• Asian Pacific Journal of Cancer Prevention
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• v.16 no.16
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• pp.7359-7363
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• 2015

Background: As a result of significant progress made in treatment of many types of cancers during the last few decades, there have been an increased number of patients who do not experience mortality. We refer to these observations as cure or immune and models for survival data which include cure fraction are known as cure rate models or long-term survival models. Materials and Methods: In this study we used the data collected from 438 female patients with breast cancer registered in the Cancer Research Center in Shahid Beheshti University of Medical Sciences, Tehran, Iran. The patients had been diagnosed from 1992 to 2012 and were followed up until October 2014. We had to exclude some because of incomplete information. Phone calls were made to confirm whether the patients were still alive or not. Deaths due to breast cancer were regarded as failure. To identify clinical, pathological, and biological characteristics of patients that might have had an effect on survival of the patients we used a non-mixture cure rate model; in addition, a Weibull distribution was proposed for the survival time. Analyses were performed using STATA version 14. The significance level was set at $P{\leq}0.05$. Results: A total of 75 patients (17.1%) died due to breast cancer during the study, up to the last follow-up. Numbers of metastatic lymph nodes and histologic grade were significant factors. The cure fraction was estimated to be 58%. Conclusions: When a cure fraction is not available, the analysis will be changed to standard approaches of survival analysis; however when the data indicate that the cure fraction is available, we suggest analysis of survival data via cure models.

• Asian Pacific Journal of Cancer Prevention
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• v.16 no.17
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• pp.7923-7927
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• 2015

Background: The Cox PH model is one of the most significant statistical models in studying survival of patients. But, in the case of patients with long-term survival, it may not be the most appropriate. In such cases, a cure rate model seems more suitable. The purpose of this study was to determine clinical factors associated with cure rate of patients with breast cancer. Materials and Methods: In order to find factors affecting cure rate (response), a non-mixed cure rate model with negative binomial distribution for latent variable was used. Variables selected were recurrence cancer, status for HER2, estrogen receptor (ER) and progesterone receptor (PR), size of tumor, grade of cancer, stage of cancer, type of surgery, age at the diagnosis time and number of removed positive lymph nodes. All analyses were performed using PROC MCMC processes in the SAS 9.2 program. Results: The mean (SD) age of patients was equal to 48.9 (11.1) months. For these patients, 1, 5 and 10-year survival rates were 95, 79 and 50 percent respectively. All of the mentioned variables were effective in cure fraction. Kaplan-Meier curve showed cure model's use competence. Conclusions: Unlike other variables, existence of ER and PR positivity will increase probability of cure in patients. In the present study, Weibull distribution was used for the purpose of analysing survival times. Model fitness with other distributions such as log-N and log-logistic and other distributions for latent variable is recommended.

• The Korean Journal of Applied Statistics
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• v.27 no.1
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• pp.21-30
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• 2014

Ordinary survival analysis cannot be applied when a significant fraction of patients may be cured. A cure rate model is the combination of cure fraction and survival model and can be applied to several types of cancer. In this article, the cure rate model is considered in the interval censored data with a cluster effect. A shared frailty model is introduced to characterize the cluster effect and an EM algorithm is used to estimate parameters. A simulation study is done to evaluate the performance of estimates. The proposed approach is applied to the smoking cessation study in which the event of interest is a smoking relapse. Several covariates (including intensive care) are evaluated to be effective for both the occurrence of relapse and the smoke quitting duration.

• Communications for Statistical Applications and Methods
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• v.24 no.4
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• pp.397-419
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• 2017

A four-parameter extended fatigue lifetime model called the odd Birnbaum-Saunders geometric distribution is proposed. This model extends the odd Birnbaum-Saunders and Birnbaum-Saunders distributions. We derive some properties of the new distribution that include expressions for the ordinary moments and generating and quantile functions. The method of maximum likelihood and a Bayesian approach are adopted to estimate the model parameters; in addition, various simulations are performed for different parameter settings and sample sizes. We propose two new models with a cure rate called the odd Birnbaum-Saunders mixture and odd Birnbaum-Saunders geometric models by assuming that the number of competing causes for the event of interest has a geometric distribution. The applicability of the new models are illustrated by means of ethylene data and melanoma data with cure fraction.

• Annals of Hepato-Biliary-Pancreatic Surgery
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• v.26 no.1
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• pp.47-57
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• 2022

Backgrounds/Aims: It is challenging to assess the efficacy of partial hepatectomy (PH) as a treatment option for patients with hepatocellular carcinoma (HCC) accompanied by cirrhosis. This study aimed to determine the cure fraction of PH for HCC accompanied by cirrhosis compared to that for HCC without cirrhosis. Methods: A systematic review was performed on outcomes of previous studies that compared recurrence-free survival (RFS) after PH in patients with HCC with or without cirrhosis. A meta-analysis was conducted to obtain the cumulative hazard ratio for two patient groups: cirrhosis and non-cirrhosis. Cure fractions after PH in both groups were determined using a cure model analysis. Results: A total of 18 studies were eligible for meta-analysis and 13 studies were selected for the cure model analysis. The cumulative hazard ratio for RFS of the cirrhosis group compared to that of the non-cirrhosis group was 1.66 (95% confidence interval [CI], 1.43-1.93). Survival data of 3,512 patients in both groups were reconstructed from survival curves of original articles for cure model analysis. The probability of being statistically cured after PH for HCC was 14.1% (95% CI, 10.6%-18.1%) in the cirrhosis group lower than that (32.5%) in the non-cirrhosis group (95% CI, 28.6%-36.4%). Conclusions: The prognosis after PH for HCC accompanied by cirrhosis is inferior to that for HCC without cirrhosis. However, a cure can be expected for one-seventh of patients with HCC accompanied by cirrhosis after PH.

• The Korean Journal of Applied Statistics
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• v.17 no.2
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• pp.253-267
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• 2004

In some clinical trials, one may see that a significant fraction of patients are cured and their original disease does not recur even after termination of treatment and pro-longed follow-up. This situation occurs frequently in pediatric cancer trials where there are excellent therapeutic results. In such cases, interest concentrated on the difference of cure rates rather than other types of differences in failure distributions. Various authors have investigated the parametric and nonparametric methods for testing the difference of cure rates. In this study, we compare by simulation the power and size of a parametric test and five nonparametric tests in a various range of the alternatives, censoring rates and cure rates. Our objectives are to determine if any test was preferable on the basis of size and power in various situation, and to investigate the effect of the model misspecification.

• Communications for Statistical Applications and Methods
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• v.25 no.5
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• pp.471-488
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• 2018

In this paper, we propose extending proportional hazards frailty models to allow a discrete distribution for the frailty variable. Having zero frailty can be interpreted as being immune or cured. Thus, we develop a new survival model induced by discrete frailty with zero-inflated power series distribution, which can account for overdispersion. This proposal also allows for a realistic description of non-risk individuals, since individuals cured due to intrinsic factors (immunes) are modeled by a deterministic fraction of zero-risk while those cured due to an intervention are modeled by a random fraction. We put the proposed model in a Bayesian framework and use a Markov chain Monte Carlo algorithm for the computation of posterior distribution. A simulation study is conducted to assess the proposed model and the computation algorithm. We also discuss model selection based on pseudo-Bayes factors as well as developing case influence diagnostics for the joint posterior distribution through ${\psi}-divergence$ measures. The motivating cutaneous melanoma data is analyzed for illustration purposes.

• Communications for Statistical Applications and Methods
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• v.24 no.6
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• pp.605-625
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• 2017

This paper presents proportional odds cure models to allow spatial correlations by including spatial frailty in the interval censored data setting. Parametric cure rate models with independent and dependent spatial frailties are proposed and compared. Our approach enables different underlying activation mechanisms that lead to the event of interest; in addition, the number of competing causes which may be responsible for the occurrence of the event of interest follows a Geometric distribution. Markov chain Monte Carlo method is used in a Bayesian framework for inferential purposes. For model comparison some Bayesian criteria were used. An influence diagnostic analysis was conducted to detect possible influential or extreme observations that may cause distortions on the results of the analysis. Finally, the proposed models are applied for the analysis of a real data set on smoking cessation. The results of the application show that the parametric cure model with frailties under the first activation scheme has better findings.

• Asian Pacific Journal of Cancer Prevention
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• v.15 no.22
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• pp.9673-9678
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• 2014

Background: 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. Materials and Methods: 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. Results: 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. Conclusions: 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.

• Communications for Statistical Applications and Methods
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• v.25 no.3
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• pp.245-261
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• 2018

Attempts have been made to define new classes of distributions that provide more flexibility for modelling skewed data in practice. In this work we define a new extension of the generalized gamma distribution (Stacy, The Annals of Mathematical Statistics, 33, 1187-1192, 1962) for Marshall-Olkin generalized gamma (MOGG) distribution, based on the generator pioneered by Marshall and Olkin (Biometrika, 84, 641-652, 1997). This new lifetime model is very flexible including twenty one special models. The main advantage of the new family relies on the fact that practitioners will have a quite flexible distribution to fit real data from several fields, such as engineering, hydrology and survival analysis. Further, we also define a MOGG mixture model, a modification of the MOGG distribution for analyzing lifetime data in presence of cure fraction. This proposed model can be seen as a model of competing causes, where the parameter associated with the Marshall-Olkin distribution controls the activation mechanism of the latent risks (Cooner et al., Statistical Methods in Medical Research, 15, 307-324, 2006). The asymptotic properties of the maximum likelihood estimation approach of the parameters of the model are evaluated by means of simulation studies. The proposed distribution is fitted to two real data sets, one arising from measuring the strength of fibers and the other on melanoma data.