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Year : 2016  |  Volume : 12  |  Issue : 3  |  Page : 1184-1188

Application of accelerated failure time models for breast cancer patients' survival in Kurdistan Province of Iran

1 Social Determinants of Health Research Center, Kurdistan University of Medical Sciences, Sanandaj, IR Iran
2 Department of Epidemiology, Faculty of Health, Ilam University of Medical Sciences, Ilam, IR Iran
3 Prevention of Psychosocial Injuries Foundation, Research Center, Ilam, IR Iran

Date of Web Publication4-Jan-2017

Correspondence Address:
Kourosh Sayehmiri
Prevention of Psychosocial Injuries Foundation, Research Center, Ilam
IR Iran
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Source of Support: None, Conflict of Interest: None

DOI: 10.4103/0973-1482.168966

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 > Abstract 

Context: Breast cancer is the most common cancer and the second common cause of cancer-induced mortalities in Iranian women. There has been a rapid development in hazard models and survival analysis in the last decade.
Aims: The aim of this study was to evaluate the prognostic factors of overall survival (OS) in breast cancer patients using accelerated failure time models (AFT).
Setting and Design: This was a retrospective-analytic cohort study.
Subjects and Materials: About 313 women with a pathologically proven diagnosis of breast cancer who had been treated during a 7-year period (since January 2006 until March 2014) in Sanandaj City, Kurdistan Province of Iran were recruited.
Statistical Analysis Used: Performance among AFT was assessed using the goodness of fit methods. Discrimination among the exponential, Weibull, generalized gamma, log-logistic, and log-normal distributions was done using Akaik information criteria and maximum likelihood.
Results: The 5 years OS was 75% (95% CI = 74.57–75.43). The main results in terms of survival were found for the different categories of the clinical stage covariate, tumor metastasis, and relapse of cancer. Survival time in breast cancer patients without tumor metastasis and relapse were 4, 2-fold longer than other patients with metastasis and relapse, respectively.
Conclusion: One of the most important undermining prognostic factors in breast cancer is metastasis; hence, knowledge of the mechanisms of metastasis is necessary to prevent it so occurrence and treatment of metastatic breast cancer and ultimately extend the lifetime of patients.

Keywords: Accelerated failure time models, breast cancer, prognostic factors, survival analysis

How to cite this article:
Karimi A, Delpisheh A, Sayehmiri K. Application of accelerated failure time models for breast cancer patients' survival in Kurdistan Province of Iran. J Can Res Ther 2016;12:1184-8

How to cite this URL:
Karimi A, Delpisheh A, Sayehmiri K. Application of accelerated failure time models for breast cancer patients' survival in Kurdistan Province of Iran. J Can Res Ther [serial online] 2016 [cited 2017 Oct 18];12:1184-8. Available from:

 > Introduction Top

Breast cancer is one of the most common diseases among women in the world with an incidence of more than 1000,000 and death rate of 410,000 in 2012.[1]

Although breast cancer is frequent in postmenopausal women, the presentation of the disease is high in premenopausal women in undeveloped countries.[2]

Identifying prognostic factors of patients' survival time in breast cancer is important, not only because it enables physicians to detect the factors whose changes affect patients' survival time, but also helps them to make the best decision about patients' treatment.

The etiology of breast cancer is largely unknown; therefore there is no established primary prevention strategy. So, the main strategy is the establishment of screening protocols and early detection programs, which at least theoretically can improve the survival rates. Despite the increasing incidence, the survival rates of breast cancer patients in many developed countries were substantially improved. According to national cancer registry project report, breast cancer is the most common cancer and also the most common cause of cancer-related deaths of the female population in Iran.[3]

For cancer patients, survival rates have been accepted as the main criteria to measure the impact of treatment on cancer control.[4] A calculating mean lifetime in different groups of populations and assessment of effective factors in order to achieve healthy life is one of the challenges of scientists in various branches of biology and medicine. The population lifetime is a random statistical variable, therefore predicting it is not possible except through the use of statistical methods.[5],[6] The survival of breast cancer patients depends on factors such as genetic, age at diagnosis, access to care, stage of cancer, weight, physical activity status, alcohol consumption, social, economic, environmental factors, and ethnicity.[7]

Recently, accelerated failure time (AFT) models as parametric models have attracted considerable attention, because not only they do not need proportional hazard (PH) assumption but also thanks to availability of standard methods such as maximum likelihood, parameter estimation, and testing can be done readily.[6]

When survival time has a specific statistical distribution, the statistical power of parametric survival model is higher than nonparametric or semiparametric survival. The exponential, Weibull, generalized gamma (GG), log-normal, and log-logistic are among parametric distributions commonly used for study survival time analysis. Survival estimates obtained from parametric survival models typically yield plots that are more consistent with a theoretical survival curve.[8]

Like Cox model, parametric survival models can be used in regression forms. The interpretations of parameters for AFT models are also different from Cox PH models. The AFT assumption is applicable for a comparison of survival time whereas the PH assumption is applicable for the comparison of hazards.[6]

Since recently, AFT models have not been used very often, and a few usages of these models are found in breast cancer.[9] In this paper we tried fitting AFT models, chose the one with the best fitness and used it to determine prognostic factors for survival in breast cancer patients.

 > Subjects and Methods Top

Through a retrospective study, data were sourced mainly from pathology report of the patients and hospital database records. Three hundred and thirteen patients with breast cancer who had been hospitalized in Sanandaj City in Kurdistan Province of Iran were recruited. Inclusion criterion was a definite diagnosis of breast cancer during a 7-year period from 2006 onward. Clinical data such as the stage of disease were obtained through a structured questionnaire and the patients' clinical record. Vital statues and date of death were determined by a phone call and also by official death certificates with a maximum follow-up of 96 months. Survival time (in a month) was calculated from the date of diagnosis till the date of death or last follow-up (the end of March 2014). Patients who were alive at the end of the follow-up period were censored. Finally, 84 patients were excluded from analyses according to exclusion criteria (5 cases were an outlier, 79 patients due to the indeterminate date of death or current status, most of them were Iraq subsidiary). Overall 229 patients were enrolled. If the date of death for survival analysis was unknown, the patient excluded from survival analysis but remained for other assessments (descriptive variables). Clinical and pathologic variables were age of patient, clinical stage of disease (determined according to American Joint Committee on Cancer tumor node metastasis staging system for breast cancer),[10] date of diagnosis, type of surgery (modified radical mastectomy or lumpectomy), tumor laterality (right or left), estrogen receptor status, progesterone receptor status, P53 amplification, human epidermal growth factor receptor 2 (HER-2) positivity, metastasis of tumor, and the site of metastasis.

Time ratio

AFT models coefficients are most intuitively expressed in the exponential form, a time ratio (TR) >1 associated with prolonged survival time whereas the TR <1 associated with a decreased in survival time.[11]

Statistical analysis

The probability of overall survival (OS) was estimated using Kaplan–Meier estimator. AFT models such as the exponential, Weibull, GG, log-normal, and log-logistic distributions were used to finding the best distribution fitted to time to even (death). To find the best fitted model among GG family distributions such as: The exponential, Weibull, log-normal, and GG we used logarithm likelihood (LL).[12]

AFT model was used for finding prognostic factors of breast cancer patients' survival. Smoothed hazard function was estimated using Kernel smoothing method.[13] P < 0.05 was considered as significant. Analyses were done using SPSS Version 16 (Inc. Chicago, IL, USA) and STATA Version 11 software.

 > Results Top

The mean age of patients was 46.10 ± 10.81 years. Based on Kaplan–Meier curve 5 years survival rate was 75% (95% CI = 74.57–75.43) [Figure 1]. As expected the survival curve decreases as long as time increases. Patients have a predicted median survival of approximately 81 months. [Table 1] shows the characteristics of patients who were included in the study. The survival is nearly 96% for a patient with 1-year of survival time [Table 1].
Figure 1: The overall survival curve in breast cancer patients by Kaplan–Meier method

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Table 1: Breast cancer patient's characteristics in Kurdistan Province between 2006-2014

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Specifically of the 229 patients diagnosed with breast cancer that we could follow-up them, about 79% were alive at the end of follow-up (right-censored).

All of the patients who were at stage 4 of cancer in diagnosis time had died 5 years later. In contrast, those who were HER-2 positive had maximum 5 years survival (89%) among the breast cancer patients.

Univariate analysis (Kaplan–Meier method) showed that there is a significant association between OS and relapse of disease (P = 0.001), tumor metastasis (P = 0.0001), stage of cancer (P = 0.031), and site of metastasis (P = 0.0001).

Variables with significant level <0.05 in univariate analysis were considered in the multivariate models. Based on Akaike information criterion (AIC) criteria (AIC = 2log likelihood + 2P, where P is the number of parameters in the model, with the smallest AIC, is the best)[14] among exponential, log-logistic, log-normal, GG, and Weibull distributions of AFT models, finally GG, and Weibull distributions were better fitted models on data [Table 2].
Table 2: Discrimination among distributions using maximum likelihood for metastasis factor

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However, LL in these two models does not have a significant difference so, we choose Weibull distribution because it has fewer parameters and simple interpretation. The interpretation of hazard ratios of Cox model may be questionable. When PH assumption is not met for a model, we can usually use AFT or Cox model with time-varying covariates.

The results showed there was a strong significant association between tumor metastasis and OS in breast cancer patients (P = 0.0001, TR = 0.25) indicating that survival time in patients without tumor metastasis are 4 times higher than patients with tumor metastasis in breast cancer. [Table 3] shows that there is a significant correlation between OS and breast cancer patients with relapse (P = 0.0001, TR = 0.5) median OS in patients who have had relapse of breast cancer was about 2 times shorter than other patients without relapse.
Table 3: Prognostic factors of OS in univariate using Weibull AFT model

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Although there was not a significant association between clinical stage of breast cancer in divided groups, one who were at stages 1 and 2 of breast cancer and another who were at stages 3rd and 4th of breast cancer, but TR between two groups was notable and survival time in patients in advanced stages of cancer was 34% shorter than other group.

The shape of hazard function for mortality revealed a decreasing trend as a hazard of dying in patients with tumor metastasis was higher than patients that had no metastasis [Figure 2].
Figure 2: Smoothed hazard death function in breast cancer patients with tumor metastasis and without metastasis

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 > Discussion Top

Our objective was to identify prognostic factors of OS using parametric models (AFT models). In many researches, Cox PH regression models were used to consider prognostic factors of OS in breast cancer patients. Although parametric PH models are very applicable to analyze survival data, there are relatively few probability distributions for the survival time that can be used with these models. The main assumption of Cox regression hazards is PHs, where PH assumption is not met, it is improper to use standard Cox PH model as it may entail serious bias and loss of power when estimating or making inference about the effect of a given prognostic factors on mortality.[15],[16] In these situation, AFT models is an alternative to the PH model for the analysis of survival data. Under AFT models, we measure the direct effect of explanatory variables on the survival time instead of hazards, as we do in the PH model.

In the other hand, the AFT models can be interpreted in terms of the speed of progression of a disease. The effect of the covariates in an AFT model is to change the scale, and not the location of a baseline distribution of survival times.[12]

Moreover, AFT models not only can specify a direct relation between the logarithm of survival time and a set of explanatory variables, but also permits a clearer interpretation of the effect of each covariate on survival, allowing estimating the median event time.

In a study conducted by Alfonso et al.[9] in Cuba showed that the GG AFT model was the best model fitted to data of breast cancer. Our study is consistent with the study of Rafiquhhah Khanet al.[7] they suggested that the exponentiated Weibull model was a better fit for White non-Hispanic females' breast cancer survival data. The current study also showed GG and Weibull AFT models were better fitted to data too, but do to some advantages of Weibull model we used it.

The biggest difference in terms of survival was found for breast cancer with tumor metastasis. There are a few studies that compared the survival rates of with tumor metastases. In patients with metastases in the brain, the risk of death had been very higher compared to other parts of the body.[17] The survival time among patients without tumor metastasis is 75% higher than breast cancer patients with tumor metastasis. For that reason, it is extremely important to detect cancer at early stages and on time treatment to prolong the survival time. Although death TR in two groups of breast cancer patients in different clinical stages was not same and survival time in patients in clinical stages of 1 and 2 of cancer was 66% higher than patients in advanced stages of breast cancer but this difference was not statistically significant (P = 0.08, TR = 0.66). In Anet Garsia Alfonso study [9] the survival time was about 40% shorter in breast cancer patients who had been diagnosed at the second clinical stage in comparison with those at the first clinical stage. Whereas, this difference was increased up to about 50% and 60% for patients with the clinical stage of 3rd and 4th of breast cancer, respectively. In another study conducted by [18] showed the significant effects of stage and revealed that women diagnosed around 38s have consistently higher survival rates than either younger or older women. In this study, the highest survival was seen in patients with positive HER-2 statue but the difference of survival time in negative and positive HER-2 patients was not statistically significant, while in [19] study, shorter survival time was observed in patients with positive HER-2 44 months versus 62 months. Elevated serum levels of HER-2 were associated with several factors related to tumor aggressiveness of breast cancer, such as tumor size, advanced stage, lymph node involvement poor histological differentiation, and shorter disease-free and/or OS.[20],[21]

Financial support and sponsorship


Conflicts of interest

There are no conflicts of interest.

 > References Top

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Tripsianis G, Papadopoulou E, Romanidis K, Katotomichelakis M, Anagnostopoulos K, Kontomanolis E, et al. Overall survival and clinicopathological characteristics of patients with breast cancer in relation to the expression pattern of HER-2, IL-6, TNF-a and TGF-ß1. Asian Pac J Cancer Prev 2013;14:6813-20.  Back to cited text no. 19
Azizun-Nisa, Bhurgri Y, Raza F, Kayani N. Comparison of ER, PR and HER-2/neu (C-erb B 2) reactivity pattern with histologic grade, tumor size and lymph node status in breast cancer. Asian Pac J Cancer Prev 2008;9:553-6.  Back to cited text no. 20
Kong Y, Dai S, Xie X, Xiao X, Lv N, Guo J, et al. High serum HER2 extracellular domain levels: Correlation with a worse disease-free survival and overall survival in primary operable breast cancer patients. J Cancer Res Clin Oncol 2012;138:275-84.  Back to cited text no. 21


  [Figure 1], [Figure 2]

  [Table 1], [Table 2], [Table 3]


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