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ORIGINAL ARTICLE
Year : 2019  |  Volume : 10  |  Issue : 1  |  Page : 39-44  

Assessment of the fitness of Cox and parametric regression models of survival distribution for Iranian breast cancer patients' data


1 Departments of Health and Community Medicine, Medical School, Shahid Beheshti University of Medical Sciences, Tehran, Iran
2 Department of Community Medicine, Medical School, Shahid Beheshti University of Medical Sciences, Tehran, Iran
3 Iranian Research Center on Healthy Aging, Sabzevar University of Medical Sciences, Sabzevar, Iran
4 Department of Vascular Surgery, Sina Hospital, Tehran University of Medical Sciences, Tehran, Iran
5 Department of Surgery, School of Medicine, Sina Hospital, Tehran University of Medical Sciences, Tehran, Iran
6 Department of Epidemiology and Biostatistics, School of Public Health, Shahroud University of Medical Sciences, Shahroud, Iran
7 Department of Community Medicine, School of Medicine, Arak University of Medical Sciences, Arak, Iran
8 Community Based Participatory Research Center, Iranian Institute for Reduction of High-Risk Behaviors, Tehran University of Medical Sciences, Tehran, Iran
9 Health Management Research Center & Department of Community Medicine, Faculty of Medicine, Baqiyatallah University of Medical Sciences, Tehran, Iran

Date of Web Publication12-Feb-2019

Correspondence Address:
Dr. Esmat Davoudi-Monfared
Department of Community Medicine, Health Management Research Center, Faculty of Medicine, Baqiyatallah University of Medical Sciences, Tehran
Iran
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Source of Support: None, Conflict of Interest: None


DOI: 10.4103/japtr.JAPTR_360_18

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  Abstract 

Factors affecting the time of survival after breast cancer (BC) diagnosis remain unknown. However, some of the prognostic factors have been identified. The aim of this study was to investigate the effects of biologic and socioeconomic factors on long-term survival of BC patients. This was a descriptive chart review and survey of all women with a confirmed diagnosis of BC registered in Shohada-e-Tajrish Cancer Research Center database from March 2004 to March 2015. The checklist of study consisted of biologic, demographic, reproductive, genetic, medical, and therapeutic information of patients. The minimum time of follow-up was 3 years and the maximum was 10 years. We then evaluated possible associations of these variables with BC survival using Cox and parametric regression models of survival analysis. The study population was 1276 BC patients. Their mean survival was 23 (range 1–120) months. Between the parametric models, Weibull regression model demonstrated the lowest Akaike information criterion and thus the best fit, and tumor size, number of lymph nodes, BC stage, educational level, and high-fat diet were significant in this model. Based on our findings, educational level, consumption of fat, and characteristics of tumor at the time of diagnosis (disease stage, tumor size, number of involved lymph nodes) are the most important prognostic factors affecting long-term survival of BC patients. We suggest that future studies assess the efficacy of possible interventions for these factors.

Keywords: Breast cancer, hazard models, Iran, survival


How to cite this article:
Mohseny M, Shekarriz-Foumani R, Amiri P, Vejdani M, Farshidmehr P, Mahmoudabadi HZ, Amanpour F, Mohaghegh P, Tajdini F, Sayarifard A, Davoudi-Monfared E. Assessment of the fitness of Cox and parametric regression models of survival distribution for Iranian breast cancer patients' data. J Adv Pharm Technol Res 2019;10:39-44

How to cite this URL:
Mohseny M, Shekarriz-Foumani R, Amiri P, Vejdani M, Farshidmehr P, Mahmoudabadi HZ, Amanpour F, Mohaghegh P, Tajdini F, Sayarifard A, Davoudi-Monfared E. Assessment of the fitness of Cox and parametric regression models of survival distribution for Iranian breast cancer patients' data. J Adv Pharm Technol Res [serial online] 2019 [cited 2020 Sep 24];10:39-44. Available from: http://www.japtr.org/text.asp?2019/10/1/39/252127




  Introduction Top


Breast cancer (BC) is the most common cancer in developed countries, roughly affecting one in every 10 females. It constitutes nearly 28% of cancers in women[1] and ranks second only after lung cancer as the most frequent cause of cancer deaths in women.[2]

Over the past few decades, the survival rate of BC patients has improved after diagnosis. Between 1999 and 2005, the 5-year survival rate among women who were diagnosed with cancer was 90%, compared with 1975–1977, when this being 75%.[3] Moreover, in 2017, the average 5-year survival rate for people with BC was 90%. The average 10-year survival rate is 83%.[4]

According to the current evidence, long survival time has improved due to advances in BC treatment approach and implementation of population-based screening programs of women at risk of BC. Unfortunately, all of women population does not show the same increase in survival. This difference in increasing the survival rate of women may depend on different factors. Many studies have examined these factors.

The etiology of BC remains unknown, but a broad range of factors have been identified that contribute to its high prevalence. These include biologic factors (age, family history, and ethnicity), social determinants of health (childhood conditions, social status, and educational level),[5] lifestyle-related factors (alcohol consumption, obesity, lack of physical exercise, stress, and smoking), and disease-related factors (stage at diagnosis, tumor grade, and comorbid conditions).[6] In addition, higher incidence has been commonly reported in women with higher socioeconomic status (SES), which may contribute to differences in lifestyle, family planning, and access to healthcare services.[7] On the other hand, women with higher SES survive more than the lower group, paradoxically.[8] The most important factors of long survival time in women with BC were socioeconomic factors such as regional variations, race/ethnicity, SES, and urbanization in previous studies.[9],[10],[11]

Nevertheless, evidence is inconclusive, and controversial results still exist.[12],[13] Specifically, studies evaluating associations of individual factors as well as community determinants of SES with BC survival are lacking. We aimed to investigate the effects of biological and lifestyle factors on BC survival using parametric regression models of survival distribution analysis.


  Materials and Methods Top


In this descriptive chart review, we surveyed all women who had a record in the Shohada-e-Tajrish Cancer Research Center database with a confirmed diagnosis of BC, from March 2004 to March 2015. Our inclusion criteria were a confirmed BC diagnosis, living in or in proximity of Tehran, and having initiated treatment after the diagnosis. Women with missing data were excluded. The minimum number of patients required for this study at an alpha error of 5% and a beta error of 20% was 380.

We designed a specific checklist for this study. We considered years of education as a criterion for SES since it has been shown that it is a valid and reliable determinant of SES in social health studies in Iran. Our biologic and demographic variables included age, time of diagnosis, education level, marital status, fat content of diet, and smoking. Reproductive variables included gravidity, parity, miscarriages/abortions, breastfeeding duration, hormone consumption, duration of hormone consumption, age at first menstrual period, and age at menopause. Disease-related factors included disease stage, tumor grade, final pathology, and lymph node involvement. Genetic variables included family history of BC, estrogen receptor (ER) status, progesterone receptor (PR) status, and HER2, P53, and KI67 gene mutations. Finally, treatment-related factors included receiving chemoradiotherapy, hormonal therapy, and herceptin, as well as recurrence/metastasis.

Survival was evaluated during the aforementioned 10-year period with 3 years being the minimum acceptable duration of follow-up. Age, disease stage, and similar variables were assessed using Kaplan–Meier curves. Significant variables were then entered into the Cox and parametric regression models to investigate their correlation with survival outcomes.


  Results Top


This study population consisted of 1276 BC patients. The mean survival time was 23 (range 1–120) months. [Table 1] presents the demographic characteristics of the study participants.
Table 1: Case summary of patients with breast cancer

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Tumor size, number of involved lymph nodes, BC stage, tumor grade, PR positivity, lymphovascular invasion, educational level, and high-fat diet were statistically significant in Kaplan–Meier modeling and were selected for Cox and parametric regression models. We excluded tumor grade in this step because of its overlap with tumor size and included age in all of our models because of its previously established importance although it failed to show significance in the Kaplan–Meier model in our study.

Assumptions of Cox model were analyzed using Schoenfeld residuals method, which approved the assumption of similarity of hazard ratios (HRs) for all variables. This showed that the risk of death was similar between different treatment groups in time, enabling the calculation of a constant for its effect.

Risk distribution of the mortality of BC was determined using Weibull regression, lognormal, log-logistic, and Gompertz models. The goodness of fit of these models was then tested by fragility analysis, which evaluates the changes of survival over time not accounted for by the variables in the model. All models were compared by Akaike information criterion (AIC), where lower AIC shows better fit.

All parametric models showed a lower AIC than the Cox model. Moreover, between the parametric models, Weibull regression model demonstrated the lowest AIC and thus the best fit. Different models are compared in [Table 2].
Table 2: Fitness of survival models in patients with breast cancer

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We further investigated the goodness of fit using Cox-Snell residuals, which also confirmed the superiority of the Weibull model [Figure 1]. Risk distribution curve is illustrated in [Figure 2].
Figure 1: Cox-Snell residue for Weibull distribution in patients with breast cancer

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Figure 2: The risk distribution curve of the Weibull in patients with breast cancer

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Fragility model did not show any statistical significance in any of the parametric regression models.

The effect estimates were presented by HRs in proportional hazard models and by survival time ratios in accelerated failure time models. Tumor size, number of lymph nodes, BC stage, educational level, and high-fat diet were significant in the Weibull regression model.

Patients with a larger tumor (HR = 1.20), stage 4 BC (vs. stage 1) (HR = 9.84), and high-fat diet (HR = 2.7) had higher risk of mortality, while patients with a high-school diploma or higher level of education had lower mortality risk compared with those with lower educational levels.


  Discussion Top


Between the parametric models of survival analysis, Weibull regression model demonstrated the lowest AIC and thus the best fit.

In the present study, we evaluated the relationship between long-time survival of BC and various biologic and demographic (age, time of diagnosis, education level, marital status, fat content of diet, and smoking), reproductive (gravidity, parity, miscarriages/abortions, breastfeeding duration, hormone consumption, duration of hormone consumption, age at first menstrual period, and age at menopause), genetic (included family history of BC, ER status, PR status, and HER2, P53, and KI67 gene mutations), disease (disease stage, tumor grade, final pathology, and lymph node involvement), and treatment-related (receiving chemoradiotherapy, hormonal therapy, and herceptin, recurrence/metastasis) factors.

We found that educational level, high-fat diet, and disease characteristics such as cancer stage, tumor size, and number of positive lymph nodes were important prognostic factors that influenced survival.

The effect of educational level on BC survival is a controversial topic. While previous studies demonstrated higher incidence of BC in more educated patients,[14] better survival rates have been reported in this patient population,[15] similar to our findings. In Herndon et al.'s study, the level of education below high-school diploma was a risk factor for death in women with BC.[16]

The level of education is closely related to the SES of individuals. Therefore, the difference in the level of education shows the different social and economic status of individuals. Higher BC incidence rates in educated patients may be explained by other SES components such as reproductive behavior, number of children, older age at first pregnancy, and shorter duration of breastfeeding.[17] Better survival, on the other hand, can be due to the fact that these patients are more inclined toward BC screening programs.[18],[19] This inclination, in turn, would also translate into higher incidence rates in these patients, but at earlier stages, enabling more effective treatment of BC and hence better survival.

Another possible explanation of this difference in survival could be due to lead-time bias in studies in which educated patients are found to have better survival, while in fact the earlier diagnosis of their condition results in a false notion of better survival because of the longer period until death. In addition, women with lower SES tend to resist the complementary axillary surgery and adjuvant chemotherapy, which creates a poor outcome in treatment and can affect survival.[20] Better coverage by health insurance and thus accessibility to healthcare services are another possible advantages in educated patients, whereas those with lower educational levels may geographically and economically struggle to have such access to receive the most effective treatments.[21]

There is strong evidence that obesity is a potent risk factor for both cancer development and the prognosis of BC which is defined by anthropometric measurements and body mass index (BMI).[22]

We demonstrated that high-fat diet is another prognostic factor in BC patients.

This is similar to previous findings showing a direct relationship between fat consumption and recurrence and survival rates in BC patients. The studies suggested lower intake of saturated fat in the diet of BC patients in postdiagnosis period was associated with improved survival after BC diagnosis.[23],[24] A meta-analysis by Xing et al., moreover, showed that following a low-fat diet in BC patients reduced recurrence rate and in turn increased survival.[25] This relationship has been observed in both ER+ and ER− tumors, which may be explained by attenuated inflammatory processes and lower levels of inflammatory mediators in tissues. On the other hand, many studies have evaluated the effect of diet on incidence of BC, but the evidence is still inconclusive.[26] While the effect of Western high-fat diet is widely studied, we showed that an equivalent high-fat Eastern diet also adversely affected the survival in BC patients. This finding supports the notion that the fat content is the major player irrespective of type of diet. Having ruled out reproductive behavior in our study as a possible influence, we may conclude that diet could be considered the most important lifestyle element for survival in BC patients.

Besides education and diet, we emphasized the significant effects of disease characteristics such as stage, tumor size, and number of involved lymph nodes on survival. Many studies have shown the effect of tumor size independently of the number of lymph nodes on mortality rates in BC; our study further confirmed this finding.[27]


  Conclusion Top


Among the various biologic, demographic, genetic, reproductive, and pathophysiologic factors associated with BC, the most important factors affecting long-term survival included educational level, high-fat diet, and disease characteristics at the time of diagnosis. We suggest that future studies focus on interventions on these factors and evaluate their effectiveness regarding patient survival.

Financial support and sponsorship

Nil.

Conflicts of interest

There are no conflicts of interest.



 
  References Top

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Herndon JE 2nd, Kornblith AB, Holland JC, Paskett ED. Effect of socioeconomic status as measured by education level on survival in breast cancer clinical trials. Psychooncology 2013;22:315-23.  Back to cited text no. 16
    
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    Figures

  [Figure 1], [Figure 2]
 
 
    Tables

  [Table 1], [Table 2]



 

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