JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (4): 108-116.doi: 10.6040/j.issn.1671-9352.0.2022.465

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Model averaging study with a cured group right-censored data

Shuying WANG(),Yanan ZHANG,Yunfei CHENG,Lifang ZHOU*()   

  1. School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, Jilin, China
  • Received:2022-09-07 Online:2024-04-20 Published:2024-04-12
  • Contact: Lifang ZHOU E-mail:wangshuying0601@163.com;2283568775@qq.com

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Abstract:

In the existing survival analysis studies, most of them directly assume the model form of response variables and specified covariates, and then estimate the covariate effect. However, when the assumption of the model is wrong, the corresponding conclusion may be wrong. Under the right-censored data with a cured group, in order to avoid the inaccuracy caused by the construction of the model with specified covariates, an accelerated failure time model (AFT model) based on the model averaging method is proposed. In the framework of maximum likelihood estimation, model selection and model averaging based on information criteria are used for statistical inference. The numerical simulation results show that under the right-censored data with a cured group, the estimation and prediction accuracy of the AFT model based on the model averaging method is higher than that of model selection method. Finally, the feasibility and practicability of the proposed method are verified by analysis of trial data on melanoma clinical.

Key words: right-censored data, model averaging, mixture cure model, accelerated failure time model, maximum likelihood estimation

CLC Number: 

  • O212

Table 1

True value setting of three groups of parameters"

参数 n=200 n=400
η0 η0 β1 γ1 γ2 γ2 μ σ η0 η0 β1 γ1 γ2 γ2 μ σ
设置A 0.6 0.3 0.3 -0.5 0.3 -0.3 0.5 0.4 0.6 0.3 0.3 -0.5 0.3 -0.3 0.5 0.4
设置B 0.6 0.3 0.3 -0.5 -0.3 0.3 0.5 0.4 0.6 0.3 0.3 -0.5 -0.3 0.3 0.5 0.4
设置C 0.6 0.3 -0.3 -0.5 0.3 0.3 0.5 0.4 0.6 0.3 -0.3 -0.5 0.3 0.3 0.5 0.4

Table 2

EMS and EMSP of five indicators of interest under two sample sizes for set A"

评价指标 样本量 感兴趣指标 S-AIC AIC S-BIC BIC
EMS n=200 (a) 0.222 5 0.418 2 0.223 2 0.453 6
(b) 0.460 4 0.842 7 0.462 0 0.913 5
(c) 0.168 1 0.314 9 0.168 3 0.341 7
n=400 (a) 0.222 5 0.418 2 0.223 2 0.453 6
(b) 0.460 4 0.842 7 0.462 0 0.913 5
(c) 0.168 1 0.314 9 0.168 3 0.3417
EMSP n=200 (d) 0.000 4 0.000 4 0.000 4 0.000 4
(e) 0.000 2 0.000 2 0.000 2 0.000 2
n=400 (d) 0.000 2 0.000 2 0.000 2 0.000 2
(e) 0.000 1 0.000 1 0.000 1 0.000 1

Table 3

EMS and EMSP of five indicators of interest under two sample sizes for set B"

评价指标 样本量 感兴趣指标 S-AIC AIC S-BIC BIC
EMS n=200 (a) 0.229 4 0.434 8 0.229 8 0.466 1
(b) 0.474 9 0.876 3 0.475 8 0.938 9
(c) 0.173 3 0.327 2 0.173 3 0.350 8
n=400 (a) 0.110 8 0.326 9 0.111 0 0.361 2
(b) 0.229 3 0.657 1 0.229 6 0.725 7
(c) 0.083 7 0.245 8 0.083 7 0.271 7
EMSP n=200 (d) 0.000 4 0.000 5 0.000 4 0.000 5
(e) 0.000 2 0.000 2 0.000 2 0.000 2
n=400 (d) 0.000 2 0.000 2 0.000 2 0.000 2
(e) 0.000 1 0.000 1 0.000 1 0.000 1

Table 4

EMS and EMSP of five indicators of interest under two sample sizes for set C"

评价指标 样本量 感兴趣指标 S-AIC AIC S-BIC BIC
EMS n=200 (a) 0.225 1 0.413 4 0.226 0 0.456 0
(b) 0.466 3 0.833 2 0.468 2 0.918 4
(c) 0.170 2 0.311 3 0.170 5 0.343 5
n=400 (a) 0.114 7 0.354 1 0.115 0 0.388 2
(b) 0.237 1 0.711 2 0.237 7 0.779 7
(c) 0.086 7 0.266 1 0.086 7 0.2918
EMSP n=200 (d) 0.000 3 0.000 5 0.000 3 0.000 5
(e) 0.000 2 0.000 2 0.000 2 0.000 2
n=400 (d) 0.000 2 0.000 2 0.000 2 0.000 2
(e) 0.000 1 0.000 1 0.000 1 0.000 1

Fig.1

Kaplan-Meier curve of test group and control group"

Table 5

Estimation results of parameters of interest in melanoma clinical trial data"

参数 估计 S-AIC S-BIC AIC/BIC
μ1 估计值(标准差) 0.740 3(0.392 7) 0.740 2(0.392 7) -0.448 5(0.254 2)
95%置信区间 (-0.029 5, 1.510 0) (-0.029 5, 1.510 0) (-0.946 8, 0.049 8)
μ2 估计值(标准差) 0.562 8(0.263 0) 0.562 9(0.263 0) 0.309 1(0.185 6)
95%置信区间 (0.047 3, 1.078 3) (0.047 4, 1.078 3) (-0.054 7, 0.672 9)
μ3 估计值(标准差) 0.002 3(0.008 1) 0.002 3(0.008 1) —
95%置信区间 (-0.013 6, 0.018 2) (-0.013 6, 0.018 2) —
μ4 估计值(标准差) -2.6250e-05(2.5502e-05) -4.5440e-06(5.6240e-06) -0.038 6(0.188 0)
95%置信区间 (-7.6333e-05, 2.3734e-05) (-1.5567e-05, 6.4800e-06) (-0.407 1, 0.330 0)
μ5 估计值(标准差) 1.305 4(0.663 9) 1.305 4(0.663 9) -0.178 0(0.627 9)
95%置信区间 (0.004 2, 2.606 6) (0.004 2, 2.606 6) (-1.408 7, 1.052 7)

Table 6

Predictive value of survival probability of patients with melanoma"

样本数 指标 S-AIC S-BIC AIC BIC
160 均值 0.561 0 0.560 8 0.558 0 0.557 6
中位数 0.511 7 0.508 6 0.501 9 0.500 7
180 均值 0.562 3 0.562 1 0.559 4 0.558 9
中位数 0.514 8 0.511 5 0.502 9 0.501 8
200 均值 0.563 1 0.562 8 0.559 9 0.559 7
中位数 0.515 2 0.512 7 0.503 7 0.502 9
220 均值 0.563 5 0.562 9 0.559 9 0.559 9
中位数 0.516 0 0.512 9 0.503 8 0.503 0
240 均值 0.564 0 0.564 0 0.560 4 0.560 3
中位数 0.516 0 0.513 3 0.504 1 0.503 2
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