Survival of patients with metastatic breast cancer: twentyyear data from two SEER registries
 Patricia Tai^{1}Email author,
 Edward Yu^{2},
 Vincent VinhHung^{3},
 Gábor Cserni^{4} and
 Georges Vlastos^{5}
DOI: 10.1186/14712407460
© Tai et al; licensee BioMed Central Ltd. 2004
Received: 22 April 2004
Accepted: 02 September 2004
Published: 02 September 2004
Abstract
Background
Many researchers are interested to know if there are any improvements in recent treatment results for metastatic breast cancer in the community, especially for 10 or 15year survival.
Methods
Between 1981 and 1985, 782 and 580 female patients with metastatic breast cancer were extracted respectively from the Connecticut and San FranciscoOakland registries of the Surveillance, Epidemiology, and End Results (SEER) database. The lognormal statistical method to estimate survival was retrospectively validated since the 15year causespecific survival rates could be calculated using the standard lifetable actuarial method. Estimated rates were compared to the actuarial data available in 2000. Between 1991 and 1995, further 752 and 632 female patients with metastatic breast cancer were extracted respectively from the Connecticut and San FranciscoOakland registries. The data were analyzed to estimate the 15year causespecific survival rates before the year 2005.
Results
The 5year period (1981–1985) was chosen, and patients were followed as a cohort for an additional 3 years. The estimated 15year causespecific survival rates were 7.1% (95% confidence interval, CI, 1.8–12.4) and 9.1% (95% CI, 3.8–14.4) by the lognormal model for the two registries of Connecticut and San FranciscoOakland respectively. Since the SEER database provides followup information to the end of the year 2000, actuarial calculation can be performed to confirm (validate) the estimation. The KaplanMeier calculation for the 15year causespecific survival rates were 8.3% (95% CI, 5.8–10.8) and 7.0% (95% CI, 4.3–9.7) respectively. Using the 1991–1995 5year period cohort and followed for an additional 3 years, the 15year causespecific survival rates were estimated to be 9.1% (95% CI, 3.8–14.4) and 14.7% (95% CI, 9.8–19.6) for the two registries of Connecticut and San FranciscoOakland respectively.
Conclusions
For the period 1981–1985, the 15year causespecific survival for the Connecticut and the San FranciscoOakland registries were comparable. For the period 1991–1995, there was not much change in survival for the Connecticut registry patients, but there was an improvement in survival for the San FranciscoOakland registry patients.
Background
Prospective trials have the disadvantages of requiring a long time to complete, and using highly selected patient subgroups in tertiary centers. While one waits for the results to mature, this delays additional research to improve treatment. If there were a method that allowed earlier prediction of the results of prospective trials, advances in cancer treatment could be attained within a shorter time period.
There is a parametric lognormal model, proposed by Boag [1–3] that had been retrospectively validated in the literature, and could be used prospectively for clinical trials to predict longterm survival rates several years earlier than would otherwise be possible using the standard lifetable/actuarial KaplanMeier method of calculation [4].
The prognosis for metastatic breast cancer is generally poor and therefore it is believed that statistical prediction models for longterm survival rates are not needed. Nevertheless, specific subgroups of metastatic breast cancer patients exist, for which depending on the treatment given, the prognosis is improved so that some patients can survive for some time, particularly for those with limited organs involvement such as involvement with bone and/or skin only. In this situation, for which the present study was relevant, a prediction model, even for metastatic breast cancer, can be useful.
Breast cancer, among other cancers, has the highest incidence in women, and many studies are currently in progress to assess treatment regimens. If, even for a subgroup of patients, the 10 and 15year survival rates can be predicted from followup data available only 3 years after a 5year diagnosis period, this would be a useful means of obtaining study results earlier than would otherwise have been possible. For example, a 15year survival rate calculated by the KaplanMeier method requires at least some patients to have been followed for 15 years. In addition prediction model such as the lognormal model can also be used to review the progress of treatment results for a specific period from a treatment center, and to compare that with another specific period of the same treatment center to evaluate the potential impact for any possible change in treatment policy or guideline.
Boag's lognormal model for longterm cancer survival rates has been available for use for some 50 years. When the lognormal model was first proposed in the 1940s, it was difficult to implement because of a lack of computing power, and lack of good quality longterm followup data from cancer registries. Since 1970s the model has been used by some authors in breast cancer, cervix uteri cancer, head and neck cancer, intraocular melanoma, choroidalciliary body melanoma, and small cell lung cancer [5–10]. Currently, although the computing power is sufficient, good quality followup data on a sufficient number of patients are seldom available, and it can be a limitation for its application. Large data registry such as the Surveillance, Epidemiology, and End Results (SEER) data [11] with good longterm followup data available can overcome this potential limitation.
Methods
Between 1981 and 1985, 782 and 580 female patients of metastatic breast cancer were extracted respectively from the Connecticut and San FranciscoOakland registries from the SEER database using SEER*Stat 5.0 software. The two registries were chosen because they are two of the earliest registries, with a large population. The data used were survival time, vital status, cause of death, age at diagnosis, and race.
The causespecific survival was defined as the interval from the date of diagnosis to the date of death from breast cancer or the last followup date for censoring purposes, if the patient was alive and still being followed at the time of analysis. The survival time of the uncured group of patients who died of breast cancer had been verified to follow a lognormal distribution previously [12].
Next, between 1991 and 1995, 752 and 632 female patients of metastatic breast cancer were extracted respectively from the two registries. The data were used to estimate the 15year causespecific survival rates before the year 2005. To be comparable, for both the 1981–1985 and 1991–1995 cohorts, the staging system used was the SEER historical system (classified as localized, regional, or distant, based on combined pathologic and clinical data). The choice of 1981–1985 and 1991–1995 has the advantage that the two time periods are not too far apart otherwise there would be too much changes of medical practice. These time periods have a minimum of 5 years followup.
The overall survival rates (OSR) of the two time periods were calculated using the KaplanMeier method. The actual relative survival rates (RSR) were calculated using SEER*Stat 5.0 software. The modified version of period analysis [13] was applied using the Hakulinen method [14] to obtain more uptodate absolute survival rates (ASR) and relative survival rates (RSR) for comparison purpose with a computer program run by Microsoft Excel software.
Validation of the lognormal model
The validation of the lognormal model has two phases. Phase 1 tests the goodness of fit to a lognormal distribution of the survival time of those cancer patients who died with their disease present, termed an uncured group with a fraction of 1C, where C is the cured proportion of patients. The lognormal distribution is similar to the normal distribution in that if the variable in the normal is time t, the variable in the lognormal is the logarithm of t. In other words, the investigators attempt to show that the logarithm of the survival time follows a normal distribution. Phase 2 attempts to show that the lognormal model, using shortterm followup data, can predict longterm survival rates comparable to those calculated by the KaplanMeier lifetable method with longterm available. This model can be used to estimate longterm causespecific survival rates (CSSR) by a maximum likelihood method (e.g., 10year and 15year survival rates) from only shortterm followup data. The maximum likelihood method is used to estimate the CSSR at time τ, and is calculated as [C+(1C)·Q]·100%, where Q is the integral of the lognormal distribution between the limits time τ and infinity.
The lognormal statistical model had been validated in stages III and IV breast cancer in a previous publication that survival rates could be estimated several years earlier than is possible using the standard lifetable actuarial method [12]. The survival time of unsuccessfully treated cases could be represented by a lognormal distribution, the longterm survival rates were predicted by Boag's method using a computer program run by Microsoft Excel. In this parametric lognormal model, the standard deviation S was fixed, and only the two remaining parameters, mean M and proportion cured C, were kept floating when using the maximum likelihood method. Multiple iterations converged to a stable solution for C.
A 5year period of diagnosis could be selected and patients followed as a cohort for an additional 3 years. The current study was for metastatic breast cancer patients treated between 1981 and 1985, with followup to the end of year 2000, making the series ideal for validating purposes. For example, for cases diagnosed during the 5year period, prediction of the 15year survival rate was made using data at the followup cutoff date of December 31, 1988 (i.e., 3 years after 1985). The 15year survival rate prediction was then validated by KaplanMeier lifetable calculations using the followup data available in 2000.
For metastatic breast cancer patients treated between 1991 and 1995, and followup to the end of year 2000, prediction of the 15year survival rate was made using data at the followup cutoff date of December 31, 1998 (i.e., 3 years after 1995) before the year 2005.
Results
From the cohort of 1981–1985 inclusively, 782 patients from the Connecticut registry were followed to the end of 1988. The lognormal model predicted the 15year CSSR to be 7.1% (95% CI, 1.8–12.4). The 15year CSSR was 8.3% (95% CI, 5.8–10.8) validated by the KaplanMeier calculation using actuarial followup data up to the end of year 2000.
From the cohort of 1981–1985 inclusively, 580 patients from the San FranciscoOakland registry were followed to the end of 1988. The lognormal model predicted the 15year CSSR to be 9.2% (95% CI, 3.9–14.5). The 15year CSSR was 7.0% (95% CI, 4.3–9.7) validated by the KaplanMeier calculation using actuarial followup data up to the end of year 2000.
Using the same method, the cohort of 1991–1995 inclusively, 752 patients from the Connecticut registry were followed to the end of 1998. The lognormal model predicted the 10year CSSR to be 12.6% (95% CI, 7.3–17.9). The 10year CSSR was 11.3% (95% CI, 7.8–14.8) validated by the KaplanMeier calculation using actuarial followup data up to the end of year 2000. The lognormal model predicted the 15year CSSR to be 9.1% (95% CI, 3.8–14.4), which cannot be validated before 2005.
For the cohort of 1991–1995 inclusively, 632 patients from the San FranciscoOakland registry were followed to the end of 1998. The lognormal model predicted the 10year CSSR to be 17.0% (95% CI, 12.1–21.9). The 10year CSSR was 15.9% (95% CI, 11.4–20.4) validated by the KaplanMeier calculation using actuarial followup data up to the end of year 2000. The lognormal model predicted the 15year CSSR to be 14.7% (95% CI, 9.8–19.6), which cannot be validated before 2005.
10 and 15year causespecific survival rates for Connecticut and San FranciscoOakland registries for 1981–1985 and 1991–1995 cohorts calculated by lognormal model (LN) and KaplanMeier (KM) method with 95% confidence intervals in brackets
Connecticut  San FranciscoOakland  

Year  1981–1985  1991–1995  1981–1985  1991–1995  
LN  KM  LN  KM  LN  KM  LN  KM  
10  11.5 (6.2–16.8)  11.0 (8.5–13.5)  12.6 (7.3–17.9)  11.3 (7.8–14.8)  12.3 (7.0–17.6)  9.7(6.8–12.6)  17.0 (12.1–21.9)  15.9 (11.4–20.4) 
15  7.1 (1.8–12.4)  8.3 (5.8–10.8)  9.1 (3.8–14.4)  N.A.  9.2 (3.9–14.5)  7.0 (4.3–9.7)  14.7 (9.8–19.6)  N.A. 
10 and 15year OSR^{a}, RSR^{b}, ASR^{c}, RSR^{d} for Connecticut registry for 1981–1985 and 1991–1995 cohorts with 95% confidence intervals in brackets
Connecticut  

Year  1981–1985  1991–1995  
OSR^{a}  RSR^{b}  ASR^{c}  RSR^{d}  OSR^{a}  RSR^{b}  ASR^{c}  RSR^{d}  
10  6.4 (4.6–8.2)  9.1 (6.7–11.5)  13.0 (12.2–13.8)  16.7 (15.7–17.7)  7.2 (3.7–10.7)  9.7 (6.4–13.0)  15.6 (14.6–16.6)  20.7 (19.5–21.9) 
15  3.2 (2.0–4.4)  5.7 (3.5–7.9)  4.4 (4.0–4.8)  6.4 (6.0–6.8)  N.A.  N.A.  5.8 (5.4–6.2)  8.9 (6.2–9.5) 
10 and 15year OSR^{a}, RSR^{b}, ASR^{c}, RSR^{d} for San FranciscoOakland registry for 1981–1985 and 1991–1995 cohorts with 95% confidence intervals in brackets
San FranciscoOakland  

Year  1981–1985  1991–1995  
OSR^{a}  RSR^{b}  ASR^{c}  RSR^{d}  OSR^{a}  RSR^{b}  ASR^{c}  RSR^{d}  
10  4.6 (2.8–6.4)  6.6 (4.2–9.0)  13.3 (12.3–14.3)  16.9 (15.7–18.1)  8.8 (5.7–11.9)  11.4 (7.9–14.9)  14.7 (13.7–15.7)  18.4 (17.2–19.6) 
15  2.4 (1.2–3.6)  4.1 (1.9–6.3)  4.6 (4.2–5.0)  6.6 (6.0–7.2)  N.A.  N.A.  5.3 (4.9–5.7)  7.4 (6.8–8.0) 
Discussion
Lognormal model
Rutqvist studied the fit of Boag's lognormal model to the survival times of 8170 breast cancer cases reported to the Swedish Cancer Registry during 1961–1963. The model fitted the 1961–1963 data well for the entire case material and for patients aged less than 70 years. In this registry, the lognormal model did not fit the data for patients aged greater than 70 years, who were more likely to be censored because of coincidental causes of death. Another disadvantage stated by the author was that large number of patients was required to obtain estimates with reasonably small standard errors for breast cancer.
With another series of the Norwegian Cancer Registry of 14,000 breast cancer cases, Rutqvist et al. [15] deduced that lognormal is the best model because other models did not fit the observed survival in all stages, ages, and time periods (twoparameter models, such as exponential or extrapolated actuarial, or threeparameter models, such as sum of two exponential, exponential with shoulder, Weibull). Both the exponential and extrapolated actuarial models assume that the conditional relative survival is lowest immediately after treatment. With the lognormal model, the survival curve has a low initial mortality that rapidly increases to a maximum, with a slow decrease in the mortality after the maximum has occurred.
Requirements for using the lognormal model
The lognormal model can only predict causespecific survival, because other coincidental causes of death are too unpredictable (e.g., the rate of stroke). Therefore, overall survival cannot be predicted. The maximum likelihood method is the most accurate method for fitting the lognormal model with the smallest mean squared error. However, there are some requirements for its use. The maximum likelihood method fails to converge to a stable solution using the initial estimates if there is extensive censoring within the data. This occurs if patients are lost to followup or die from coincidental noncancerous causes. The frequency of failure to yield a successful fit for lognormality was greater when onefourth of cases were designated as lost to followup. Gamel et al. established a stable linear algorithm for fitting the lognormal model to survival data. To achieve convergence, some authors have fixed one or two parameters of the lognormal model to preselected values to simplify the iterative procedure required for convergence [6].
Some prognostic factors follow lognormal distribution
Prognostic factors in patients with distant metastases at the time of diagnosis were investigated by Rudan et al. [16], and Chapman et al. [17], primary tumor size was a significant prognostic factor. Engel et al. [18] found that the number of metastatic cases and the time to metastasis depended on the tumor diameter at diagnosis. Cell growth is essential for the development of tumors. Tumor size is therefore the most important factor in describing tumor biology. As the tumor size increases, the probability of nodepositivity increases. Another study group also found this correlation up to 5 cm [19]. Tubiana and Koscielny [20] have found a highly significant correlation between tumor size and the probability of distant metastasis. The distribution of tumor sizes at metastatic spread was lognormal with a median diameter equal to 3.5 cm. The patients were subdivided into 3 groups according to the histological grade. In each subgroup there was a significant correlation between tumor size and the probability of distant spread. The distributions were lognormal and the median size was markedly larger for grade 1 tumors.
A number of quantitative postmortem observations regarding the size distribution of metastases have been published [21–23]. These studies revealed a skewed distribution with a high proportion of smaller metastases, and a significant tail extending to the larger metastases, consistent with a lognormal distribution. The more detailed measurements from human liver metastases provided by Yamanami et al. were found to approximate the lognormal distribution reasonably well.
A hypothesis was proposed by Kendal [24] that the time available for the growth of metastases is normally distributed, presumably as a consequence of the summation of multiple independently distributed time intervals from each of the steps and of the Central Limit Theorem. For exponentially growing metastases, the corresponding size distribution would be lognormal; Gompertzian growth would imply a modified (Gompertznormal) distribution, where larger metastases would occur less frequently as a consequence of a decreased growth rate. These two size distributions were evaluated against 18 human autopsy cases where precise size measurements had been collected from over 3900 macroscopic hematogenous organ metastases. The lognormal distribution provided an approximate agreement. Its main deficiency was a tendency to overrepresent metastases greater than 10 mm diameter. These observations supported the hypothesis of normally distributed growth times, and qualified the utility of the lognormal and Gompertznormal distributions for the size distribution of metastases.
Cancer sites with survival times demonstrated to follow the lognormal distribution in the literature as at year 2004
Cancer sites  Author 

Head and neck cancer  Berg [25], Mould[7] 
Nasal sinus cancer  Berg [25] 
Mouth and throat cancer  Boag [3] 
Mouth  Berg [25] 
Thyroid  Tai*[26] 
Larynx, tongue  Mould & Tai*[27] 
Non small cell lung cancer  Berg [25] 
Small cell lung cancer  Tai*[10] 
Intraocular melanoma  Gamel [8] 
Cutaneous melanoma  Gamel [9] 
Breast cancer  Boag [3], Berg [25], Rutqvist [5,15], Gamel [28,29], Haybittle [30], Royston [31], Tai*[12] 
Bone sarcomas  Berg [25] 
Cancer of uterine cerivx  Mould & Boag*[6], Berg [25] 
Ovarian cancer  Berg [25], Tai*[32], Royston [31] 
Hypernephroma  Berg [25] 
Bladder cancer  Berg [25] 
Prostate Cancer  Mould & Tai*[33] 
Gastric cancer  Berg [25], Maetani [34] 
Lymphoma  Berg [25] 
Chronic leukemia  Tivey [35] 
Brain tumors  Berg [25] 
42 SEER cancer sites  Tai [36] 
Variation of survival rates over time
In order to determine whether current programs for the management of metastatic breast cancer have led to improved patient survival, Debonis et al. [39] determined the median survival times for fiveyear intervals of 849 patients admitted to the City of Hope National Medical Center with metastatic breast cancer from 1955 to 1980. Survival times in each of the clinical subsets remained unchanged during the period of observation, regardless of the therapeutic modalities included in the treatment regimens. The study indicates that changes in palliative therapy for metastatic breast cancer during the 25 years of observation have not influenced overall survival. On the contrary, Dickman et al. [40] studied the survival of cancer patients in Finland during the years 1955–1994. The 5year RSR for distant metastases breast cancer had increased from 10% for the period 1955–1964 to 22% for 1985–1994.
The tumor registry at YaleNew Haven Hospital, which began recording data in 1920, was utilized by Todd et al. [41] to examine the ultimate outcome of all breast cancer patients who were initially diagnosed at Yale with metastatic breast cancer. The median survival of these patients increased steadily from 21 months in 1920 to 41 months in the decade from 1970 to 1980. The percentage of women actually surviving 5 years increased from 5% in the 1920s to approximately 25% in the 1960s. Despite the use of combination drug programs in the 1970s, the percentage of these patients remaining alive at 5 years remained near 25%. Firm conclusions cannot be made from a retrospective study spanning 60 years, although the trends depicted the lack of continued improvement indicate that the current therapeutic approach to metastatic breast cancer in that period may not result in dramatic improvement in overall survival.
Geographical variation of survival rates
Farrow et al. [42] documented substantial geographical variation in patterns of treatment of cancer and other diseases. Because cancer treatment is not uniform nationwide in the States, survival following the diagnosis of cancer might also be expected to vary geographically. Survival data from the nine populationbased registries in the SEER Program were analyzed for cancers of the stomach, colon, rectum, lung, breast, uterus, ovary, prostate, and bladder. The patients included all nonHispanic white patients diagnosed with cancer of one of the selected sites during 1983–1991. Regional variation in crude fiveyear survival rates across the nine SEER areas was most marked for cancers of the uterus and prostate. For uterine cancer, for example, fiveyear survival ranged from 73.2% in Connecticut to 84.0% in Hawaii. Less marked variation was observed for cancers of the colon, rectum, and breast. For cancers of the bladder, ovary, stomach, and lung, survival rates five years after diagnosis were relatively invariant across the SEER areas.
Maggard et al. [43] also found that variations in the breast cancer mortality rates exist between states. A nearly 50% increase is observed between the states with the highest and lowest mortality rates. Adjusted analyses demonstrated that stage at presentation is a more important predictor of mortality variation than treatment differences. Goodwin et al. [44] examined breast cancer incidence, survival, and mortality in the 66 health service areas covered by the SEER program for women aged 65 and older at diagnosis. They found that there was considerable geographic variation in survival from breast cancer among older women, and this contributed to variation in breast cancer mortality. The elevated mortality in the Northeast is apparent only in older women [45]. For women aged 65 years and older, breast cancer mortality is 26% higher in New England than in the South, while incidence is only 3% higher. Breast cancer mortality for older women by state correlates poorly with incidence (r = 0.28).
The abovementioned results are consistent with that from the present study: the Connecticut registry has lower CSSR than the San FranciscoOakland registry for the period 1991–1995. The Connecticut cohort has median age at diagnosis of 66 (range 25–103), while the San FranciscoOakland cohort has lower median age of 63 (range 26–96). It could be argued that new treatments evolved in the recent decade have improved the survival of the breast cancer patients, and younger patients benefit more than the older patients. Apart from treatment offered, changes of survival rates over time or geographical areas can be due to comorbidities or other characteristics such as race, age, and differences in staging procedures.
Conclusions
For the period 1981–1985, the 15year causespecific survival for the Connecticut and the San FranciscoOakland registries were comparable. For the period 1991–1995, there was not much change in survival for the Connecticut registry patients, but there was an improvement in survival for the San FranciscoOakland registry patients.
List of abbreviations
 CSSR:

Causespecific survival
 SEER:

Surveillance, Epidemiology, and End Results
 OSR:

Overall survival rate
 ASR:

Absolute survival rate
 RSR:

Relative survival rate
Declarations
Acknowledgments
PT: Saskatchewan Cancer Agency Research Grant Award 2792.
GC: János Bolyai Research Fellowship from the Hungarian Academy of Sciences.
Authors’ Affiliations
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