Cure Models as a Useful Statistical Tool for Analyzing Survival

Fred Hutchinson Cancer Research Center, Seattle, WA 98117, USA.
Clinical Cancer Research (Impact Factor: 8.72). 06/2012; 18(14):3731-6. DOI: 10.1158/1078-0432.CCR-11-2859
Source: PubMed


Cure models are a popular topic within statistical literature but are not as widely known in the clinical literature. Many patients with cancer can be long-term survivors of their disease, and cure models can be a useful tool to analyze and describe cancer survival data. The goal of this article is to review what a cure model is, explain when cure models can be used, and use cure models to describe multiple myeloma survival trends. Multiple myeloma is generally considered an incurable disease, and this article shows that by using cure models, rather than the standard Cox proportional hazards model, we can evaluate whether there is evidence that therapies at the University of Arkansas for Medical Sciences induce a proportion of patients to be long-term survivors.

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    • "This situation is common in oncology studies and Othus et al. (2012) discuss the preference of cure models over Cox model for analyzing such data (Yin and Ibrahim, 2005; Othus et al., 2012b). No one can be cured of death, therefore term " long survivors " is sometimes used instead of " cured patients " as this long survivorship causes a K-M curve with a plateau tail (Othus et al., 2012a). Since metastatic breast cancer is considered to be incurable, exploring the factors associated with the long term from primary to metastatic breast cancer would be of great value for clinicians and oncology researchers. "
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    ABSTRACT: Breast cancer is a fatal disease and the most frequently diagnosed cancer in women with an increasing pattern worldwide. The burden is mostly attributed to metastatic cancers that occur in one-third of patients and the treatments are palliative. It is of great interest to determine factors affecting time from cancer diagnosis to secondary metastasis. Cure rate models assume a Poisson distribution for the number of unobservable metastatic-component cells that are completely deleted from the non-metastasis patient body but some may remain and result in metastasis. Time to metastasis is defined as a function of the number of these cells and the time for each cell to develop a detectable sign of metastasis. Covariates are introduced to the model via the rate of metastatic-component cells. We used non-mixture cure rate models with Weibull and log-logistic distributions in a Bayesian setting to assess the relationship between metastasis free survival and covariates. The median of metastasis free survival was 76.9 months. Various models showed that from covariates in the study, lymph node involvement ratio and being progesterone receptor positive were significant, with an adverse and a beneficial effect on metastasis free survival, respectively. The estimated fraction of patients cured from metastasis was almost 48%. The Weibull model had a slightly better performance than log-logistic. Cure rate models are popular in survival studies and outperform other models under certain conditions. We explored the prognostic factors of metastatic breast cancer from a different viewpoint. In this study, metastasis sites were analyzed all together. Conducting similar studies in a larger sample of cancer patients as well as evaluating the prognostic value of covariates in metastasis to each site separately are recommended.
    Asian Pacific journal of cancer prevention: APJCP 12/2014; 15(15):9673-9678. DOI:10.7314/APJCP.2014.15.22.9673 · 2.51 Impact Factor
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    • "need to use the Cox PH cure model, a newly developed statistical method. The Cox PH cure model is well known in the field of statistics [10] but is not as widely known in the clinical setting [11]. This model includes both a logistic regression component for the cure rate and a Cox regression component for the hazard for uncured patients. "
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    ABSTRACT: In prognostic studies for breast cancer patients treated with neoadjuvant chemotherapy (NAC), the ordinary Cox proportional-hazards (PH) model has been often used to identify prognostic factors for disease-free survival (DFS). This model assumes that all patients eventually experience relapse or death. However, a subset of NAC-treated breast cancer patients never experience these events during long-term follow-up (>10 years) and may be considered clinically "cured." Clinical factors associated with cure have not been studied adequately. Because the ordinary Cox PH model cannot be used to identify such clinical factors, we used the Cox PH cure model, a recently developed statistical method. This model includes both a logistic regression component for the cure rate and a Cox regression component for the hazard for uncured patients. The purpose of this study was to identify the clinical factors associated with cure and the variables associated with the time to recurrence or death in NAC-treated breast cancer patients without a pathologic complete response, by using the Cox PH cure model. We found that hormone receptor status, clinical response, human epidermal growth factor receptor 2 status, histological grade, and the number of lymph node metastases were associated with cure.
    12/2013; 2013(5):354579. DOI:10.1155/2013/354579
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    • "For example, disease-free survival (DFS) data on breast cancer patients who received neoadjuvant chemotherapy (NAC) should be analyzed by using the cure model because there are disease-free patients in 10 years after receiving NAC (Rastogi et al., 2008). Likewise, cure models to describe progression-free survival trends for multiple myeloma patients were introduced by Othus et al. (2012). In cancer prognostic studies involving patients with long-term censored survival, we often need to identify the clinical variables that affect the cure rate and long-term outcomes in order to develop a predictive prognostic model. "
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    ABSTRACT: A cure rate model is a survival model incorporating the cure rate on the assumption that a population contains both uncured and cured individuals. It is a powerful statistical tool for cancer prognostic studies. In order to accurately predict long-term outcome the proportional hazards (PH) cure model requires variable selection methods. However, no specific variable selection method for the PH cure model has been established in practice. In this study, we present a stepwise variable selection method for the PH cure model with a logistic regression for the cure rate and a Cox regression for the hazard for uncured patients. We conducted simulation studies to evaluate the operating characteristics of the stepwise method in comparison to those of the best subset selection method based on Akaike information criterion and of the convenience variable selection method that puts all variables in the PH cure model and selects the significant ones. The results demonstrated that in many cases the stepwise method outperformed other methods with respect to false positive determinations and estimation bias for the survival curve. In addition, we demonstrated the usefulness of the stepwise method for the PH cure model by applying it to analyze clinical data on breast cancer patients.
    09/2013; 34(1):21-34. DOI:10.5691/jjb.34.21
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