Modeling HIV/AIDS progression is critical for understanding disease dynamics and improving patient care. This study compares the Exponential and Weibull survival models, focusing on their ability to capture state-spec...Modeling HIV/AIDS progression is critical for understanding disease dynamics and improving patient care. This study compares the Exponential and Weibull survival models, focusing on their ability to capture state-specific failure rates in HIV/AIDS progression. While the Exponential model offers simplicity with a constant hazard rate, it often fails to accommodate the complexities of dynamic disease progression. In contrast, the Weibull model provides flexibility by allowing hazard rates to vary over time. Both models are evaluated within the frameworks of the Cox Proportional Hazards (Cox PH) and Accelerated Failure Time (AFT) models, incorporating critical covariates such as age, gender, CD4 count, and ART status. Statistical evaluation metrics, including Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), log-likelihood, and Pseudo-R2, were employed to assess model performance across diverse patient subgroups. Results indicate that the Weibull model consistently outperforms the Exponential model in dynamic scenarios, such as younger patients and those with co-infections, while maintaining robustness in stable contexts. This study highlights the trade-off between flexibility and simplicity in survival modeling, advocating for tailored model selection to balance interpretability and predictive accuracy. These findings provide valuable insights for optimizing HIV/AIDS management strategies and advancing survival analysis methodologies.展开更多
This study investigates the application of the two-parameter Weibull distribution in modeling state holding times within HIV/AIDS progression dynamics. By comparing the performance of the Weibull-based Accelerated Fai...This study investigates the application of the two-parameter Weibull distribution in modeling state holding times within HIV/AIDS progression dynamics. By comparing the performance of the Weibull-based Accelerated Failure Time (AFT) model, Cox Proportional Hazards model, and Survival model, we assess the effectiveness of these models in capturing survival rates across varying gender, age groups, and treatment categories. Simulated data was used to fit the models, with model identification criteria (AIC, BIC, and R2) applied for evaluation. Results indicate that the AFT model is particularly sensitive to interaction terms, showing significant effects for older age groups (50 - 60 years) and treatment interaction, while the Cox model provides a more stable fit across all age groups. The Survival model displayed variability, with its performance diminishing when interaction terms were introduced, particularly in older age groups. Overall, while the AFT model captures the complexities of interactions in the data, the Cox model’s stability suggests it may be better suited for general analyses without strong interaction effects. The findings highlight the importance of model selection in survival analysis, especially in complex disease progression scenarios like HIV/AIDS.展开更多
Markov modeling of HIV/AIDS progression was done under the assumption that the state holding time (waiting time) had a constant hazard. This paper discusses the properties of the hazard function of the Exponential dis...Markov modeling of HIV/AIDS progression was done under the assumption that the state holding time (waiting time) had a constant hazard. This paper discusses the properties of the hazard function of the Exponential distributions and its modifications namely;Parameter proportion hazard (PH) and Accelerated failure time models (AFT) and their effectiveness in modeling the state holding time in Markov modeling of HIV/AIDS progression with and without risk factors. Patients were categorized by gender and age with female gender being the baseline. Data simulated using R software was fitted to each model, and the model parameters were estimated. The estimated P and Z values were then used to test the null hypothesis that the state waiting time data followed an Exponential distribution. Model identification criteria;Akaike information criteria (AIC), Bayesian information criteria (BIC), log-likelihood (LL), and R2 were used to evaluate the performance of the models. For the Survival Regression model, P and Z values supported the non-rejection of the null hypothesis for mixed gender without interaction and supported the rejection of the same for mixed gender with interaction term and males aged 50 - 60 years. Both Parameters supported the non-rejection of the null hypothesis in the rest of the age groups. For Gender male with interaction both P and Z values supported rejection in all the age groups except the age group 20 - 30 years. For Cox Proportional hazard and AFT models, both P and Z values supported the non-rejection of the null hypothesis across all age groups. The P-values for the three models supported different decisions for and against the Null hypothesis with AFT and Cox values supporting similar decisions in most of the age groups. Among the models considered, the regression assumption provided a superior fit based on (AIC), (BIC), (LL), and R2 Model identification criteria. This was particularly evident in age and gender subgroups where the data exhibited non-proportional hazards and violated the assumptions required for the Cox Proportional Hazard model. Moreover, the simplicity of the regression model, along with its ability to capture essential state transitions without over fitting, made it a more appropriate choice.展开更多
在生存分析研究中,多数文章假定感兴趣的失效时间和删失时间是独立的,但这一假设在实际情况中未必合理。如果忽略失效时间与删失时间的相依性,可能会导致错误的结论。所以本文考虑在带有信息的K型区间删失数据下,采用基于两步估计的极...在生存分析研究中,多数文章假定感兴趣的失效时间和删失时间是独立的,但这一假设在实际情况中未必合理。如果忽略失效时间与删失时间的相依性,可能会导致错误的结论。所以本文考虑在带有信息的K型区间删失数据下,采用基于两步估计的极大似然估计方法对误差项服从标准正态分布的加速失效时间模型(accelerated failure time model,AFT)进行参数估计。同时还进行了数值模拟以验证提出方法的有效性。最后,应用所提出的方法分析艾滋病的临床试验数据。展开更多
本文研究用有限元法计算桥梁涡激振动的时程响应。应用条带假设和半经验半解析的Scanlan第二涡激作用力模型实现涡激作用力在时间和空间上的离散化;针对Scanlan模型中Van der Pol性质的时间频率混合项,引入时频混合格式的AFT方法来计算...本文研究用有限元法计算桥梁涡激振动的时程响应。应用条带假设和半经验半解析的Scanlan第二涡激作用力模型实现涡激作用力在时间和空间上的离散化;针对Scanlan模型中Van der Pol性质的时间频率混合项,引入时频混合格式的AFT方法来计算涡振时程响应,并通过算例验证了该方法的可行性。与传统的连续模型和随机振动理论计算桥梁涡激响应方法相比,时程计算可以考虑多振型的组合作用,结构非线性等多种影响,具有更大的灵活性。展开更多
目的:探讨Cox比例风险模型与加速失效时间模型(accelerated failure time model,AFT)在基因表达数据生存分析中的应用及比较。方法:针对基因表达数据高维小样本的特性,首先采用偏最小二乘法对基因数据集进行降维,然后以降维后的成分为...目的:探讨Cox比例风险模型与加速失效时间模型(accelerated failure time model,AFT)在基因表达数据生存分析中的应用及比较。方法:针对基因表达数据高维小样本的特性,首先采用偏最小二乘法对基因数据集进行降维,然后以降维后的成分为协变量对两类生存模型进行拟合并比较其性能。结果:两类模型中病人生存时间的对数秩检验表明,不同风险组生存时间的差异均有统计学意义(P<0.01),而AFT模型比Cox模型具有更大的检验统计量的值。结论:Cox模型和AFT模型都适用于基因表达数据的生存分析,在某些实际应用中AFT模型的拟合效果可能更优于Cox模型。展开更多
文摘Modeling HIV/AIDS progression is critical for understanding disease dynamics and improving patient care. This study compares the Exponential and Weibull survival models, focusing on their ability to capture state-specific failure rates in HIV/AIDS progression. While the Exponential model offers simplicity with a constant hazard rate, it often fails to accommodate the complexities of dynamic disease progression. In contrast, the Weibull model provides flexibility by allowing hazard rates to vary over time. Both models are evaluated within the frameworks of the Cox Proportional Hazards (Cox PH) and Accelerated Failure Time (AFT) models, incorporating critical covariates such as age, gender, CD4 count, and ART status. Statistical evaluation metrics, including Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), log-likelihood, and Pseudo-R2, were employed to assess model performance across diverse patient subgroups. Results indicate that the Weibull model consistently outperforms the Exponential model in dynamic scenarios, such as younger patients and those with co-infections, while maintaining robustness in stable contexts. This study highlights the trade-off between flexibility and simplicity in survival modeling, advocating for tailored model selection to balance interpretability and predictive accuracy. These findings provide valuable insights for optimizing HIV/AIDS management strategies and advancing survival analysis methodologies.
文摘This study investigates the application of the two-parameter Weibull distribution in modeling state holding times within HIV/AIDS progression dynamics. By comparing the performance of the Weibull-based Accelerated Failure Time (AFT) model, Cox Proportional Hazards model, and Survival model, we assess the effectiveness of these models in capturing survival rates across varying gender, age groups, and treatment categories. Simulated data was used to fit the models, with model identification criteria (AIC, BIC, and R2) applied for evaluation. Results indicate that the AFT model is particularly sensitive to interaction terms, showing significant effects for older age groups (50 - 60 years) and treatment interaction, while the Cox model provides a more stable fit across all age groups. The Survival model displayed variability, with its performance diminishing when interaction terms were introduced, particularly in older age groups. Overall, while the AFT model captures the complexities of interactions in the data, the Cox model’s stability suggests it may be better suited for general analyses without strong interaction effects. The findings highlight the importance of model selection in survival analysis, especially in complex disease progression scenarios like HIV/AIDS.
文摘Markov modeling of HIV/AIDS progression was done under the assumption that the state holding time (waiting time) had a constant hazard. This paper discusses the properties of the hazard function of the Exponential distributions and its modifications namely;Parameter proportion hazard (PH) and Accelerated failure time models (AFT) and their effectiveness in modeling the state holding time in Markov modeling of HIV/AIDS progression with and without risk factors. Patients were categorized by gender and age with female gender being the baseline. Data simulated using R software was fitted to each model, and the model parameters were estimated. The estimated P and Z values were then used to test the null hypothesis that the state waiting time data followed an Exponential distribution. Model identification criteria;Akaike information criteria (AIC), Bayesian information criteria (BIC), log-likelihood (LL), and R2 were used to evaluate the performance of the models. For the Survival Regression model, P and Z values supported the non-rejection of the null hypothesis for mixed gender without interaction and supported the rejection of the same for mixed gender with interaction term and males aged 50 - 60 years. Both Parameters supported the non-rejection of the null hypothesis in the rest of the age groups. For Gender male with interaction both P and Z values supported rejection in all the age groups except the age group 20 - 30 years. For Cox Proportional hazard and AFT models, both P and Z values supported the non-rejection of the null hypothesis across all age groups. The P-values for the three models supported different decisions for and against the Null hypothesis with AFT and Cox values supporting similar decisions in most of the age groups. Among the models considered, the regression assumption provided a superior fit based on (AIC), (BIC), (LL), and R2 Model identification criteria. This was particularly evident in age and gender subgroups where the data exhibited non-proportional hazards and violated the assumptions required for the Cox Proportional Hazard model. Moreover, the simplicity of the regression model, along with its ability to capture essential state transitions without over fitting, made it a more appropriate choice.
文摘在生存分析研究中,多数文章假定感兴趣的失效时间和删失时间是独立的,但这一假设在实际情况中未必合理。如果忽略失效时间与删失时间的相依性,可能会导致错误的结论。所以本文考虑在带有信息的K型区间删失数据下,采用基于两步估计的极大似然估计方法对误差项服从标准正态分布的加速失效时间模型(accelerated failure time model,AFT)进行参数估计。同时还进行了数值模拟以验证提出方法的有效性。最后,应用所提出的方法分析艾滋病的临床试验数据。
文摘本文研究用有限元法计算桥梁涡激振动的时程响应。应用条带假设和半经验半解析的Scanlan第二涡激作用力模型实现涡激作用力在时间和空间上的离散化;针对Scanlan模型中Van der Pol性质的时间频率混合项,引入时频混合格式的AFT方法来计算涡振时程响应,并通过算例验证了该方法的可行性。与传统的连续模型和随机振动理论计算桥梁涡激响应方法相比,时程计算可以考虑多振型的组合作用,结构非线性等多种影响,具有更大的灵活性。
文摘目的:探讨Cox比例风险模型与加速失效时间模型(accelerated failure time model,AFT)在基因表达数据生存分析中的应用及比较。方法:针对基因表达数据高维小样本的特性,首先采用偏最小二乘法对基因数据集进行降维,然后以降维后的成分为协变量对两类生存模型进行拟合并比较其性能。结果:两类模型中病人生存时间的对数秩检验表明,不同风险组生存时间的差异均有统计学意义(P<0.01),而AFT模型比Cox模型具有更大的检验统计量的值。结论:Cox模型和AFT模型都适用于基因表达数据的生存分析,在某些实际应用中AFT模型的拟合效果可能更优于Cox模型。
