• Journal of the Korean Data and Information Science Society
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• v.7 no.2
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• pp.179-188
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• 1996

Accelerated life testing(ALT) of products quickly yields information on life. In this paper, we investigate asymptotic normalities of maximum likelihood(ML) estimators of parameters for ALT model under Type II censored data using results of Bhattacharyya(1985). Further illustrations include the treatment of asymptotic of the exponential and Weibull regression models.

• Asian Pacific Journal of Cancer Prevention
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• v.13 no.5
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• pp.1829-1831
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• 2012

Background: The generalized gamma distribution statistics constitute an extensive family that contains nearly all of the most commonly used distributions including the exponential, Weibull and log normal. A saturated version of the model allows covariates having effects through all the parameters of survival time distribution. Accelerated failure-time models assume that only one parameter of the distribution depends on the covariates. Methods: We fitted both the conventional GG model and the saturated form for each of its members including the Weibull and lognormal distribution; and compared them using likelihood ratios. To compare the selected parameter distribution with log logistic distribution which is a famous distribution in survival analysis that is not included in generalized gamma family, we used the Akaike information criterion (AIC; r=l(b)-2p). All models were fitted using data for 369 women age 50 years or more, diagnosed with stage IV breast cancer in BC during 1990-1999 and followed to 2010. Results: In both conventional and saturated parametric models, the lognormal was the best candidate among the GG family members; also, the lognormal fitted better than log-logistic distribution. By the conventional GG model, the variables "surgery", "radiotherapy", "hormone therapy", "erposneg" and interaction between "hormone therapy" and "erposneg" are significant. In the AFT model, we estimated the relative time for these variables. By the saturated GG model, similar significant variables are selected. Estimating the relative times in different percentiles of extended model illustrate the pattern in which the relative survival time change during the time. Conclusions: The advantage of using the generalized gamma distribution is that it facilitates estimating a model with improved fit over the standard Weibull or lognormal distributions. Alternatively, the generalized F family of distributions might be considered, of which the generalized gamma distribution is a member and also includes the commonly used log-logistic distribution.

• Asian Pacific Journal of Cancer Prevention
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• v.15 no.19
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• pp.8371-8376
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• 2014

Background: The use of statistical methods has become an imperative tool in breast cancer survival data analysis. The purpose of this study was to develop the best statistical probability model using the Bayesian method to predict future survival times for the black non-Hispanic female breast cancer patients diagnosed during 1973-2009 in the U.S. Materials and Methods: We used a stratified random sample of black non-Hispanic female breast cancer patient data from the Surveillance Epidemiology and End Results (SEER) database. Survival analysis was performed using Kaplan-Meier and Cox proportional regression methods. Four advanced types of statistical models, Exponentiated Exponential (EE), Beta Generalized Exponential (BGE), Exponentiated Weibull (EW), and Beta Inverse Weibull (BIW) were utilized for data analysis. The statistical model building criteria, Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC), and Deviance Information Criteria (DIC) were used to measure the goodness of fit tests. Furthermore, we used the Bayesian approach to obtain the predictive survival inferences from the best-fit data based on the exponentiated Weibull model. Results: We identified the highest number of black non-Hispanic female breast cancer patients in Michigan and the lowest in Hawaii. The mean (SD), of age at diagnosis (years) was 58.3 (14.43). The mean (SD), of survival time (months) for black non-Hispanic females was 66.8 (30.20). Non-Hispanic blacks had a significantly increased risk of death compared to Black Hispanics (Hazard ratio: 1.96, 95%CI: 1.51-2.54). Compared to other statistical probability models, we found that the exponentiated Weibull model better fits for the survival times. By making use of the Bayesian method predictive inferences for future survival times were obtained. Conclusions: These findings will be of great significance in determining appropriate treatment plans and health-care cost allocation. Furthermore, the same approach should contribute to build future predictive models for any health related diseases.

• Journal of Preventive Medicine and Public Health
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• v.52 no.2
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• pp.140-144
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• 2019

Objectives: Investigating the survival of patients with cancer is vitally necessary for controlling the disease and for assessing treatment methods. This study aimed to compare various statistical models of survival and to determine the survival rate and its related factors among patients suffering from lung cancer. Methods: In this retrospective cohort, the cumulative survival rate, median survival time, and factors associated with the survival of lung cancer patients were estimated using Cox, Weibull, exponential, and Gompertz regression models. Kaplan-Meier tables and the log-rank test were also used to analyze the survival of patients in different subgroups. Results: Of 102 patients with lung cancer, 74.5% were male. During the follow-up period, 80.4% died. The incidence rate of death among patients was estimated as 3.9 (95% confidence [CI], 3.1 to 4.8) per 100 person-months. The 5-year survival rate for all patients, males, females, patients with non-small cell lung carcinoma (NSCLC), and patients with small cell lung carcinoma (SCLC) was 17%, 13%, 29%, 21%, and 0%, respectively. The median survival time for all patients, males, females, those with NSCLC, and those with SCLC was 12.7 months, 12.0 months, 16.0 months, 16.0 months, and 6.0 months, respectively. Multivariate analyses indicated that the hazard ratios (95% CIs) for male sex, age, and SCLC were 0.56 (0.33 to 0.93), 1.03 (1.01 to 1.05), and 2.91 (1.71 to 4.95), respectively. Conclusions: Our results showed that the exponential model was the most precise. This model identified age, sex, and type of cancer as factors that predicted survival in patients with lung cancer.