompertzian growth), which is usually, but not always true. It must also be understood that the volume doubling time of metastases may be considerably faster than that of the primary tumor.

Fred Grannis MD

Section of Thoracic Surgery

City of Hope National Medical Center

Duarte, CA

by Mona Verducci | January 25, 2011 8:02 PM EST

It should make total sense for patients.... because the whole point is that cancer is not a local disease, its systemic. The tumor in the breast is not what kills people, its the metastatic disease that has been seeded from the tumor over 5 or 6 years, that ends up being the killer. Patients need to understand this so that they really understand the value of therapeutic options. Having a mastectomy is not going to effect the ability to eradicate disseminated tumor cells that are already seeded into distant locations. Systemic therapy, even for "early"stages of tumor growth, is where the focus needs to be. Patients need to be told the truth, and not to be under false notions of "cure" with local removal.

by Tammy Ellis | January 25, 2011 12:27 PM EST

I would think this data will be difficult for patients to understand. They are told to have their mammograms, colonoscopies and xrays and in the end when they are diagnosed we are going to tell them the cancer has been growing for 5 or 6 years! Even more difficult to understand because they have had yearly mammograms for the last 5 years and it took 5 years to show up. Doesn't make a whole lot of sense.

This article reviewed

How Heterogeneous Cell Populations, Cancer Cell Dormancy, and Minimal Residual Disease Influence the Natural History of Cancers

Understanding the Kinetics of Cancer: Implications from Prevention to Prognostication

Cancer Age: Can We Reliably Estimate and Apply This Knowledge?

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