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Tree-Based Model for Breast Cancer Prognostication

From the Department of Biostatistics, University of Michigan, Ann Arbor; Barbara Ann Karmanos Cancer Institute and the Center for Healthcare Effectiveness Research, Wayne State University, Detroit, MI; and the Department of Management Science and Statistics, The University of Texas at San Antonio, San Antonio, TX

Address reprint requests to Mousumi Banerjee, PhD, Department of Biostatistics, University of Michigan, 1420 Washington Heights, Ann Arbor, MI 48109-2029; e-mail: mousumib{at}umich.edu

	ABSTRACT

TOP ABSTRACT INTRODUCTION PATIENTS AND METHODS RESULTS DISCUSSION Authors' Disclosures of... REFERENCES

 
PURPOSE: To define prognostic groups for recurrence-free survival in breast cancer, assess relative effects of prognostic factors, and examine the influence of treatment variations on recurrence-free survival in patients with similar prognostic-factor profiles.

PATIENTS AND METHODS: We analyzed 1,055 patients diagnosed with stage I-III breast cancer between 1990 and 1996. Variables studied included socioeconomic factors, tumor characteristics, concurrent medical conditions, and treatment. The primary end point was recurrence-free survival (RFS). Multivariable analyses were performed using recursive partitioning and Cox proportional hazards regression.

RESULTS: The most significant difference in prognosis was between patients with fewer than four and those with at least four positive nodes (P < .0001). Four distinct prognostic groups (5-year RFS, 97%, 78%, 58%, and 27%) were developed, defined by the number of positive nodes, tumor size, progesterone receptor (PR) status, differentiation, race, and marital status. Patients with fewer than four positive nodes and tumor 2 cm, PR positive, and well or moderately differentiated had the best prognosis. RFS in this group was unaffected by type of adjuvant therapy (P = .38). Patients with at least four positive nodes and PR-negative tumors had the worst prognosis, and those treated with tamoxifen plus chemotherapy had the best outcome in this group (P = .0001). Among patients in the two intermediate-risk groups, those treated with tamoxifen or a combination of tamoxifen and chemotherapy had the best outcome.

CONCLUSION: Lymph node status, PR status, tumor size, differentiation, race, and marital status are valuable for prognostication in breast cancer. The prognostic groups derived can provide guidance for clinical trial design, patient management, and future treatment policy.

	INTRODUCTION

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Breast cancer is the most common malignancy diagnosed among women and the second leading cause of cancer mortality in the United States.¹ In 2004, approximately 215,990 new cases of female invasive breast cancer will be diagnosed in the United States, and 40,110 women will die of the disease.¹ A decline in breast cancer mortality rates has been observed since 1990.^2,3 Results from two large population-based studies suggest the decline is due to adjuvant tamoxifen treatment in women older than 50 years and adjuvant chemotherapy in women younger than 50 years.^4,5 Still, patients treated with adjuvant chemotherapy or tamoxifen present great heterogeneity in terms of recurrence-free survival, suggesting that patient and/or tumor characteristics may influence outcome more strongly than modifications in standard therapeutic approaches. An analysis of the association of recurrence-free survival (RFS) with patient and tumor characteristics, as well as treatment-related variables, is necessary to assure reliable evaluation of new approaches for treatment of breast cancer.

The goals of the current study, which uses a nonparametric statistical technique known as recursive partitioning (RP), are to (1) analyze the relative contributions of patient and tumor-related prognostic factors to the RFS of patients with stage I-III breast cancer; (2) identify patient subgroups with similar outcome within a group but different outcomes between groups (ie, prognostic grouping of patients); and (3) examine influence of treatment variations on RFS in patients with similar prognostic-factor profiles. Prognostic groups are important in assessing disease heterogeneity and for design and stratification of future clinical trials. Because patterns of breast cancer treatment are changing so rapidly, it was important that the results of the present analysis be applicable to contemporary patients. Hence, we chose a cohort of patients diagnosed between 1990 and 1996, using RFS as the end point to avoid the inaccuracies inherent in death-certificate reports and to maximize the number of cancer-specific events within the shortest time possible.

RP, or tree-based analysis,^6-11 was selected to analyze the data rather than the traditional Cox regression analysis for several reasons. Discovery of interactions is difficult using Cox regression, because the interactions must be specified a priori. In contrast, RP automatically detects important interactions. Furthermore, unlike Cox analysis, RP is adept in uncovering variables that may be largely operative within a specific patient subgroup but may have minimal effect or none in other patient subgroups. Also, RP provides a superior means for prognostic classification.^9-11 Rather than fitting a model to the data, RP sequentially divides the patient group into two subgroups based on prognostic factor values (eg, age > 50 years v 50 years). The repeated partitioning creates "bins" of observations that are approximately homogeneous. This permits the use of Kaplan-Meier estimation to compare prognosis between the "bins." The combination of binning and the interpretability of the resulting tree structure make RP extremely well suited for developing prognostic stratifications for use in clinical-trial design.

	PATIENTS AND METHODS

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Study Cohort and Sources of Information
Eligible women were newly diagnosed patients with stage I, II, or III breast cancer, diagnosed between January 1, 1990, and December 31, 1996, at the Wayne State University–affiliated Harper Hospital (Detroit, MI), and treated at the Karmanos Cancer Institute (KCI), a National Cancer Institute (NCI)–designated comprehensive cancer center. Detailed demographic, clinical, pathologic, and treatment information was obtained from the Surveillance, Epidemiology, and End Results database, Harper Hospital records, clinics of the KCI, individual physicians attending Harper but not affiliated with KCI, and 1990 census data. Follow-up information regarding recurrence was obtained from clinic records or pathologic reports.

Study Variables
RFS was the primary end point of the study, defined as the interval between diagnosis and documented regional, local, or distant recurrence but excluding new primary breast cancer. Pretreatment explanatory variables included sociodemographic variables, concurrent medical conditions, and factors characterizing tumor. The sociodemographic variables examined were age, race, marital status, and socioeconomic status (SES). A census-derived socioeconomic rank,¹² using 1990 census data as reference, was used as a proxy for SES. For concurrent medical conditions, the variables examined were obesity, diabetes, hypertension, heart disease, stroke, and cholesterol level at the time of breast cancer diagnosis. Body mass index was calculated as weight in kilograms divided by the square of height in meters. Patients were classified as obese if their body mass index was 30, in accordance with the WHO.¹³ Tumor size, number of positive lymph nodes, tumor differentiation, tumor-node-metastasis system stage,¹⁴ estrogen receptor (ER), and progesterone receptor (PR) status were used to describe tumor characteristics. Tumor size was categorized as: 1 cm, 1.1 to 2 cm, 2.1 to 5 cm, and 5.1 cm. Lymph node status was categorized as 0, 1 to 3, 4 to 9, and 10 positive nodes. Tumors were categorized as well, moderately, and poorly differentiated. Detailed information on primary and adjuvant therapy was available, including the type of surgery, receipt or nonreceipt of adjuvant radiation, and the type of adjuvant systemic therapy.

Statistical Methods
RP^6,15-20 was used to define distinct prognostic subgroups with similar outcome within each subgroup but different outcomes between the subgroups. The RP analyses began with the entire patient cohort and found the best split into two subgroups based on a variable that identified the subgroups most different in prognosis. These two subgroups were again partitioned (each subgroup being split on the same or other variables that provided the greatest difference in prognosis), creating a tree structure. At each step, the tree-growing paradigm examined every possible cut point for each prognostic variable, to select the best split. This process was continued until the subgroups reached a minimum size. Because the resulting tree was overgrown (thereby overfitting the data), a subtree was chosen using permutation methods. The RP algorithm used the log-rank test to choose the best split into two groups at each step and permutation P values to identify the best subtree.¹⁷ Competitor splits (ie, second-best splits) were also generated at each step to assess the relative strength of the chosen best split. Only those patients without missing data on a particular variable were used to define a potential split. Incomplete observations were removed from further analysis only if they were incomplete on the chosen split. Thus, the sample was not reduced to those patients with complete data on all variables. The final tree contained "terminal" subgroups with similar RFS. Five-year RFS rate and 25th percentile of the RFS distribution were calculated as summary measures for each terminal subgroup. The largest uncensored RFS time was reported when the 25th percentile in a terminal subgroup was not estimable.

Although the RP method ensures that left and right terminal subgroups from the same parent are significantly different in terms of RFS, it is possible that terminal subgroups from distinct parents may have similar RFS profiles. Therefore, further amalgamation of terminal subgroups with similar RFS may be required. For amalgamation, we first ordered the terminal subgroups based on hazard ratio of a terminal subgroup relative to the leftmost terminal subgroup of the final tree. The monotone ordering was then coded as a single ordered covariate, and the recursive partitioning algorithm was used again^17,18 to form the final prognostic groups.

Cox proportional hazards regression²¹ analyses were also performed on this patient cohort using the same variables used in the RP analyses. Results obtained using proportional hazards analyses were compared with those generated by RP.

	RESULTS

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Characteristics of Patient Cohort
A total of 1,125 women were diagnosed between January 1990 and December 1996 with stage I-III breast cancer. Seventy were excluded (33 whites and 37 African Americans) for lack of any follow-up information after initial diagnosis, and the remaining 1,055 patients constitute our analysis cohort. Of these, 56% were African American, and 44% were white, reflecting the population served by Harper Hospital and KCI in Detroit. The median age at diagnosis was 59 years. Forty-one percent of these women presented with stage I disease, 48% with stage II disease, and 11% with stage III disease. Reflecting the pattern of care at an NCI-designated comprehensive cancer center, 39% of our patients had lumpectomy, and 61% had mastectomy. Tables 1 and 2 present frequency distributions of sociodemographic, tumor, and treatment characteristics in our cohort. The median follow-up of our cohort was 44 months. Twenty-three percent of the patients had recurrence, and among them, 75% had distant disease.

View larger version (23K): [in this window] [in a new window]   Fig 1. Regression tree for recurrence-free survival (RFS). At each level, the most significant split, corresponding log-rank (LR) and permutation P are shown. PR, progesterone receptor; circles, terminal subgroups I-VIII; R, number of recurrences; 5Yr, 5-year RFS rate; Diff'n, differentiation.

On the opposite side of the tree, the subgroup with fewer than four positive nodes was next split by tumor size (best cutoff 2 v > 2 cm; log-rank, 29.73; P < .0001). The competitor was differentiation (well or moderately v poorly differentiated; log-rank, 20.3). Thus, tumor size was 1.5-fold stronger than the second-best splitter at this step. The subgroup with fewer than four positive nodes and tumor size 2 cm was subsequently split by PR status (log-rank, 14.33; P < .0001), and the competitor was ER status (log-rank, 8.7). Thus, PR status was 1.6-fold stronger than ER status at this step. Patients with PR-positive tumors had significantly better outcome compared with the PR-negative patients. The latter formed terminal subgroup III; the 25th percentile RFS of patients in this group was 57 months.

The subgroup with fewer than four positive lymph nodes, tumors 2 cm, and positive PR status was further split by tumor differentiation (well or moderately v poorly differentiated; log-rank, 11.06; P < .0001). The competitor at this step was tumor size ( 1 cm v 1 to 2 cm), and the corresponding log-rank was 3.7. None of the resulting subgroups had any other significant split and formed terminal subgroups I and II in the tree. Notably, patients with fewer than four positive nodes, tumor size 2 cm, positive PR status, and well or moderately differentiated tumors (ie, terminal subgroup I) had the best prognosis, with a 5-year RFS of 97%.

The patient subgroup with fewer than four positive nodes and tumor size > 2 cm was then split by race (log-rank, 6.12; P < .0001). The competitor at this step was age (< 50 v 50 years), and the corresponding log-rank was 4.1. White patients had significantly better RFS than did African American patients. The latter formed terminal subgroup VI; the 25th percentile RFS of these patients was 30 months. The white subgroup with fewer than four positive nodes and tumor size > 2 cm was further split by marital status (log-rank, 7.29; P < .0001), with married patients having better prognosis. The competitor at this step was socioeconomic status (log-rank, 3.7). None of these subgroups had any other significant split and formed terminal subgroups IV and V in the tree.

There were 153, 93, 180, 77, 53, 206, 57, and 69 patients in the terminal subgroups I to VIII, respectively. The subgroups with similar RFS were amalgamated (II, III, and IV and V, VI, and VII). These, together with subgroups I and VIII, resulted in four distinct prognostic groups for RFS, designated A to D. Table 3 presents details of this amalgamation. Kaplan-Meier survival curves for the four groups are presented in Figure 2. The 5-year RFS rates for patients in groups A, B, C, and D were 97%, 78%, 58%, and 27%, respectively (P = .0001).

View larger version (17K): [in this window] [in a new window]   Fig 2. Kaplan-Meier curves of recurrence-free survival for the final four prognostic groups obtained from the recursive partitioning and amalgamation analysis. R, number of recurrences.

	DISCUSSION

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The goal of this analysis was to increase our understanding of the relative influence of prognostic variables on outcome in breast cancer patients. While the results confirm the importance of lymph node status and tumor size in patients with stage I-III breast cancer, several additional observations have been made that were not possible with the Cox regression analysis. The significance of PR status in patients with at least four positive lymph nodes was potentially the most important finding of the RP analysis. Patients with PR-positive status had much better prognosis than those with PR-negative tumors (5-year RFS, 55% v 27%, respectively) in this nodal subgroup. Furthermore, tumor size was only operative in the subgroup of patients with fewer than four positive nodes. Tumor size was a strong predictor of RFS (log-rank, 29.73; P < .0001) in patients with fewer than four positive nodes but failed to predict RFS significantly (log-rank, 2.87; P = .09) in patients with at least four positive nodes. Tumor differentiation was also relatively more important and may be largely operative in the subgroup with fewer than four positive nodes. In this nodal subgroup, tumor differentiation emerged as a significant splitter at various levels of the tree (either as the best or the competitor splitter). In contrast, tumor differentiation was only marginally significant in predicting RFS (log-rank, 6.3; P = .05) in patients with at least four positive nodes. The significance of race in patients with fewer than four positive lymph nodes and tumors > 2 cm and the selective importance of marital status in white patients with fewer than four positive lymph nodes and tumors > 2 cm were other interesting RP refinements on the results of the Cox model. The influence of these sociodemographic variables relative to tumor pathology was a unique finding of the RP analysis and may be a reflection of the patient population at the cancer center.

Racial disparities in breast cancer survival have been widely reported in the literature.^2,22-25 African Americans present a 24% increased risk of dying of breast cancer, compared with whites.¹ Poorer survival among African Americans is often attributed to a more advanced stage of disease at diagnosis. However, residual disparities remain even after adjusting for stage. The current study lends further evidence toward a racial disparity; specifically, in the patient subgroup with fewer than four positive lymph nodes and tumors > 2 cm, African Americans had significantly poorer RFS than did whites. Although race is highly correlated with SES in our population, race is an independent predictor of breast cancer survival.²⁶

Several studies^27-31 have found a significant association of marital status with breast cancer survival. Although psychosocial factors, such as stress and attitude toward life, have been shown to affect quality of life in cancer survivors, the only psychosocial factor with a documented effect on survival is external social support.^32,33 Thus, support given to women with breast cancer has not only a positive effect on their reactions to the illness but is also associated with better survival. In the present analysis, marital status may well have been acting as a proxy to external social support in affecting survival.

Recursive partitioning analyses found four prognostic groups, defined only by the number of positive nodes, PR status, tumor size, differentiation, race, and marital status. Use of the tree model could thus add an important facet to managing the individual patient. For example, Figure 1 indicates that a patient with fewer than four positive lymph nodes and PR-negative tumor 2 cm falls into an intermediate-prognosis category. However, if a patient with similar lymph node and tumor-size profiles presents with a PR-positive but poorly differentiated tumor, then her RFS might be similar to that of the patient with PR- negative disease. This additional information gleaned from the analysis using the RP method could have direct clinical application, if it were corroborated in another large cohort.

Both proportional hazards regression and RP enable assessment of prognostic factors, but the two approaches differ substantively. A detailed comparison of the two is described elsewhere,¹⁹ but one important difference is worth emphasizing. Regression favors global effects—that is, factors that have uniform effect on survival across the entire patient population. RP, however, can uncover factors that may act differently for different subgroups of patients. This is an important point, given that in an individual patient, the discriminating power of one prognostic factor may be significantly enhanced or overshadowed by the presence or absence of other factors.

The four prognostic groups created through RP and amalgamation could potentially be valuable for patient management and future clinical-trial design. For example, in group A, the 5-year RFS rate of 97% indicates that highly effective treatment had been initiated and that some patients were perhaps overtreated. Conversely, for the 69 patients with poor prognosis (Group D), the 5-year RFS rate of 27% represents a disappointing result and deserves much greater focus of research into better systemic therapies.

There are several important caveats to be applied to these suggestions. First, validation of the prognostic groups must be obtained using an independent data set, because shortcomings of RP include the instability of terminal subgroups and the potential for overfitting. These are common problems with exploratory methods. The RP methodology we used addresses the overfitting problem by using tests that adjust for the fact that one has searched for optimal cut points. One way of addressing the need for validation is to use 10% of the population as an "internal" data set for independent verification of the terminal subgroups and amalgamation. However, we chose not to do this, because for our population, the number of events in the validation set would be too small. Thus, it would be important to identify populations similar to ours to see if the prognostic value of the groupings identified in this study is reproduced and if these groupings are indeed more predictive than standard stratification factors. A second caveat is that the prognostic groups are partly conditioned by patients' choice of treatment. Questions may arise as to whether the prognostic effects of race and marital status observed in the RP analyses could be partly attributed to differences in treatment choices in the racial and marital-status groups. In our study, there were no significant differences in treatments received between African Americans and whites nor between married women and others, controlling for stage, age, and PR status. Treatment recommended based on subtleties in clinical judgment could also have altered the outcome and therefore conditioned the groupings. As a third caveat, the observed treatment differences could potentially have been influenced by unmeasured factors such as structural barriers (eg, insurance coverage) and factors that influence patient freedom of choice and/or decision making (eg, attitudes and beliefs about specific treatments, ability to navigate the medical system, and personal preferences and biases). Fourth, we did not have adequate power to detect treatment differences in group A patients and the effect of adjuvant radiation in group B patients. Fifth, it will be critical to add prognostic factors such as HER-2neu, and proliferative indices to future RP analyses. The RP method will be useful to determine if these factors, which may be more costly or time-consuming, define different prognostic groups with an improved distinction among RFS potentials, compared with subgroups derived in this investigation. Finally, the advent of microarray analysis techniques to identify important prognostic subgroups may render all previous approaches moot. This seems unlikely, and it is more realistic to imagine that microarray results would be complementary to clinically defined subgroups.

	Authors' Disclosures of Potential Conflicts of Interest

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The following authors or their immediate family members have indicated a financial interest. No conflict exists for drugs or devices used in a study if they are not being evaluated as part of the investigation. Received more than $2,000 a year from a company for either of the last 2 years: Eun Young Song, Ford Motor Company; William Hryniuk, Ford Motor Company.

	NOTES

 
Supported by grants from the National Science Foundation (DMS 9973410; M.B.) and the Ford Motor Company Foundation (W.H. and E.Y.S.).

Authors' disclosures of potential conflicts of interest are found at the end of this article.

	REFERENCES

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Submitted November 27, 2002; accepted April 7, 2004.

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