Breast CancerResearch and Treatment16: 231-242, 1990. © 1990KluwerAcademic Publishers. Printedin the Netherlands. Report

RECPAM analysis of prognostic factors in patients with Stage III breast cancer

C. Erlichman 1, P. Warde 2, T. Gadalla3, A. Ciampi4 and T. Baskerville5 1Department of Medicine, Princess Margaret Hospital and University of Toronto, Toronto, Ontario; e Department of Radiation Oncology, Princess Margaret Hospital, Toronto, Ontario; 3Biostatistics Department, Princess Margaret Hospital, Toronto, Ontario; 4Montreal Children's Hospital Research Institute, Montreal, Quebec; 5Department of Nursing, Princess Margaret Hospital, Toronto, Ontario

Key words: prognostic factors, recursive partioning and amalgamation algorithm, stage III breast cancer Abstract

A retrospective chart review was conducted of women with stage III breast cancer seen at the Princess Margaret Hospital between January 1977 and December 1980. Three hundred and sixty-nine patients were available for analysis. These cases were evaluated to determine the prognostic factors of patients presenting with this stage of the disease using a recursive partitioning technique, RECPAM, and a Cox regression model. A non-mathematical description of RECPAM is presented and the advantages of RECPAM over Cox analysis are discussed. The results identify primary tumour size, axillary node involvement, internal mammary node involvement, and estrogen receptor status as the most important prognostic variables. RECPAM identified 3 prognostic groups and simultaneously provided rules based on the prognostic variables to assign patients to poor, intermediate, or good prognosis categories. Patients with estrogen receptor negative tumours, or those with axillary node involvement, primary tumours > 5 cm, and serum alkaline phosphatase > 60IU/L, or those with internal mammary node involvement, no skin changes, and serum alkaline phosphatase > 60 IU/L, define a group with a poor prognosis. Patients with estrogen receptor positive tumours, no axillary node involvements, and primary tumours > 5 cm, or estrogen receptor positive tumours, axillary node involvement, primary tumours > 5 cm, but serum alkaline phosphatase -< 60 U/L, have an intermediate prognosis. The good prognosis group consists of those patients with estrogen receptor positive tumours who have either skin changes or primary tumours -< 5 cm. The effect of loco-regional and systemic therapy was assessed and there was no association between treatment assignment and prognostic group. On the basis of this RECPAM analysis, we have defined important prognostic variables to be used in the design of clinical trials, and three maj or patient subgroups which can be used in routine oncologic practice as a guide to patient management.

Locally advanced breast cancer is a heterogeneous and poorly defined clinical condition challenging the surgical, radiation, and medical oncologist. The exact incidence of this entity is difficult to

discern, as staging varies from series to series. Often, the term stage III carcinoma of the breast is used for locally advanced breast cancer, but the criteria used to define this entity have varied de-

Address for offprints: C. Erlichman,PrincessMargaret Hospital, 500 Sherbourne Street, Toronto, Ontario, M4X 1K9,Canada

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pending on the staging system used. Therefore, it is not surprising that the reported incidence of this stage of the disease varies also from 6.3% to 20.85

Materials and methods

Patients

[1-41 .

Tumour extent in patients as determined by any staging system is variable in stage III breast cancer [5-9]. The UICC system using the T, N, and M staging identifies T3-4, N003, M0, or T1-4, N2-3, M0 as stages which could be included in stage III breast cancer. This broad range of T and N stages would suggest that the prognosis of such patients varies widely. Clinical experience bears out this impression but does not identify those patients with good, intermediate or poor prognoses. Whereas several series have reported individual institutional experiences with this stage of the disease [10012], the importance of many clinical and laboratory parameters in patient prognosis have not been assessed adequately. These retrospective studies are limited by the information available to the investigators, and their applicability to the clinical situation may be biased by unknown factors influencing the institutions' referral patterns. Furthermore, the reports often describe only those patients who were treated with a specific treatment, and do not consider other patients with the same disease stage who were treated in another manner at that institution. We undertook this retrospective study of patients with stage III carcinoma of the breast referred to the Princess Margaret Hospital between January 1977 and December 1980 in order to define prognostic factors which were of clinical utility in the management of this patient population and which could be used in the design of clinical trials. All patients with stage III carcinoma of the breast who were seen at this institution during that time period were included. The recursive partitioning and amalgamation (RECPAM) method [13] was utilized to determine the prosnostic factors. This method is described in non-mathematical terms and is compared to the Cox regression analysis [14] in the same series of patients.

We reviewed the TNM stage of all women with carcinoma of the breast who were registered at the Princess Margaret Hospital between January 1977 and December 1980. All those that complied with the UICC stage III classification of carcinoma of the breast were examined for detailed analysis.

Factors Twenty-two clinical and laboratory variables were examined for prognostic significance (Table 1). These variables were selected because of reported associations with prognosis in breast cancer. The serum alkaline phosphatase was used as a sensitive but non-specific indicator of liver and/or bone metastases. The reference normal serum alkaline phosphatase was 60o110 U/L during the study period. Treatment of patients was categorized in 6 groups: 1) local surgery plus radiotherapy; 2) radical surgery with radiotherapy; 3) local surgery only; 4) radical surgery only; 5) radiotherapy + systemic therapy; 6) systemic therapy only. Local surgery included lumpectomy + axillary node dissection. Radical surgery involved a modified radical or radical mastectomy with axillary node dissection. Radiotherapy included any dose or fields of therapy. Systemic therapy included chemotherapy, hormonal therapy, or both.

Analysis

RECPAM was selected to analyze the data over a more conventional approach for two reasons. Firstly, the identification and definition of prognostic groups in clinical terms allows organization of retrospective information for clinical use. Secondly, the approach to the handling of missing data featured in RECPAM has definite advantages over the way the traditional regression approaches handle the same problem. This was important for our analysis since many missing data were present. Cox

RECPAM analysis of prognostic factors regression analysis [15] was performed also, and the results obtained using this method were compared to those generated by RECPAM.

The classification approach This analysis is based on a method developed by Ciampi et al. [14] which we call RECPAM, for RECursive Partition and AMalgamation. RECPAM, unlike similar methods [16, 17], is specifically designed for censored survival data. The purpose of R E C P A M analysis is to classify patients into distinct homogeneous prognostic groups further defined by statements such as: 'Patients belonging to the best prognostic group are those with all of the following characteristics:.., and at least one of the following characteristics...'. R E C P A M builds a classification tree which is similar to a decision tree. The 'decision' is to assign a patient to a number of distinct prognostic groups, determined by the data, on the basis of a given set of prognostic factors. The tree is built as follows: Given a population of patients, we look for a state-

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ment about the prognostic factors so that the survival curve of the patients that satisfy the statement is as different as possible from that of the remaining patients. The population is partitioned accordingly into two sub-populations which are called 'nodes'. For example, a statement like 'the patient is male' splits the patient population into two nodes, with those who satisfy the statement, i.e. male patients, in one node and those who do not satisfy it, i.e. female patients, in the other node. This simple step is recursively repeated on each sub-population, hence the name 'recursive partition' (RP). A stopping rule, set in advance, terminates the process of tree construction. The nodes at which the tree stops branching are called 'terminal nodes'. Amalgamation is then applied to the 'terminal nodes' of the RP tree. This is done by successively joining the sub-populations at which the RP tree stopped branching, starting from the two with the most similar survival curves. As for the RP step, a stopping rule needs to be specified so that the successive amalgamation terminates at a point determined by the data. RECPAM is controlled by: 1) the choice of dis-

Table 1. Prognostic variables evaluated

Prognostic variable

Missing values (%)

Univariate log rank p-value

Axillary node disease Tumor size Inflammation Tumor fixation Estrogen receptor Progesterone receptor Menopausal status Age Skin changes Internal mammary node disease Alkaline phosphatase Tumor growth rate Tumor differentiation Pathological tumor type CEA Body weight Smoking Family history Breast feeding Chest x-ray (done vs not done) Liver scan (done vs not done)

5.1 5.7 4.8 18.7 60.2 64.5 16.2 0.0 8.4 21.1 10.8 3.0 69.9 9.8 43.3 8.9 34.1 11.3 26.8 4.3 4.3

< 0.005 < 0.005 0.007 0.294 < 0.005 0.028 0.196 0.757 0.244 0.013 0.406 0.326 0.112 0.164 0.214 0.802 0.940 0.606 0.339 0.664 0.825

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similarity measure, i.e. a statistic for assessing the significance of the hypothesis that the survival curves of the two resulting nodes are the same; 2) the smallest allowed node size; 3) the tuning parameters, c~ and [5 [13]. a is a parameter which controls the stopping rule for both RP and amalgamation. It is a nominal significance level for the hypothesis that two survival curves are equal. The word 'nominal' refers to the fact that multiple comparisons are made at each step of the tree construction. [5 is a parameter that controls the complexity of the split defining statements in the RP tree, i.e. it controls the number of prognostic variables used in such statements. It is a type of penalty for using complex statements defined by more than one variable. For a very large [3, only statements involving one variable at a time are allowed to define splits. As [5 decreases to zero, splits can be defined by combinations of single variable statements.

Tree selection and the A I C

Varying a and [3, we obtain a family of trees. For a fixed [5, trees corresponding to different a's are nested with trees having larger a's containing those with smaller a's. The smaller the value of [3, the more complex the tree looks, since we are more likely to find split-defining statements involving more than one variable. The et and [3 are selected using a statistical criterion developed by Akaike [18], the Akaike Information Criterion, AIC. The AIC is a function of both the maximized log likelihood of the model and the number of parameters necessary to describe it. It measures the plausibility of the model in the sense that models with small A I C should be preferred to models with large AIC. However, instead of choosing the tree with the minimum AIC, sometimes we prefer to choose the one corresponding to an 'elbow' in the A I C [13]. The tree corresponding to an elbow in the AIC curve has the advantage of being smaller (i.e. simpler) than the minimum A I C tree. A full description of this procedure and its relationship to crossvalidation is discussed by Ciampi et al. [13].

Variable importance

A by-product of R E C P A M is the calculation of variable importance. For each variable, the sum of its dissimilarity statistic over all the splits is computed. The importance of a variable is the ratio expressed as a percentage of this sum to the largest of all such sums. This notion, adapted from Breiman et al. [17], is a reasonable measure of global predictive value of a variable, whereas the position of the variable in the tree exhibits its effect in particular subgroups of patients. Thus, the variable importance list can be seen as a useful complement to the tree structure in assessing the role of prognostic factors.

Missing data

To deal with the problem of missing data which is apparent in our series, the 'surrogate variable' feature of R E C P A M was used. This is a strategy specific to tree construction which has much less intrinsic bias than the missing data strategies developed in the regression context [17]. The surrogate variable method works as follows: At each node, differences between survival curves are measured and compared by simply ignoring those individuals who cannot be classified owing to missing data. However, after the partitioning variable has been selected, every individual is assigned to one of the two branches. For individuals with missing data, a 'surrogate variable' is used: this is the non-missing variable which has the greatest 'predictive association' with the partitioning variable. In other words, the variable with the strongest association to the chosen one is used to decide on which node an individual should be assigned. The measure of predictive association is the same one used by Breiman et al. [17]. As in these authors' work, when no surrogate variable has positive predictive association with the chosen one, individuals are assigned by 'majority rule', i.e. they are assigned to the branch where most of the patients are.

RECPAM analysis of prognostic factors Calculations In this work, we have fixed a priori the minimum node size to be 25 patients. As a measure of the dissimilarities between survival curves, we have chosen the likelihood ratio statistic based on a simple Cox model [14] with one dichotomous variable. The Kaplan Meier product limit estimates of survival [19] were calculated for each of the prognostic groups defined by RECPAM and the generalized Wilcoxon statistic was used to test the significance of their separation. The xZ-test of independence was used in order to establish whether or not confounding between treatment factors and prognostic classification existed.

The regression approach A Cox regression model was developed for our series in order to compare its findings with those of the RECPAM analysis. The choice of the prognostic factors for this model was determined by a 'stepwise' selection procedure so that at each step the variable which added the most significant increase in the overall predictive ability of the model was entered into the model. Dichotomous variables were coded as 'zero' for negative cases and 'one' for positive cases. Missing values for each variable were set to equal the proportion of positive cases among all known cases for that variable. Missing values of 'alkaline phosphatase' were set to equal the mean of the known values, and missing values of 'skin changes' were coded as 'none'. A crude ranking of the variables Table 2. Clinical T and N distribution of all 369 patients T1

T2

T3

T4

Total

NO N1 N2 N3

2 2

7 4

43 34 5 4

109 105 30 20

152 139 44 30

Total

4

11

86

264

365

In 4 cases the T stage was unknown.

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based on improvement of ~2 was prepared and compared with the variable importance list produced by RECPAM. AIC was calculated for each of the two regression models with a-level to enter 0.05 and 0.10 and compared with the AIC from classification trees with similar a's and with ~ -- ~.

Results

Three hundred and sixty-nine patients with stage III breast cancer were seen at the Princess Margaret Hospital during the period of review. The median follow-up for all patients was 5.4 years. Table 2 shows the T and N stage distribution in our patient population. The median age for the population was 58 years with a range of 25 to 93 years. Three hundred and ten patients had infiltrating duct carcinomas, 12 had lobular carcinomas, 5 each had medullary and comedo carcinomas, and in 37 cases the pathological type was not specified. Forty-seven patients were categorized as having inflammatory carcinoma of the breast. A breast mass was the most common presenting symptom (88.8%). Pain and erythema was often associated with the breast mass, while skin retraction, discharge, and axillary masses were less frequent. Ninety-seven patients presented with more than two of these symptoms. One hundred and ninetytwo patients presented with axillary lymphadenopathy and 25 with supraclavicular lymphadenopathy. The median age of patients with positive estrogen receptor status was 57.5 years, and of patients with negative estrogen receptor was 53 years. Estrogen and progesterone receptor assays were reported in 147 patients. Receptor data was not available on the remaining patients because this laboratory test was not widely available in the early years of the study period. The classification of patients with unknown estrogen receptor status illustrates the unique strength of the RECPAM technique. The surrogate variable feature of RECPAM was used to deal with the missing data. Inflammation was selected as the surrogate variable because of its strong association with estrogen receptor negative status. Patients having inflamma-

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Fig. 1. AIC curves for ~ = 0.00 (...), 15= 0.25 (- ..... ), [5= 0.50 (---), and 13-> 0.75 (

tion (n = 22) were classified as estrogen receptor negative and those with no inflammation (n = 185) were classified as estrogen receptor positive. Fifteen patients with unknown estrogen and progesterone receptor data and unknown inflammation were classified as estrogen receptor positive because the majority of the other patients were found in this category. Twenty-two prognostic variables were analyzed in a univariate log rank analysis. Six of these variables found to be significant (p < 0.05) were considered for R E C P A M analysis. Although menopausal status and tumour fixation were not significant for survival, they were when relapse-free survival was considered and so were retained in the analysis. Skin changes (which consisted of breast edema, ulceration, infiltration, and peau d'orange) and serum C E A , which have been suggested by others as important prognostic variables, were included, and alkaline phosphatase was retained as a potential marker of metastatic disease. Trees were constructed for a grid of ~ and [3. They varied in size, complexity, and the number of variables required to define each. However, three variables were repeatedly found at the root of all trees. These variables were estrogen receptor status, nodal involvement, and tumor size. AIC's

).

were calculated for all trees and plotted in Fig. 1. With the aid of the AIC chart, the choice of the best tree narrowed down to the following elbow trees: tree no. 1: ct = 0.07, ~ = oo, AIC = 2191; tree no. 2: a = 0.03, ~ = 0.00, A I C = 2187; tree no. 3: a = 0.02, ~ = 0.50, AIC = 2180. Note that in tree no. 1, ~ = ~ implies that only one prognostic variable is used to define each split, whereas in tree no. 2 with [5 = 0, a combination of any number of variables can be used to define a split. When examined in detail, tree no. 3 was considered to be the most clinically plausible. The selected tree was also the minimum AIC tree, thus, statistical and clinical preference coincided in this case. The R E C P A M procedure led to the choice of c~ = 0.02 and ~ = 0.50 for the classification tree. Figure 2 summarizes the R E C P A M process for the chosen prognostic classification scheme. Circles indicate nodes and squares, terminal nodes. Inside each circle or square, the number of patients who belong to that group is indicated. By convention, the statements are satisfied by the patients in the left branch which represents the worst prognosis.

RECPAM analysis of prognostic factors Dotted lines indicate the amalgamation steps, and hexagons represent the final R E C P A M classification. This classification scheme identifies distinct prognostic groups which we have labelled 'good prognosis', 'intermediate prognosis', and 'poor prognosis'. The model required only six variables to define the three final prognostic groups. They were estrogen receptor status, nodal involvement, tumour size, internal mammary node scan, serum alkaline phosphatase, and skin changes. The 'good prognosis' group (92 patients, median survival > 6.6 years) were characterized as those patients who had tumours which were estrogen receptor positive, axillary node negative, with no skin changes and alkaline phosphatase > 60 IU/L or tumours which were estrogen receptor positive, with skin changes and a primary tumour ~ 5 cm. Patients belonging to the intermediate prognosis category (67 patients, median survival = 5.3 years) were those with the following characteristics: 1) estrogen receptor positive tumours; 2) tumour > 5 cm; 3) serum alkaline phosphatase -> 60 IU/L; and 4) either axillary node involvement or skin changes. Patients who had the following disease characteristics fell into the poor prognosis category (210 patients, median survival= 2.8 years): 1) estrogen receptor negative tumours; 2) primary tumours > 5 cm, involved axillary nodes, and alkaline phosphatase > 6 0 I U / L ; or 3) internal mammary nodes involved, alkaline phosphatase > 6 0 I U / L , but no skin changes. The survival curves for each of the three groups, so determined, are shown in Fig. 3. The curves are well separated with a generalized Wilcoxon statistic of p < 0.0001. The relative importance of the eleven variables as calculated by R E C P A M is given in Table 3. This ranking was found to be stable over various values of the tuning parameters ~ and [3. The size of the primary tumour was found to be the most important prognostic factor followed by axillary node status, internal mammary node chain scan positivity, and estrogen receptor status, in that order. Cox proportional hazards stepwise regression analysis identified estrogen receptor status as the most significant prognostic factor for our patient

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ER(~ and skin changes or ER(~)and T 60 and -< l l 0 I U / L and 45 had values > 110 IU/L. An association of borderline significance was found between serum alkaline phosphatase > 60IU/L and the development of bone, liver, or both, as primary sites of metastases

(p = 0.07, x2). The distribution of primary treatment according to the three groups of patients is summarized in Table 5. Initial therapy appeared to be equally distributed between the three prognostic groups. No association was found between primary therapy and the patient groups defined by RECPAM (p > 0.05, X2).

Discussion

Patients with stage III breast cancer present unique problems to the clinician. Due to staging differences, it is difficult to compare different published series. Selection bias of patients reported and the retrospective nature of the analyses adds to the difficulty. There exists a need to dissect out paTable 5. Distribution of primary treatment

Primary treatment

Local surgery only Local surgery + radiotherapy Radical surgery + radiotherapy Radical surgery only Radiotherapy + / - systemic therapy Systemic therapy only

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Prognostic group Poor

Intermediate

Good

2 21 84 53 40 10

0 5 27 25 7 3

2 8 50 22 8 2

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outcome of this test. The observation that estrogen receptor positivity ranks fourth, corroborates the findings of other investigators [11, 21, 24] that this variable is a major determinant of outcome. The comparatively low ranking of progesterone receptor should be interpreted in light of the strong association with the estrogen receptor (57% of the estrogen receptor positive tumours were progesterone receptor positive also) and does not imply that progesterone receptor is unimportant. Interestingly, the identification of serum alkaline phosphatase as an important prognostic factor was unexpected. Values -< 60 IU/L are found in less than 5% of the population (normal range 60110 IU/L). The prognostic importance may relate to the association of serum alkaline phosphatase > 60 IU/L with hepatic and/or bone metastases in our data set. Ideally, a value for each patient prior to development of cancer should be used as that patient's baseline value. However, as this was not available for analysis, the normal range of an otherwise healthy population was used. This result suggests that the serum alkaline phosphatase should be assessed as a prognostic factor in patients with stage III breast cancer in a prospective manner. Skin changes, inflammation, and tumour fixation were less important albeit significant. This agrees with the report of Fracchia [24] who identifies skin edema, ulceration, or infiltration as grave signs. Similarly, these skin changes were described as 2 of 5 grave clinical signs by Haagensen and Stout [25] when they retrospectively reviewed a large series of patients undergoing radical mastectomies. Tumour fixation, axillary lymph nodes > 2.5 cm, and fixed axillary lymph nodes were the other three signs. During the period of review, the initial therapy of these patients was determined by the physicians managing the patients. No specific management policies were defined a priori. This resulted in a heterogeneous population with respect to therapy as well as extent of disease. We allocated the therapies into 6 major categories and examined the distribution of treatments according to good, intermediate, or poor prognosis groups (Table 4). No association between the prognostic group defined by R E C P A M and the 6 major treatment categories was found (p > 0.05). This lack of

an association between treatment and prognosis groups suggests that primary therapy did not influence survival and so was not used as a variable in the RECPAM analysis. The decision tree model developed using recursive partitioning employs six prognostic factors to define clinical patient subgroups with differing survival curves. Furthermore, using classification tree models adds an important facet to managing the individual patient. For example, Fig. 1 indicates that a patient with an estrogen receptor negative tumour falls into a poor prognosis category. However, if the estrogen receptor is positive but the patient has axillary nodal involvement, a large primary tumour, and serum alkaline phosphatase 60 IU/L, then her survival is similar to that of the patient with estrogen receptor negative disease. Thus, this additional information gleaned from the analysis using the recursive partitioning method can have direct clinical application. Both regression and classification approaches deal with the assessment of prognostic factors and their effects on survival. The two approaches differ in many ways. A detailed comparison of the two approaches is described elsewhere [26, 27]. We address five important differences here. Regression looks for models in which main effects are used to explain variation in survival time, whereas RECPAM looks for combinations of variables at each split. This is an important point in clinical situations in which the discriminating power of one prognostic factor may be significantly enhanced by the presence or absence of other factors. Although this may be corrected in the regression approach by adding so-called 'interaction terms' to the main effects, to include all terms of possible interactions can make the number of covariates enormous and the analysis unmanageable. Regression favours global effects, so that when each prognostic factor has a uniform effect on survival across the whole patient population, regression analysis will provide an accurate description of the data. The tree, on the other hand, offers an ideal summary of the data when some factors act differently for different subgroups of patients. This implies interaction between the variable which determines the split at one partition and the variables

RECPAM analysis of prognostic factors which determined the splits at the previous partitions. The trees which result from RECPAM analysis are in a form that is easily understood and can be used for decision making in the clinical setting, whereas, regression models are expressed as mathematical formulas which are rather difficult to rephrase in clinical terms. The surrogate variable strategy for dealing with missing data in the RECPAM approach is more consistent and less subjected to bias than the missing data strategies developed in the regression context. If the estimation of missing data introduces a distortion, this distortion affects the model only locally in RECPAM, whereas in regression, the distortion is global. Unlike regression techniques, where continuous variables can be used in their original values, RECPAM only used categorical variables. Thus, variables such as age or blood pressure need to be categorized according to different thresholds for use in the RECPAM analysis. However, the present version of the RECPAM software allows for up to 20 ordered categories, a very fine categorization. The choice of analysis method for a data set is dependent on the objectives of the investigators undertaking the analysis, familiarity with methods, and availability of different methods. As there are advantages to both RECPAM and Cox methods of analysis, the choice of methods will be influenced by the factors mentioned. However, the two methods used are complementary to each other, and their use together can give a better understanding of the underlying structure in the data than either can give alone. The classification tree and prognostic groups defined in this analysis fit our data well, but should be tested on a different data set to confirm its validity. These results will be useful in planning future clinical trials also. Patients with stage III breast cancer should be stratified according to several prognostic variables when entered on a randomized clinical trial to ensure an equal balance of the arms with respect to survival. The four most important factors which we identified in this analysis include: size of primary tumour, axillary node involvement, internal mammary node involvement, and estro-

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gen receptor status. Other parameters which may be considered include skin changes, CEA, progesterone receptor status, local inflammation, and fixation of tumour to chest wall. Our data would suggest that serum alkaline phosphatase should be used as a stratification variable too. This would be a useful method of determining its importance in a prospective study. Trials which ask questions of treatment but do not consider prognostic variables may overlook an important impact of treatment because the outcome is biased by an imbalance in prognostic variables. In conclusion, we have identified important prognostic factors which can be applied in the management of individual patients with stage III breast cancer and the investigation of new therapies for this disease. Furthermore, the classification tree analysis undertaken categorizes patients according to clinical situations physicians must face in their practice setting on a day-to-day basis. We wish to acknowledge Mrs. S. Cooke for her assistance in preparing this manuscript.

References 1. Haagensen CD: Diseases of the Breast (2nd Edition). WB Saunders, Philadelphia, 1971 2. Rubens RD, Armitage P, Winter PJ et al. : Prognosis in inoperable Stage III carcinoma of the breast. Eur J Cancer 13: 805-811, 1977 3. McWhirter R: Simple mastectomy and radiotherapy in the treatment of breast cancer. Br J Radiol 28: 128-139, 1955 4. Handley RS: In Haagensen CD. Diseases of the Breast (2nd Edition). WB Saunders, Philadelphia, 1971, p 634 5. Zucali R, Uslenghi C, Kenda R, Bonadonna G: Natural history and survival of inoperable breast cancer treated with radiotherapy and radiotherapy followed by radical mastectomy. Cancer 37: 1422-1431, 1976 6. Bruckman JE, Harris JR, Levene MB et al. : Results of treating Stage III carcinoma of the breast by primary radiation therapy. Cancer 43: 985-993, 1979 7. Arnold DJ, Lesnick GJ: Survival following mastectomy for Stage III breast cancer. Am J Surg 137: 362-366, 1979 8. B e d w i n e k J , R a o D V , P e r e z C et al. : StageIII andlocalized Stage IV breast cancer: Irradiation alone versus irradiation plus surgery. Int J Radiat Oncol Biol Phys 8: 31-36, 1982 9. Balawajder I, Antich PP, Boland J: An analysis of the role of radiotherapy alone and in combiantion with chemotherapy and surgery in the management of advanced breast carcinoma. Cancer 51: 574-580, 1983

242

C Erlichman et al.

10. Bloom HJG: The natural history of untreated breast cancer. Ann NY Acad Sci 114: 747-754, 1964 11. DeLena M, Varini M, Zucali R et al. : Multimodal treatment for locally advanced breast cancer. Cancer Clin Trials 4: 229-236, 1981 12. Fletcher GH: Local results of irradiation in the primary management of localized breast cancer. Cancer 29: 545551, 1972 13. Ciampi A, Chang CH, Hogg SA etal. : Recursive partition: a versatile method for exploratory data analysis in biostatistics. In: MacNeill IB, Umphrey GJ (eds) Biostatistics (Festschrift in honour of Professor V.M. Joshi's 70th birthday), vol. 5. Advances in the Statistical Sciences, vol. 5. D. Reidel, Dordrecht, 1987, pp 1-28 14. Ciampi A, Hogg SA, McKinney S et al. : RECPAM: a computer program for recursive partition and amalgamation for censored survival data and other situations frequently occurring in biostatistics. Comput Meth Prog in Biomed 26: 239-256, 1988 15. Cox DR: Regression models and life tables (with discussion). J R Stat Soc B 34: 187-220, 1972 16. Sonquist JA, Baker EL, Morgan JN: Searching for structure: An approach to analysis of substantial bodies of microdata and documentation for a computer program (revised edition). Ann Arbor Institute for Social Research, University of Michigan, 1974 17. Breiman L, Friedman JH, Olshen RA, Stone CJ: Classification and regression trees. (The Wadsworth Statistics/ Probability Series.) The Wadsworth International Group, Belmont CA, 1984 18. Akaike H: A new look at the statistical model identifica-

19. 20.

21.

22.

tion. System identification and time-series analysis. IEEE Trans Automatic Control, 19: 716-723, 1974 Kaplan EL, Meier P: Non-parametric estimation from incomplete observation. J Am Stat Assoc 53: 457--481, 1958 Stewart JF, King RJB, Winter PJ et aL: Oestrogen receptors, clinical features, and prognosis in Stage III breast cancer. Eur J Cancer Clin Oncol 18: 1315-1320, 1982 Treurniet-Donker AD, Hop WCJ, den Hoed-Sijtsema S: Radiation treatment of Stage III mammary carcinoma: A review of 129 patients. Int J Radiat Oncol Biol Phys 6: 1477-1482, 1980 Harris JR, Hellman S, Canellos GP, Fisher B: Cancer of the breast: treatment of locally advanced breast cancer (Stage III) In Devita VT Jr, Hellman S, Rosenberg SA (eds) Cancer. Principles and Practice of Oncology (Vol 2, 2nd edition) J.B. Lippincott Co., Philadelphia, 1985, pp 1148-1150

23. Hortobagyi GN, Blumenschein G R , Spanos W et al. : Multimodal treatment of locoregionally advanced breast cancer. Cancer 51: 763-768, 1983 24. Fracchia AA, Evans JF, Eisenberg BL: Stage III carcinoma of the breast: A detailed analysis. Ann Surg 192: 705-710, 1980 25. Haagensen CD, Stout AP: Carcinoma of the breast: Criteria of operability. Ann Surg 118: 859-870, 1943 26. Ciampi A, Lawless JF, McKinney SM, Singhal K: Regression and recursive partition strategies in the analysis of medical survival data. J Clin Epidemiol 41: 737-748, 1988 27. CookEF, Goldman L: Empiric comparison of multivariate analytic techniques: Advantages and disadvantages of recursive partitioning analysis. J Chronic Dis 37: 721-731, 1984