Table
1 gives AIC, AICc, and BIC values at varying sample sizes for each of the five models. When the table is examined, in every case, the best model according to AIC and ACIc is the frailty model. According to BIC, the best model is the marginal Cox model. For all cases, the AIC, AICc and BIC values obtained from the frailty and marginal Cox models were very close to each other. This situation does not change depending on the sample size. However, the worst performing models vary depending on the sample size. The worst performing models in small sample sizes are the marginal Weibull, classic Cox, and stratified Cox models based on all three information criteria, respectively. For example, for the case of k = 4, n = 200, the worst models are the classical Cox, marginal Weibull and strafied Cox models. When the sample size increased further, the ranking became classic Cox, stratified, and marginal Weibull models. In the study, while the best model does not change for all three information criteria, the order of the models with the worst performance changes. The classic Cox model has the worst performance among the models, especially when the sample size increases. According to Table
1, while the worst model in small sample size is marginal Weibull, with the increase in sample size the worst model is obtained as the classical Cox model.
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Table 1: AIC, AICc and BIC values obtained for the methods when the cluster size is 4 and the number of individuals is 50, 100, 200, 500 and 1000 |
As a result of the findings, the marginal Cox model with the lowest BIC = 524.18 value was obtained as the best model in the case of k=4, n=50. This condition does not change with the increase in the sample size. For the case of k=4, n=1000, the best model was obtained as the marginal Cox model with the lowest BIC=17641,84 value. Results are similar for AIC and AICc. Regardless of the sample size, the best models according to these criteria are the frailty models. For k=4, n=50 condition, AIC=501.29 and AICc=473.20 were obtained and according to these results, the best model was the frailty model. The results are similar for the case k=4, n=1000 (AIC=16891.75, AICc=16133.08). Considering AIC, AICc and BIC the worst models vary depending on the increase in sample size. For k=4, n=100, the worst model was the marginal Weibull model for all three criteria (BIC=3012.84, AIC=2996.88, AICc=2996.98).
The second worst model is the Cox model (BIC=2834.34, AIC=2827.21, AICc=2827.24). In small samples, the worst model is the marginal Weibull model with the highest value among all three information criteria (k=4, n=50; BIC=1550.72, AIC=1537.53, AICc=1537.73). As the sample size increases, the Cox model tends to get the highest values (k=4, n=200; BIC=6323.94, AIC=6315.46, AICc=6315.48). Considering the results obtained, in parallel with the increase in the sample size, the marginal Weibull with the worst performance was obtained as the third best model in the k=4, n=500 scenario. In addition, while the stratified Cox model was the third best model, it was obtained as the second worst model due to the increase in the number of units (BIC=16407.03, AIC=16396.71, AICc=16396.71).
In Table 2, cases where the cluster size is not equal, 75% of the data has a cluster size of 4 and 25% of the data has a cluster size of 2 are represented. The number of individuals varies as 50, 100, 200, 500 and 1000. The aim here is to compare performances between models when cluster sizes are unbalanced. The findings obtained in this context are given in Table 2. For the unbalanced cluster size n=50, 100 and 200 individuals, the best model for AIC and AICc was obtained as the frailty model. The best model obtained for BIC is the marginal Cox model. For all three information criteria, the values obtained from frailty and marginal Cox were close to each other. In addition, according to all three information criteria, stratified Cox model was ranked third, the Cox model was ranked fourth and the marginal Weibull model was ranked fifth. The best models did not change according to the information criteria at n=500 and 1000 individuals. However, as the sample size increased, the worst third model became the marginal Weibull model, the fourth model became the stratified model and the fifth worst model became the Cox model.
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Table 2: AIC, AICc and BIC values obtained for the methods when 75% of the data has a cluster size of 4, 25% of the data has a cluster size of 2 and the number of individuals are 50, 100, 200, 500 and 1000. |
Table 3 aims to examine whether there is a difference between model performances at varying cencor rates when k = 4 and n = 500. In simulation studies conducted for this purpose, cencor rates vary between 10% and 70%. When the results for each scenario in the study were examined, the best model was obtained as marginal Cox at each censor rate for the BIC value. The model with the best performance for AIC and AICc values was the frailty model. For each information criteria, the values obtained from the frailty model and marginal Cox model were close to each other. Additionally, marginal Weibull became the third, and stratified Cox became the fourth model. The worst performing model for the entire conditions was the Cox model, which ignores the cluster structure.
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Table 3: AIC, AICc and BIC values obtained from the models when k=4, n=500 and censor rates are 10%-70% |
According to Table 1, the best models obtained are the frailty model according to AIC and AICc. According to BIC, the best model was obtained as marginal Cox. The ranking of the worst models obtained changes with the increase in sample size. In Table 2, the best models obtained with unbalanced cluster size are found to be similar to Table 1. Again, as in Table 1, the worst models obtained change depending on the sample size. In Table 3, the best models obtained with changing cencor rates are again similar to Tables 1 and 2. In Table 3, the worst models obtained are the marginal Weibull third and the stratified Cox fourth models. The worst performing model for all cases is the Cox model, which ignores the clustering structure.