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Survival Analysing of the Breast Cancer Patients Using Cure Model

AUTHORS

Enayatollah Bakhshi 1 , Ayeh Sheikhaliyan 2 , Keivan Atashgar 3 , Maryam Kooshesh 4 , Akbar Biglarian 5 , *

AUTHORS INFORMATION

1 Associate Professor of Biostatistics, Department of Biostatistics, University of Social Welfare and Rehabilitation Sciences, Tehran, Iran

2 MSc of Industrial Engineering, Department of Industrial Engineering, Malek Ashtar University of Technology, Tehran, Iran

3 Assistant Professor Industrial Engineering, Department of Industrial Engineering, Malek Ashtar University of Technology, Tehran, Iran

4 MD, Tehran University of Medical Sciences, Tehran, Iran

5 PhD, Associate Professor of Biostatistics, Department of Biostatistics, Pediatric Neurorehabilitation Research Center, University of Social Welfare and Rehabilitation Sciences, Tehran, Iran

How to Cite: Bakhshi E, Sheikhaliyan A, Atashgar K, Kooshesh M, Biglarian A. Survival Analysing of the Breast Cancer Patients Using Cure Model, Iran Red Crescent Med J. 2017 ; 19(7):e55575. doi: 10.5812/ircmj.55575.

ARTICLE INFORMATION

Iranian Red Crescent Medical Journal: 19 (7); e55575
Published Online: July 15, 2017
Article Type: Research Article
Received: January 9, 2017
Revised: April 5, 2017
Accepted: April 23, 2017
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Abstract

Background: Breast cancer (BC) is the most leading cause of cancer and the second most common cause of cancer-related death among females worldwide. The survival time of the disease and its risk factors are important for physicians.

Objectives: The current study aimed at applying the Cox, cure, and frailty models to identify the risk factors related to the survival of patients with BC.

Methods: The current historical cohort study investigated 499 patients with a confirmed diagnosis of BC, from March 2010 to March 2014, and followed-up to March 2015 in Besaat hospital in Tehran, Iran. The Cox regression, cure, and frailty models were used for the survival analysis (SA) of the patients. Data analysis was carried out by R3.2.2 software.

Results: The mean (± SD) age of the patients was 50.39 (± 11.13) years and the mean survival time was 53.44 months (95% CI: 51.41 - 55.48). In addition, the 1-year overall survival rate was 0.92 (95% CI: 0.89 - 0.94). Age at diagnosis, tumor size, and metastasis covariates were significant in all models (P < 0.05). Stage covariate were significant in frailty, cure, and failure time distribution model (P < 0.001). Familial history (P = 0.016) and pathology (P = 0.012) were significant only in the frailty model.

Conclusions: The cure and frailty models were better than the Cox model to estimate the parameters. When some patients have a long-term survival, cure models can be an interesting method to study survival and also describe the short-term and long-term effects.

Keywords

Survival Analysis Breast Cancer Cox Proportional Hazards Models Cured Model

Copyright © 2017, Iranian Red Crescent Medical Journal. This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/) which permits copy and redistribute the material just in noncommercial usages, provided the original work is properly cited.

1. Background

Breast cancer (BC) is the most leading cause of death after non-melanoma skin cancer (1), and the second most common cause of cancer-related death among females worldwide (2, 3). In recent years, approximately 1.7 million new cases were diagnosed annually and 0.5 million deaths (per year) were caused by BC worldwide (3, 4). In the US, BC caused approximately 231 000 newly diagnosed cases and about 40 000 deaths (17.3%) in 2015 (5, 6). In Iran, BC is the most frequent cancer among malignancies in females and it caused 24.4% of all neoplasms with an incidence rate of 17.81 in 2006 (6). There are many risk factors related to BC such as older age (55 years and above), genetic risk factors (BRCA1 and BRCA2), a positive family history, late menopause, early menstruation, using oral contraceptive pill (OCP), prolonged nulliparity, hormone replacement therapy (HRT) after menopause, obesity after menopause, and alcohol use (7, 8). For metastasis of BC, there are several prognostic and predictive factors such as high tumor grade, lack of estrogen-receptor (ER) expression, over expression of human epidermal growth factor receptor 2 (HER2), and large tumor size (9). Despite some developments in systemic neoadjuvant or adjuvant therapies such as chemotherapy, radiotherapy, and hormonal therapy that can largely improve the prognosis of BC in recent years, the survival outcomes of patients with BC, especially in the elderly and the patients with long-term use of oral contraceptives, are still not optimistic (3). Due to the advances in early detection and the understanding of the molecular bases of the BC biology, the majority of patients are diagnosed at the early stage and a 5-year survival rate after treatment is nearly 90% (3), but the disease is recurrent in almost 30% of females with early-stage BC (1). Approximately one-third of the patients after surgery have the outcome of local recurrence and/or distant metastasis. Both local recurrence and distant metastasis tend to decrease the survival time in patients with BC. Recurrence of BC has a major role in cancer-related deaths in patients and overall survival after occurrence of metastasis is even shorter (9). As cancer survival is a key index of the overall effectiveness of health services to manage patients (10), therefore, identifying the BC risk factors is important to determine therapeutic and preventive strategies to improve overall survival of patients and also their disease-free survival (DFS).

In time-to-death studies, survival analysis is used as a statistical method to study and model the relationship between the risk factors of the disease (11, 12). In survival analysis of medical data, using the Cox regression model, also named the Cox proportional hazard model, is most popular (11-14); compared with parametric models, it relies on fewer assumptions (11, 14).

Plateaus at tails of survival curves or long plateaus at survival plots lead to failure in the assumption of proportional hazards. In this case, cure models can be used to determine risk factors with either short-term or long-term effects (15). This model can be used in medical research, especially in breast cancer studies (16). Regardless of proportionality of hazards (as a fundamental assumption), a restriction of this model occurs with time-dependent covariate. In this case, misleading effect estimates can be resulted (12, 17). For time variable model, frailty model can be used. It is a random-effects model, where the random effect (the frailty) has a multiplicative effect on the hazard. Indeed, it is an extension of the proportional hazards model in which the hazard function depends on an unobservable random quantity, which acts multiplicatively (18). However, using appropriate survival models to analyze data, non-misleading effect (regression coefficient) estimates can be derived.

2. Objectives

The current study aimed at applying the Cox, cure, and frailty models to determine the risk factors related to the survival of patients with BC.

3. Methods

The current historical cohort study was carried out at Besaat Nahaja general hospital in Tehran, Iran. Females with a confirmed diagnosis of BC who underwent either MRM (modified radical mastectomy) or BCS (breast-conserving surgery) from March 2010 to March 2014 were enrolled in the study. Only the patients with a non-metastatic condition (M0) at the diagnosis time were included. Patients with missing information on important prognostic factors or unknown current status were excluded. All patients had undergone adjuvant therapy after surgery and were followed-up to March 2015. According to these criteria, 499 females were enrolled in and 47 patients were excluded from the study. All data were gathered by a single observer. The research ethics committee of University of social welfare and rehabilitation sciences approved the study (code no. : IR.USWR.REC.1395.1).

3.1. Characteristics of Data

The following variables at the time of diagnosis were selected and analyzed based on the expert medical opinion and review articles: age, ethnicity (Fars, other), job status (housewife, other), level of education (illiterate, primary and secondary, and postsecondary school), kind of surgery (radical mastectomy, breast saving), type of treatment (hormone therapy, chemotherapy, and radiotherapy), progesterone receptor (PR), estrogen receptor (ER), histological tumor grade (I, II, III), tumor size, stage of disease (I, II, III, IV), metastasis (no, yes), human epidermal growth factor receptor 2 (HER2), progesterone receptor (PR) at initial diagnosis, pathology (invasive ductal carcinoma (IDC), ductal carcinoma in situ (DCIS) and lymph node ratio (LNR). LNR was calculated as the percentage of involved lymph nodes to total lymph nodes excised by the surgeon. Overall follow-up time was considered from the date of treatment to the date of death (ie, event) or censoring (ie, alive).

3.2. Statistical Analysis

Descriptive statistical analysis was carried out to explore the patient and disease characteristics using mean ± SD for continuous variables, median (for times), and also frequency table for categorical variables. To analyze the data; first, the Kaplan-Meier estimator was used to quantify the median follow-up time and also as the empirical evidence of cure (Presence of a long and stable plateau with heavy censoring at the tail of the Kaplan-Meier plots indicated as the empirical evidence of cure.) (16). Then, the proportional Cox regression model was used to analyze the survival times. After univariate analysis, all significant factors were analyzed using multiple analyses. Finally, gamma frailty model with exponential baseline hazard distribution and also cure model were used to analyze the data. A P value < 0.05 was considered statistically significant. All statistical analyses were conducted using survfit, CoxPH, smcure and parfm packages in R software, version 3.2.2.

4. Results

A total of 499 females with BC were included in the current analysis. The mean ± SD for age at the time of diagnosis was 50.39 ± 11.19 years. In addition, the mean ± SD for tumor size was 3.60 ± 3.0 mm. Of the 499 patients, 85.0% were housewives, 91.2% had no familial history, 67.5% were Fars ethnicity, 52.7% had postsecondary education, 63.3% were in stage II, 53.3% were in grade III, 77.4% had no metastasis, 54.3% were negative for Her2, 61.5% carried LNI, 66.1% had ER+ and PR+, 88.0% had DCIS, 66.7% received hormonal therapy (HoR+), 89% undergone radiotherapy, 97.8% undergone chemotherapy, and only 26.9% of the patients undergone breast conserving surgery (Table 1). In the current study, 113 (22.6%) patients died of BC until March 2015. Mean survival time was 53.44 months (95% CI: 51.41 - 55.48). Using the life-table method, the 1-year overall survival rate was 0.92 (95% CI: 0.89 - 0.94). Figure 1 shows a long and stable plateau with heavy censoring, which means cure.

Table 1. Characteristics of Patients with BC and Their Association with Survival Time Using Univariate Analysisa
Risk FactorsLevelsNo. (%)EstimateSEP Value
AgeMean ± SD, median50.39 ± 11.19, 51.00.0410.100< 0.001
Tumor sizeMean ± SD, median3.60 ± 2.37, 3.00.2250.026< 0.001
Job statusHousewife424 (85.0)
Employee75 (15.0)0.4270.3290.194
Familial historyNo455 (91.2)
Yes44 (8.8)0.5630.3350.093
EthnicityFars337 (67.5)
Other162 (32.5)0.0500.2250.823
Level of educationIlliterate42 (8.4)
Primary and secondary school194 (38.9)-0.8900.3450.009
postsecondary school263 (52.7)0.8790.3380.001
StageaI77 (15.5)
II316 (63.3)0.2170.3330.515
III87 (17.4)1.1150.3590.002
IV19 (3.8)2.5750.429< 0.001
GradeI26 (5.2)
II207 (41.5)0.3520.5700.538
III266 (53.3)1.0020.5610.074
MetastasisNo386 (77.4)
Yes113 (22.6)2.4640.212< 0.001
Her2Negative271 (54.3)
Positive228 (45.7)-0.3410.2250.129
LNINo192 (38.5)
Yes307 (61.5)-0.0340.2190.878
ER and PRNegative169 (33.9)
Positive330 (66.1)-0.3270.2180.134
PathologyIDC60 (12.0)
DCIS439 (88.0)1.2350.4480.006
HoRNegative166 (33.3)
Positive333 (66.7)-0.3710.2180.089
RadiotherapyWithout55 (11.0)
With444 (89.0)0.4270.3480.219
ChemotherapyWithout11 (2.2)
With488 (97.8)-0.3040.6730.651
Kind of surgeryRadical Mastectomy365 (73.1)
Breast saving134 (26.9)-0.2900.2670.277

Abbreviations: DCIS, ductal carcinoma in situ; ER, estrogen receptor; HoR, hormone receptor; IDC, invasive ductal carcinoma; LNI, lymph node involvement; PR, progesterone receptor.

a Stage classification according to 7th edition of AJCC staging.

The Kaplan-Meier Survival Curve of the Patients with BC
Figure 1. The Kaplan-Meier Survival Curve of the Patients with BC

In univariate analysis of age at diagnosis, tumor size, employment, level of education, stage of the disease, metastasis, and pathology had a statistically significant effect on the survival of patients with BC (Table 1). Multivariate analysis was used for all biological, clinical, and pathological variables. The results of CoxPH and frailty model are presented in Table 2. The Kaplan-Meier plots for survival function of patients with BC indicate that there may be a long plateau (with some long-term survivors); ie, there is an evidence of cure (Figure 1). Therefore, the results of cure probability and failure time distribution models are presented in Table 3.

Table 2. Survival Analysis of Patients with BC Using Multivariate Survival Analysisa
Risk FactorsLevelsCoxPH ModelFrailty Modela
EstimateSEP ValueEstimateSEP Value
Age0.0470.012< 0.0010.0320.0110.003
Tumor size0.2400.0720.0010.2050.030< 0.001
Job statusHousewife
Employee0.3360.3390.3220.4210.3360.210
Familial historyNo
Yes0.4640.3070.1300.7180.2990.016
EthnicityFars
Other0.1620.2200.4610.1350.2110.523
Level of educationIlliterate
Primary and secondary -0.4670.3060.127-0.5620.2880.051
postsecondary-0.0880.3390.794-0.3010.3090.329
StageI
II-0.2070.3680.5750.1900.3390.574
III-0.1200.4950.8091.0520.3720.005
IV-02260.7940.7762.3050.473< 0.001
GradeI
II-0.3160.5530.567-0.5310.5400.325
III-0.3440.5450.528-0.5440.5360.311
MetastasisNo
Yes2.4700.225< 0.0012.3740.213<0.001
Her2Negative
Positive-0.3220.2120.129-0.1670.1950.393
LNINo
Yes-0.3270.2230.143-0.3210.1960.101
ER and PRNegative
Positive1.58029.30.995-0.2720.1930.158
PathologyIDC
DCIS0.1830.5280.7281.4120.5590.012
HoRNegative
Positive-0.16229.30.995-0.3200.2170.140
RadiotherapyWithout
With0.2010.4700.669-0.3160.4820.512
ChemotherapyWithout
With-0.5690.7390.441-0.2830.7730.714
Kind of surgeryRadical mastectomy
Breast saving0.3390.2610.193-0.2570.2640.330

a Survival frailty model was conducted using gamma frailty distribution with exponential baseline hazard distribution.

Table 3. Cure Probability and Failure Time Distribution Model to Analyze the Survival of Patients with BC
Cure Probability ModelFailure Time Distribution Model
Risk FactorsLevelsEstimateSEP ValueEstimateSEP Value
Age0.0700.0230.0030.0250.0170.150
Tumor size0.3150.095< 0.0010.1620.0550.003
Job statusHousewife
Employee-0.0600.2950.840-0.1100.4180.793
Familial historyNo
Yes0.5550.4880.2550.4480.4320.299
EthnicityFars
Other0.1520.3160.631-0.2460.3820.520
Level of educationIlliterate
Primary and secondary0.1520.3160.6310.2140.2910.464
postsecondary0.0980.1650.5540.1680.2400.484
StageI
II0.5210.3680.887-0.2250.3600.532
III0.0580.2640.8270.2190.4490.625
IV0.945a0.209< 0.0010.9940.4510.028
GradeI
II-0.4200.2480.0.90-0.1892.3290.935
III-0.1460.1920.446-0.7372.2920.748
MetastasisNo
Yes3.2600.298< 0.0011.5900.4690.001
Her2Negative
Positive-0.1820.4350.677-0.0940.2310.685
LNINo
Yes-0.5580.4240.188-0.3040.2800.277
ER and PRNegative
Positive-0.4090.4370.350-0.0830.3010.782
PathologyIDC
DCIS0.5800.6040.3370.9510.6450.140
HoRNegative
Positive-0.3630.2930.2160.9510.6450.140
RadiotherapyWithout
With0.6510.4430.142-0.1930.4940.696
ChemotherapyWithout
With-0.4590.5480.402-0.2491.1090.822
Kind of surgeryRadical mastectomy
Breast saving0.2610.3600.470-0.1280.3190.687

a The hazard ratio estimate for stage IV was HR = exp (0.945) = 2.57. It means that the stage IV had a hazard rate about 2.8 times more than that of the stage I on the hazard of the event.

According to the results of multivariate analysis presented in Table 2, in the CoxPH model, age at diagnosis (P < 0.001), tumor size (P = 0.001) and metastasis (P < 0.001) covariates, and in frailty model age at diagnosis (P = 0.003), tumor size (P < 0.001), familial history (P = 0.016), stage III (P = 0.005) and IV (P < 0.001), metastasis (P < 0.001), and DCIS pathology (P = 0.012) had a statistically significant effect on the survival of patients with BC. In addition, according to the results of multivariate analysis presented in Table 3, in cure probability model, age at diagnosis (P = 0.003), tumor size (P < 0.001), stage IV (P < 0.001) and metastasis (P < 0.001) covariates had a statistically significant effect on cure of the patients with BC; and in failure time distribution model, tumor size (P = 0.003), stage IV (P = 0.028), and metastasis (P = 0.001) had a statistically significant effect on the death of patients with BC. In cure model, the hazard ratio estimate for tumor size was HR = exp (0.315) = 1.37, adjusted for other variables; it means that the tumor size had a hazard rate about 1.37 times more than that of the event, if 1 unit increased in the tumor size. The hazard ratio estimate for stage IV was HR = exp (0.945) = 2.57. It means that the stage IV had a hazard rate about 2.8 times more than that of the stage I on the hazard of the event. The hazard ratio estimate metastasis was HR = exp (3.26) = 26.05. It means that the metastasis group had a hazard rate about 26 times more than that of the non-metastasis group on the hazard of the event.

Finally, the standard errors (SE) in cure and frailty models were better than the Cox model (Tables 2 and 3).

5. Discussion

BC is second most common cause of cancer related death (2, 3), which has high incidence rate among females worldwide (4). In many studies, the CoxPH model was used as a standard method to determine the prognostic factors of survival of patients with BC. However, this method cannot support long-term survival (19). Now, if a model assesses the risk factors for long-term survival, it is more appropriate. In the current paper, the CoxPH, frailty, and cure models were used to analyze the survival of patients with BC and their results were reported.

The mean age of the patients in the current study was 50.4 years (median = 51 years), consistent with other studies from Iran (9, 20-22) and also similar to that of Arab nations (23). In the current study, age was a significant factor for the survival of patients with BC in all models. Compared with Western countries, Iranian females had a higher risk of developing breast cancer in their middle age (24). This may be due to young population structure of the I.R. Iran and also lower age at the first pregnancy (average of 28 years) (25).

Metastasis and tumor size covariates were the significant risk factors in all models. These risk factors were also reported as significant factors in other studies (9, 10, 20, 22, 26). In these cases, some studies suggested a linear and others suggested a nonlinear effect of tumor size (27). It is mentioned that some studies reported that tumor size increased the risk of metastasis in patients with BC (20, 28-30).

Stage covariate was a significant risk factor in cure and frailty models. This risk factor was also reported as a significant factor in other studies (9, 13, 20, 26).

Family history and pathology covariates were significant only in the frailty model. These risk factors were also reported as significant factors in other studies from Iran (20, 31) and USA (30).

Use of adjuvant chemotherapy tends to increase in cure fraction, particularly for the oldest age group. Huang for the first time estimated the cure fraction for the patients with ER breast cancer (32). The cure fraction was 58% (26), 20% (33), and was estimated 68% in the current study. This controversy may be due to different follow-up intervals.

In the current study, other covariates had no significant effects on the survival of patients with BC. Some of these risk factors, such as ER and PR, HoR, and Her2, are still controversial and a number of studies reported their importance (34-37).

It was mentioned that the results of the cure models can provide estimates of the probability of being a long-term survivor, which the other models cannot. For cancers in which some patients may have a long and stable plateau with heavy censoring, the cure models can be an interesting method to analyze data (12).

5.1. Limitation

All data were collected retrospectively. The sample size in the current study was related to the armed forces and their families. In the current study, it was assumed that patient censoring was not related to the BC death. In addition, an increase in the follow-up time (in years) may make stronger results for BC survival parameters in the cure model.

5.2. Conclusion

Cure models are an underused statistical tool and not yet very popular in the survival studies on cancer. This statistical method could be useful for a wide range of cancers such as head and neck, colon cancer, stomach, breast, etc. However, when some patients are the long-term survivors, cure models can be interesting methods to study survival and also describe their short-term and long-term effects. The current study showed that the tumor size had an increased effect on the hazard of the event, adjusted for other variables. In addition, stage IV of the disease and also metastasis increased the effects on the hazard of the event. Finally, a large cohort study of BC survival and comparison between cure fractions in different categories is suggested.

Acknowledgements

Footnotes

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