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© 1999 American Society for Clinical Oncology Frequency of First Metastatic Events in Breast Cancer: Implications for Sequencing of Systemic and Local-Regional TreatmentFrom the Departments of Biomathematics and Radiation Oncology, The University of Texas M.D. Anderson Cancer Center, Houston, TX. Address reprint requests to Howard D. Thames, Department of Biomathematics, Box 237, The University of Texas M.D. Anderson Cancer Center, 1515 Holcombe Blvd, Houston TX 77030; email hdt{at}odin.mdacc.tmc.edu
PURPOSE: The sequencing of treatment for early breast cancer is controversial. The purpose of this study was to quantify the risk of delaying surgery, using estimates of the frequency of first metastases from breast primary tumors. PATIENTS AND METHODS: The probability that 560 (node-negative), 657 (with one to three positive nodes), and 505 (with more than three positive nodes) women treated without adjuvant chemotherapy would be free of distant disease at presentation was fit to a mathematical model of the seeding of distant metastases and combined with estimates of the growth rate to calculate the frequency of first distant disseminations per month. RESULTS: Frequencies of first distant metastases were approximately 1% to 2% per month, 2% to 4% per month, and 3% to 6% per month in T1 patients who were node-negative, had one to three positive nodes, or more than three positive nodes, respectively. As a result, the typical patient with T1 disease, who has a 70% to 80% chance of being free of distant disease, runs a 1% to 4% risk of distant dissemination for each month surgery is delayed. Assuming a 30% reduction in mortality caused by adjuvant chemotherapy, the model predicts that T1 patients treated with neoadjuvant chemotherapy would potentially have a higher rate of distant metastasis development than those treated with an initial surgical resection followed by adjuvant chemotherapy. CONCLUSION: We formulate the hypothesis that optimal sequencing of surgery and systemic treatment of breast cancer may be size-dependent, with a disadvantage or no benefit from neoadjuvant treatment for T1 patients but an increasing benefit with increasing size of the primary tumor.
THE RATIONALE FOR early administration of chemotherapy to patients with early-stage breast cancer is intuitive to most oncologists. Randomized trials1-3 have demonstrated that chemotherapy reduces the risk of distant metastatic disease even in favorable subsets of breast cancer patients, such as women with negative lymph nodes. In addition, a randomized study comparing radiation and chemotherapy sequencing following breast-conserving surgery4 found that earlier administration of chemotherapy resulted in a risk for distant metastases that was lower than that in the group for whom chemotherapy was delayed so that radiation treatment could be given first. A sequencing strategy using neoadjuvant chemotherapy minimizes the time period from diagnosis to systemic treatment of potential micrometastases, which is clearly of critical importance when the risk of metastatic disease is high.
The likelihood of distant dissemination at the time of diagnosis is dependent on the primary tumor volume and grade and other factors, such as the status of axillary lymph nodes.5 Women who present with stage I disease (a tumor 2 cm or less in diameter with negative axillary lymph nodes) have less than a 20% probability of harboring microscopic distant disease. The number of such early-stage cancers has increased while the incidence of stage II to IV breast cancer has decreased, because of the increasing use of mammography and public education about breast cancer.6 The sequencing of systemic and local-regional treatment for early breast cancer is, therefore, an important, although still controversial, clinical question. The current trend is to extend the use of neoadjuvant treatment to T1 (tumor diameter Breast cancer usually becomes a life-threatening disease only after it has spread systemically. In this article, we consider the question of whether the neoadjuvant strategy is optimal when the risk of micrometastases is low, as with most T1 tumors. We used a mathematical model to estimate the risk of delaying surgery for any reason, including the use of neoadjuvant chemotherapy, in terms of the number of women who present free of distant disease but experience a first distant metastasis during the delay of surgery.
Data Data were extracted from publications describing the following: (1) The relationship between tumor volume/nodal status and the incidence of distant disease in women treated without chemotherapy and observed for long times.5 These data are replotted in Fig 1, which shows the proportion of women free of distant disease at long follow-up times with increasing primary tumor diameter ranging from 2 to 7 cm, for node-negative patients (n = 560) and patients with one to three (n = 657) or more than three (n = 505) positive axillary nodes. The median follow-up on these women was at least 15 years, and we assume here that freedom from distant disease after such long follow-up is equivalent to freedom from distant disease at presentation.
(2) Axillary node status as a function of primary tumor volume8 (data not shown). These results were used to reconstruct the distribution, with primary tumor size, of patients in the different node categories. (3) The volume-dependent growth rate of primary breast tumors9-11 and screening data for the age-dependent growth rate of primary breast tumors.12,13 These data were used to estimate the primary tumor growth rates in patients younger than 50 years old. The estimated numbers of women free of distant disease at presentation as listed in Table 1 were reconstructed as follows. (1) In Fig 6 of their article, Koscielny et al5 show the proportion of patients with distant metastases by nodal status, eg, among node-negative patients, 21% of those with a tumor diameter of 1.9 cm, 32% of those with a tumor diameter of 4.2 cm, etc, had distant metastases. Among women with one to three positive nodes, 26% of those with a tumor diameter of 1.9 cm presented with distant disease, as did 58% of those with a tumor diameter of 4.2 cm, etc, and similarly for women with more than three positive nodes. (2) Numbers of women at risk in these subgroups were taken from Koscielny et al's5 Table 2 (total number of women with no positive nodes, 560; total number with one to three positive nodes, 657; total number with more than three positive nodes, 505). (3) Figure 3 of Koscielny et al's later study8 (cumulative proportions of women with one or more, two or more, etc, positive axillary nodes by primary tumor volume) was used to estimate proportions of women by nodal status at the volumes for which data are available for incidence of distant metastases (as in item 1 above), eg, for node-negative patients, 37.4% would be expected to have distant metastases at a tumor diameter of 1.9 cm, implying 209 women = 0.374 x 560 at risk (of whom 44 = 0.21 x 209 with distant disease and 165 without), 24.3% would be expected to have distant metastases at a tumor diameter of 4.2 cm, implying 105 women at risk (of whom 34 with distant disease and 71 without), and so on.
Assumptions
Detailed Calculations
Model
 is a parameter vector with probability distribution  , and the volume-specific growth rate f' =  f/t decreases with time. Examples of such growth models are the power-law,9 Gompertz,10 and logistic11 models. Hart et al9 suggest that large-scale mammography screening–trial data are not as consistent with the Gompertz and logistic growth models as with a simple power-law model, wherein:
We used one model of each type (power-law and Gompertz). The volume-specific growth rates are given by f' =
Seeding of metastases.
No seeding occurs until the primary tumor reaches the threshold volume vT. The threshold volumes vT, which are reached at times tT, are distributed in the patient population with probability distribution
 i(, v, v)] = 1. The probabilities  and exp (-i) are independent of each other, so we may define s0i(, v) as average frequency, per unit volume of primary tumor, of first seeding to site i:
and without distant metastases. Invoking assumption 5, this can be calculated from data describing the incidence of metastases across a range of volumes. Averaging equation 6 over the growth rates, we obtain
 . denotes "average." The observed decrease in the proportion of women presenting free of distant disease with increasing primary tumor volume (Fig 1) is the sum over the possible sites of distant dissemination, ie,
It should be emphasized that we deal here with averages, which likely describe widely different degrees of malignancy, estrogen receptor status, etc. Consequently, replotting Fig 1 for particular prognostic subgroups, an exercise that must await the availability of raw data, may give a different picture from that presented in Fig 1. Our conclusions, on the other hand, are relevant to the average breast tumor for a particular primary tumor diameter and pathologic node status found in women in a particular age range (see below). A second point is that no distinction was made in the articles published by Koscielny et al5 between local failures and cures, which undoubtedly differ in the frequency of distant failure. However, the frequencies of first metastases that we estimate depend on the slope, not the absolute value, of the relationship in Fig 1, and slopes are likely much less sensitive to differences in distant failure rate between local cures and failures.
Estimated Absolute Frequency of First Seedings
According to equations 6 through 9, we obtain estimates of the frequency of first seedings per unit volume s0(v) by multiplying the slope estimate from Table 2 by the volume-specific growth rate, eg, for women younger than 50 years old. Therefore,
Proportion of Women With Distant Failure
According to the methods developed above, the frequency with which first metastases are seeded from breast primary tumors is the product of three factors: (1) the volume v of the primary tumor, (2) the slope of the curve (Fig 1) that relates the proportion of patients free of distant disease at presentation to the volume v of the primary tumor (Table 1), and (3) the volume-specific growth rate of the primary tumor at volume v. The slopes of the curves in Fig 1 (presented in Table 2) are the average for all prognostic groups (modeled here as determined by threshold volume for initiation of distant seeding and primary tumor proliferation rate) of the ratio of the frequency of first metastatic seedings per unit volume of primary tumor to the growth rate of the primary tumor. For clarity, we emphasize here that although the methods developed above apply to both regional and distant metastases, the words "metastasis," "distant dissemination," and so forth are restricted to mean only the seeding of distant metastatic sites, not axillary lymph nodes. The slopes are multiplied by the volume-specific growth rates to calculate the frequency per month of first metastatic events in T1 patients younger than 50 years old as set out in Table 3. Depending on choice of model of primary tumor growth kinetics, frequencies range from 0.01 to 0.02 per month (in node-negative women), from 0.02 to 0.04 per month (in women with one to three positive nodes), and from 0.03 to 0.06 per month (in women with more than three positive nodes), with diameters ranging from 1 to 7 cm. It must be kept in mind that a diameter of 1 cm is outside the range of diameters in the original data,5,8 and thus our estimates must be understood as extrapolations based on the fits in Fig 1.
These results, which are to be understood as hypothesis-generating and not conclusively proven, have implications for the treatment options of the patient with confirmed T1 disease. First, there should be no consideration of delay of treatment for holidays, weddings, and the like. These women have a 70% to 80% chance to be free of distant disease, depending on nodal status, which is most likely to be node negative (60%8) or one to three positive nodes. The results shown in Table 3 imply that with each month surgery is delayed, the patient with T1 disease runs a 1% to 4% risk of dropping out of the favored group that is free of distant metastases. The second consequence relates to the sequencing of systemic treatment. To compare the number of patients who potentially might not benefit (because of newly disseminated distant disease) from a chemotherapy-first sequencing approach with the number of patients expected to benefit from an early intervention against existing distant disease, we used the expected reduction in mortality from adjuvant chemotherapy,16 assuming that, on average, a 30% reduction in distant failure is achieved independently of disease stage. The results are shown in Fig 2, which shows, for patients younger than 50, the percent distant failure after no chemotherapy (upper dotted curve) compared with the percent distant failure after adjuvant chemotherapy (lower dotted curve). Percent distant failure after no chemotherapy is also compared with the percent distant failure after neoadjuvant chemotherapy, where the range of possible new distant disease varies between 0% (neoadjuvant therapy is completely effective against newly disseminated disease, lower solid curve) and 65% of newly seeded metastases (neoadjuvant therapy is 35% effective against newly disseminated disease, upper two solid curves according to growth assumptions used). Neoadjuvant therapy is assumed to have an advantage over adjuvant therapy because of treatment 1 to 2 months earlier of already disseminated distant disease (35% reduction in distant failure for neoadjuvant therapy versus 30% for adjuvant therapy). One might suppose that the difference between the solid curves would be about one half as big for women older than 50 because of the slower growth rate of primary tumors in these women.12 Caution must be exercised in drawing such a conclusion, however, since the slopes of the curves in Fig 1 for the different age groups are not available from the data sources used here. According to Fig 2, it would be difficult to demonstrate a difference in outcome based on sequencing. Nevertheless, the trend is clear: the benefit of neoadjuvant chemotherapy seems to be stage-dependent and highest among the more advanced tumors. Thus in the node-positive patients, the number of patients who benefit from neoadjuvant treatment outnumbers those who don't benefit once the tumor diameter is about 3 cm or greater, consistent with clinical experience with locally advanced tumors17 (Fig 2B and 2C). On the other hand, the possibility of new distant disease leads to a potential disadvantage, or no advantage, from neoadjuvant treatment in node-negative patients with tumors less than approximately 3 cm in diameter (Fig 2A) and for T1 patients in general, whatever the nodal status. The typical T1 patient (likely node negative or with one to three positive nodes and 70% to 80% likely to present free of distant disease) runs the highest risk of a disadvantage or no advantage from neoadjuvant treatment (Fig 2A and 2B).
We have presented a method to estimate, from a reconstruction (Table 1) of published data (Fig 1), the average frequency of first distant metastatic events as a function of volume of primary tumor (Table 3), using the slope (Table 2) of the curves in Fig 1. The method has been applied to calculate how often such events occur on average in breast cancer patients who present free of distant disease and might therefore expect a cure from immediate local treatment (Fig 2A through 2C). These results lead us to propose the hypothesis that the delay of surgery in T1 patients for any reason carries an appreciable risk for development of new distant disease and, further, that optimal sequencing of surgery and chemotherapy for breast cancer depends on the size of the primary tumor, such that the higher the stage of disease, the greater the advantage to be expected from neoadjuvant systemic treatment rela-tive to adjuvant treatment (because of earlier intervention against existing metastatic disease). On the other hand, it may be disadvantageous or of no benefit for T1 patients (because of the potential for seeding new metastases before surgery in women who present free of distant involvement). The use of the word "average" in the previous paragraph is important. It is in such a broad sense that our predictions are to be understood, because the data on which they are based take account only of primary tumor diameter, pathologic node status, and, in the case of the volume-specific primary tumor growth rates, patient age. As important as these are for prognosis, there will clearly be exceptions, such as the patient who is estrogen receptor–negative with a high-grade tumor. When the method developed here can be applied to raw data, where stratification is possible for the increasing range of potentially important prognostic factors, then it will be possible to define the seeding frequencies of new metastases in each of these prognostic factor categories. Until that time, our hypothesis applies most strongly to the "average" breast cancer of a given diameter and with a given level of axillary lymph node involvement for a woman younger than 50, and possibly to a somewhat lesser extent in older patients. The comparison between adjuvant and neoadjuvant treatment pictured in Fig 2 is certainly consistent with the results of the randomized trial NSABP B-18,24 in that there is little expectation of a significant difference in outcomes based on sequencing in a varied patient population. The point being made here rather is that a trend is evident in Fig 2A through 2C, a trend that suggests a disadvantage or no advantage for neoadjuvant treatment in women with T1 tumors, the majority of whom present free of distant disease. There is no advantage to early intervention in these women, but there is (as we have attempted to quantify) the chance of newly seeded distant disease. In more advanced disease, on the other hand, many women present with distant involvement. Consequently, there is an advantage from early intervention with chemotherapy and little possibility of newly disseminated disease.
Four randomized trials that included more than 100 patients and were published in peer-reviewed journals have addressed the sequencing of systemic and local treatment of breast cancer (Table 4). The results are either equivocal or show an advantage for neoadjuvant treatment. Few of the patients accessed in these trials had early disease, and the question being asked was often the effectiveness of neoadjuvant chemotherapy for breast conservation with locally advanced disease. The NSABP B-18 trial25 is an exception with regard to early cancer, in that 28% of patients had primary tumor sizes under 2 cm and 43% in the postoperative group had pathologically negative lymph nodes.26 The 5-year outcome with respect to disease-free survival, distant disease-free survival, and overall survival was nearly identical between the group randomized to four cycles of preoperative chemotherapy and the group randomized to the same chemotherapy given postoperatively. There was no statistically significant difference, in either disease-free survival or survival at 5 years, between the groups when they were analyzed by clinical tumor size, clinical node status, and age. It is intriguing, however, that disease-free survival, when read from Fig 3 in the article by Fisher et al,25 was either slightly higher in the postoperative group, eg, in the
The frequencies in Table 3 are consistent with the results of periodic mammographic surveillance among 3,184 nonpalpable breast lesions.27 The protocol called for repeat mammography of the ipsilateral breast 6 months after first detection and follow-up bilateral mammography 6 to 12 months later. Of 17 cancers found in the study population, two (12%) demonstrated an axillary node metastasis. The seeding frequency of axillary nodes is about 40% higher than that of distant metastases (based on data in8, calculation not shown). Therefore, assuming for simplicity that the 17 women were node-free at detection and had 1.3-cm lesions (the median size at detection27), we would expect the proportion developing a positive axillary node 6 months later to lie near the estimates provided by the two growth models for a 1.3-cm tumor. These are approximately 6 x 1.2 x 1.4 (10.1%) and 6 x 1.8 x 1.4 (15.1%), ie, 1.7 and 2.6 patients (number of patients observed, 2). For distant metastases, we would expect the proportion to lie near 6 x 1.2 (7.2%) and 6 x 1.8 (10.8%), ie, 1.2 and 1.8 patients (no patients observed after median follow-up of 60 months). The assumptions on which the calculations are based deserve comment. The assumption of decelerating growth (assumption 1) is nearly certainly true, but there are qualitative differences between the predictions of models that describe it: growth according to the power-law model9 slows relatively quickly over the clinical range of volumes, whereas there is a relatively slow deceleration of growth for the Gompertz10 and logistic11 models. For this reason, we used both types of model in the calculations, producing the two upper solid curves in Fig 2 and two sets of entries in Table 3. It is worth noting that growth rates estimated from mammography screening studies generally are lower than those seen clinically, for two reasons. The first is the selection bias for slower-growing tumors, and the second is that the growth rate in the predetectable period is faster than that predicted by the models.11 These would lead to an underestimate of the frequency of first seedings. On the other hand, the errors in the slopes estimated at 1-cm diameter (Table 2) are much higher than at larger diameters, and this reflects the fact that the smallest diameter in the source data5,8 was about 2 cm, as explicitly shown in Fig 2. Assumption 2, that distant metastasis occurs from the primary tumor only, was necessary for the mathematics and will likely not hold for the odd case, eg, the small T2with extensive axillary disease, capsular rupture, etc. In these cases, our estimate (which is for the averagetumor) of the frequency of first seedings from the primary tumor will be too high. The assumption of a threshold volume (assumption 3) seems inescapable, given what is known about the preinvasive stages in the evolution of malignant tumors. However, we discuss average behavior, and our modeling can include the possibility that the distribution of threshold volumes is centered close to zero. We see this variable, on the other hand, as a marker of malignancy that was very widely distributed in the large population of breast cancer patients on which this analysis was based.5,8,12,13 The effect of chemotherapy on the seeding frequency is unknown, and we have chosen to assume simply that no change occurs (assumption 4). We made this choice, even though neoadjuvant chemotherapy results in a measurable volume reduction in upward of 80% of patients, small tumors included, and occasionally in a complete clinical response. The choice was based on two considerations. First, metastatic propensity is likely related to the total number of metastatically capable clonogenic cells in the primary tumor, and a significant number of these clonogens would remain even after a 90% eradication of the primary tumor, eg, a decrease from 1,000,000 to 100,000. This would argue for some modest reduction in the metastatic rate. Second, pretreatment of experimental tumors with cytotoxic drugs has been shown to increase the proliferation rate of the primary tumor,18 which could potentially increase the metastatic rate. In the final analysis, no one knows what effect cytotoxic treatment has on the metastatic frequency, and we chose to stick with the assumption that it remains constant. Lastly, assumption 5 is a restatement of Hellman's spectrum hypothesis14 for the natural history of breast cancer. This seems increasingly plausible in contrast to its main contender, Fisher's systemic theory,19 when one takes into account the Danish20 and Canadian21 randomized trials showing that survival is influenced significantly by local-regional treatment. The monthly seeding frequencies shown in Table 3 have interesting implications for physicians counseling patients before they choose among treatment options. Suppose a 48-year-old woman presents clinically node negative with a clinical tumor diameter of 2 cm. Then, absent other information, her chances to be node negative are about 60%8 and to be free of distant dissemination about 80%,5 and according to Table 3, she runs a 1% risk each month of dropping out of this favored group. If she has axillary node involvement, on the other hand, this is most likely limited to one to three positive nodes, and her likelihood to be free of distant dissemination will be about 70%.5 In this case, she runs a 2% to 4% risk each month of dropping out of this favored group. In other words, even with such an initially favorable outlook, and regardless of whether chemotherapy is given postoperatively or not, there should be no room in the discussion for delaying treatment for any reason. Because of the small differences evident in Fig 2, it is unlikely that a randomized trial of sequencing limited to T1 tumors could address the hypothesis presented here. However, patients with T1c to T3 tumors are currently being accessed in a trial in which all arms receive neoadjuvant chemotherapy.7 A subgroup analysis of this trial, or longer follow-up on an earlier trial,25 might provide confirmation of the predicted trend. In regard to the present results, the prediction is that optimal sequencing of systemic and local treatment depends on tumor size, in that chemotherapy for breast cancer should be delivered after local treatment of T1 tumors and before local treatment of T2 tumors and locally advanced cancer. Delay of treatment should be avoided, even for favorable T1 tumors.
1. Fisher B, Redmond C, Dimitrov NV, et al: A randomized clinical trial evaluating sequential methotrexate and fluorouracil in the treatment of patients with node-negative breast cancer who have estrogen-receptor-negative tumors. N Engl J Med 320:473-478, 1989[Abstract] 2. Mansour EG, Gray R, Shatila AH, et al: Efficacy of adjuvant chemotherapy in high-risk node-negative breast cancer. N Engl J Med 320:485-490, 1989[Abstract] 3. The Ludwig Breast Cancer Study Group: Prolonged disease-free survival after one course of perioperative adjuvant chemotherapy for node-negative breast cancer. N Engl J Med 320:491-496, 1989[Abstract]
4.
Recht A, Come SE, Henderson IC, et al: The sequencing of chemotherapy and radiation therapy after conservative surgery for early-stage breast cancer. N Engl J Med 334:1356-1361, 1996 5. Koscielny S, Tubiana M, Lê MG, et al: Breast cancer: Relationship between the size of the primary tumour and the probability of metastatic dissemination. Br J Cancer 49:709-715, 1984[Medline] 6. Osteen RT, Cady B, Chmiel JS, et al: 1991 National Survey of Carcinoma of the Breast by the Commission on Cancer. J Am Coll Surg 178:213-219, 1994[Medline] 7. National Surgical Adjuvant Breast and Bowel Project Protocol B-27: Docetaxel before or after surgery or no docetaxel in treating women with operable breast cancer. Http://www.nsabp.pitt.edu/B-27.htm 8. Koscielny S, Lê MG, Tubiana M: The natural history of human breast cancer: The relationship between involvement of axillary lymph nodes and the initiation of distant metastases. Br J Cancer 59:775-782, 1989[Medline] 9. Hart D, Shochat E, Agur Z: The growth law of primary breast cancer as inferred from mammography screening trials data. Br J Cancer 78:382-387, 1998[Medline] 10. Norton L: A Gompertzian model of human breast cancer growth. Cancer Res 48:7067-7071 11. Spratt JA, von Fournier D, Spratt JS, et al: Decelerating growth and human breast cancer. Cancer 71:2013-2019, 1993[Medline] 12. Peer PGM, van Dijck JAAM, Hendriks JHCL, et al: Age-dependent growth rate of primary breast cancer. Cancer 71:3547-3551, 1993[Medline]
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Peer PGM, Holland R, Hendriks JHCL, et al: Age-specific effectiveness of the Nijmegen population-based breast cancer-screening program: Assessment of early indicators of screening effectiveness. J Natl Cancer Inst 86:436-441, 1994
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Hellman S: Natural history of small breast cancers. J Clin Oncol 12:2229-2234, 1994 15. Cox DR, Miller HD: The Theory of Stochastic Processes. New York, NY, John Wiley & Sons Inc, 1965, pp 146-155 16. Osborne CK, Clark GM, Ravdin PM: Adjuvant systemic therapy of primary breast cancer, in Harris JR, Lippman ME, Morrow M, et al (eds): Diseases of the Breast. New York, NY, Lippincott-Raven, 1996, pp 548-578 17. Hortobagyi GN, Singletary SE, McNeese MD: Treatment of locally advanced breast cancer, in Harris JR, Lippman ME, Morrow M, et al (eds): Diseases of the Breast. New York, NY, Lippincott-Raven, 1996, pp 585-599 18. Milas L, Nakayama T, Hunter N, et al: Dynamics of tumor cell clonogen repopulation in a murine sarcoma treated with cyclophosphamide. Radiother Oncol 30:247-253, 1994[Medline]
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Fisher B: Laboratory and clinical research in breast cancer: A personal adventure—The David A. Karnovsky Memorial Lecture. Cancer Res 40:3863-3874, 1980
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Overgaard M, Hansen PS, Overgaard J, et al: Postoperative radiotherapy in high-risk premenopausal women with breast cancer who receive adjuvant chemotherapy. N Engl J Med 337:949-955, 1997
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Ragaz J, Jackson SM, Le N, et al: Adjuvant radiotherapy and chemotherapy in node-positive premenopausal women with breast cancer. N Engl J Med 337:956-962, 1997
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Mauriac L, Durand M, Avril A, et al: Effects of primary chemotherapy in conservative treatment of breast cancer patients with operable tumors larger than 3 cm. Ann Oncol 2:347-354, 1991 23. Scholl SM, Fourquet A, Asselain B, et al: Neoadjuvant versus adjuvant chemotherapy in premenopausal patients with tumours considered too large for breast conserving surgery: Preliminary results of a randomised trial—S6. Eur J Cancer 30A:645-652, 1993
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Powles TJ, Hickish TF, Makris A, et al: Randomized trial of chemoendocrine therapy started before or after surgery for treatment of primary breast cancer. J Clin Oncol 13:547-552, 1995 25. Fisher B, Bryant J, Wolmark N, et al: Effect of preoperative chemotherapy on the outcome of women with operable breast cancer. J Clin Oncol 16:2672-2685, 1998[Abstract]
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Fisher B, Brown A, Mamounas E, et al: Effect of pre-operative chemotherapy on local-regional disease in women with operable breast cancer: Findings from National Surgical Adjuvant Breast and Bowel Project B-18. J Clin Oncol 15:2483-2493, 1997
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Sickles EA: Periodic mammographic follow-up of probably benign lesions: Results in 3,184 consecutive cases. Radiology 179:463-468, 1991 Submitted December 28, 1998; accepted May 21, 1999. This article has been cited by other articles:
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Copyright © 1999 by the American Society of Clinical Oncology, Online ISSN: 1527-7755. Print ISSN: 0732-183X
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ABSTRACT
INTRODUCTION
2 cm) cancer, as illustrated by National Surgical Adjuvant Breast and Bowel Protocol (NSABP) B-27
, n = 560), with one to three positive axillary nodes (
, n = 657),
, n = 505). The curves are fits to the data in 
. After the primary tumor attains the volume vT, seeding to site i is modeled by a continuous-time discrete-state Poisson process, so that the probability of an event in the time interval (t, t + 
t) is given by si(t)v(t)
400 vs0(v). This approximation holds for times not greatly in excess of a few doubling times of the primary tumor. According to assumption 4, we take the seeding frequency during neoadjuvant treatment as constant and equal to its value at the beginning. The upper two solid curves (one for each model of tumor growth) give the percent distant failure after neoadjuvant chemotherapy as 65 [1 - exp (-4vs0(v))P0 (v)], under the assumption that neoadjuvant treatment will eliminate at least 35% of newly seeded metastases; the curve for the Gompertz model is the higher of the two. The calculations were carried out using volume-specific growth rates for patients younger than 50, for whom the mean volume-doubling time is 80 days.
