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AIC = 310.310, BIC = 370.703. TABLE 6 Summary result for Weibull accelerated failure time model.

Table 6 AIC = 310.310, BIC = 370.703. TABLE 6 Summary result for Weibull accelerated failure time model.

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TABLE 1 Descriptive summary of covariate variables for breast cancer patients. declined in the later months of follow-up. The hazard functions are depicted in Figure 1 (right), showing that an increase in the hazard rate has a direct relationship to the increase in time. residence. The differences that are displayed in the survival curve above show that breast cancer patients who come from urban areas have higher survival times when compared to those who came from rural areas. That means BC patients who come from urban areas have higher survival experiences than those who came from rural areas (Figure 2).
TABLE 1 Descriptive summary of covariate variables for breast cancer patients. declined in the later months of follow-up. The hazard functions are depicted in Figure 1 (right), showing that an increase in the hazard rate has a direct relationship to the increase in time. residence. The differences that are displayed in the survival curve above show that breast cancer patients who come from urban areas have higher survival times when compared to those who came from rural areas. That means BC patients who come from urban areas have higher survival experiences than those who came from rural areas (Figure 2).
The plot of the overall estimate of Kaplan—Meier survivor function (left) and hazard function (right) of BC patients Table 4 showed the mean and median survival times of eacl covariate, and the different groups of residence, stage complication, treatment, pathology, metastasis, blood type family history, and recurrence had a statistically significan difference in survival probabilities. On the other hand, th survival functions of the BMI categories were statistically) insignificant. That means there is no significant difference between obese, overweight, normal, and underweight. The It is vital to do some statistical tests that will be used as an introduction to our subsequent findings. Here we start with the test of equality of probabilities across the different groups of categorical variables using the log-rank test to look at the significance of the difference among different factors. The null
The plot of the overall estimate of Kaplan—Meier survivor function (left) and hazard function (right) of BC patients Table 4 showed the mean and median survival times of eacl covariate, and the different groups of residence, stage complication, treatment, pathology, metastasis, blood type family history, and recurrence had a statistically significan difference in survival probabilities. On the other hand, th survival functions of the BMI categories were statistically) insignificant. That means there is no significant difference between obese, overweight, normal, and underweight. The It is vital to do some statistical tests that will be used as an introduction to our subsequent findings. Here we start with the test of equality of probabilities across the different groups of categorical variables using the log-rank test to look at the significance of the difference among different factors. The null
TABLE 2 Multivariable cox proportional hazards regression model analysis. hypothesis to be tested is that there is no difference between the probabilities of an event occurring at any time point for each population. The results are summarized in Table 4. family have a lower survival experience compared to those who have no BC history in their family.
TABLE 2 Multivariable cox proportional hazards regression model analysis. hypothesis to be tested is that there is no difference between the probabilities of an event occurring at any time point for each population. The results are summarized in Table 4. family have a lower survival experience compared to those who have no BC history in their family.
Survival curves of complication status. analysis is an appropriate procedure that is used to screen out potentially important variables before directly including them in the multivariable model. In the univariable analysis, the relationship between each covariate and the survival time of BC patients was examined. This result showed that age, residence, stage, complication, treatment, pathology, metastasis, blood type, family history, and recurrence are statistically significant at a 25% significance level. But the covariate BMI is not statistically significant at the modest level of significance of 25%. In any data analysis, it is always a great idea to do some univariable analysis before proceeding to more complicated models. Single-covariate Cox proportional hazards model
Survival curves of complication status. analysis is an appropriate procedure that is used to screen out potentially important variables before directly including them in the multivariable model. In the univariable analysis, the relationship between each covariate and the survival time of BC patients was examined. This result showed that age, residence, stage, complication, treatment, pathology, metastasis, blood type, family history, and recurrence are statistically significant at a 25% significance level. But the covariate BMI is not statistically significant at the modest level of significance of 25%. In any data analysis, it is always a great idea to do some univariable analysis before proceeding to more complicated models. Single-covariate Cox proportional hazards model
overall mean and median estimated survival times of breast cancer patients under study were 43.7 and 45 months, respectively.
overall mean and median estimated survival times of breast cancer patients under study were 43.7 and 45 months, respectively.
Survival curves for family history. For our data, the multivariable Cox proportional hazards model was fitted by including all the covariates significant in the univariable analysis at a 25% level of significance. Covariates that became insignificant in the multivariable analysis were then removed one by one from the model starting with the largest p- value by using the purposeful variable selection technique. Accordingly, age, stage, complications, treatment, metastasis, blood type, and recurrence were included. The multivariable analysis of survival time of BC patients using the Cox proportional hazard model is presented in Table 2, and it indicates that the parameter estimates of coefficients for the covariates with the associated standard error, hazard ratio, 95% confidence interval for the hazard ratio, and the p-value. A hazard ratio of less than one indicates that the covariates decrease the risk of death in BC patients, and greater than one indicates that the covariates increase the risk of death in BC patients. Therefore, covariates like age, stage, complication, metastasis, blood type, and recurrence decreased the risk of death in BC patients, whereas covariate treatment increased the risk of death in BC patients.
Survival curves for family history. For our data, the multivariable Cox proportional hazards model was fitted by including all the covariates significant in the univariable analysis at a 25% level of significance. Covariates that became insignificant in the multivariable analysis were then removed one by one from the model starting with the largest p- value by using the purposeful variable selection technique. Accordingly, age, stage, complications, treatment, metastasis, blood type, and recurrence were included. The multivariable analysis of survival time of BC patients using the Cox proportional hazard model is presented in Table 2, and it indicates that the parameter estimates of coefficients for the covariates with the associated standard error, hazard ratio, 95% confidence interval for the hazard ratio, and the p-value. A hazard ratio of less than one indicates that the covariates decrease the risk of death in BC patients, and greater than one indicates that the covariates increase the risk of death in BC patients. Therefore, covariates like age, stage, complication, metastasis, blood type, and recurrence decreased the risk of death in BC patients, whereas covariate treatment increased the risk of death in BC patients.
Multivariable Cox proportional hazards model
Multivariable Cox proportional hazards model
TABLE 3 Summary of continuous variables for breast cancer patients.
TABLE 3 Summary of continuous variables for breast cancer patients.
TABLE 4 Log-rank test and mean survival time among the different groups of covariates. estimated to be 0.0001. The estimated value of the shape parameter in the Weibull gamma shared frailty model is 1.941 (p = 1.941). The Weibull shape parameter greater than one indicates the hazard of failure increases with time. The variability (unobserved heterogeneity) in the residence estimated by the selected model (Weibull-gamma shared frailty model) is 8 = 0.002. A variance of zero (8 = 0) would indicate that the frailty component does not contribute to the model. A likelihood ratio test for the hypothesis 6 = 0 is shown in Table 2 below and indicates a chi-square value of 3.17 with one degree of freedom, resulting in a highly significant p-value of 0.000. This implied that the frailty component had a significant contribution to the model. The associated Kendall’s tau (t), which measures dependence within clusters (residence), is
TABLE 4 Log-rank test and mean survival time among the different groups of covariates. estimated to be 0.0001. The estimated value of the shape parameter in the Weibull gamma shared frailty model is 1.941 (p = 1.941). The Weibull shape parameter greater than one indicates the hazard of failure increases with time. The variability (unobserved heterogeneity) in the residence estimated by the selected model (Weibull-gamma shared frailty model) is 8 = 0.002. A variance of zero (8 = 0) would indicate that the frailty component does not contribute to the model. A likelihood ratio test for the hypothesis 6 = 0 is shown in Table 2 below and indicates a chi-square value of 3.17 with one degree of freedom, resulting in a highly significant p-value of 0.000. This implied that the frailty component had a significant contribution to the model. The associated Kendall’s tau (t), which measures dependence within clusters (residence), is
TABLE 5 Comparison of AFT models using AIC and BIC for a given dataset.
TABLE 5 Comparison of AFT models using AIC and BIC for a given dataset.
TABLE 7 Comparison of Weibull Gamma frailty and Weibull Inverse- Gaussian frailty model.
TABLE 7 Comparison of Weibull Gamma frailty and Weibull Inverse- Gaussian frailty model.
TABLE 8 Comparison of Cox PH, Weibull AFT, and Weibull gamma shared frailty model.
TABLE 8 Comparison of Cox PH, Weibull AFT, and Weibull gamma shared frailty model.
P = 1.941 6 = 0.515 8 = 0.0002, AIC = 309.932 BIC = 377.885. LR test of theta = 0 chibar2 (01) = 1.0 pro =chibar2 = 0.00. 9, variance of the random effect; p, shape parameter; 6, scale parameter; AIC, Akaike information criteria; LR, likelihood ratio; prob, probability; chibar2, Chi-square; chibar2(01), Chi- square distribution with 0 and 1 degrees of freedom. TABLE 9 Results of Weibull gamma shared frailty model.
P = 1.941 6 = 0.515 8 = 0.0002, AIC = 309.932 BIC = 377.885. LR test of theta = 0 chibar2 (01) = 1.0 pro =chibar2 = 0.00. 9, variance of the random effect; p, shape parameter; 6, scale parameter; AIC, Akaike information criteria; LR, likelihood ratio; prob, probability; chibar2, Chi-square; chibar2(01), Chi- square distribution with 0 and 1 degrees of freedom. TABLE 9 Results of Weibull gamma shared frailty model.
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OncologyMedicineProportional hazards model
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