scholarly journals Profile Likelihood Estimation Applied To The Semi-parametric Models With Survival Data

2021 ◽  
Author(s):  
Khandoker Mohammad
Keyword(s):  
Survival Data ◽  
Profile Likelihood ◽  
Bootstrap Method ◽  
Score Function ◽  
Likelihood Estimation ◽  
Joint Model ◽  
Likelihood Score ◽  
Likelihood Approach ◽  
R Packages ◽  
Longitudinal And Survival Data

<p><b>In this thesis, we have investigated the efficiency of profile likelihood in the estimation of parameters from the Cox Proportional Hazards (PH) cure model and joint model of longitudinal and survival data. For the profile likelihood approach in the joint model of longitudinal and survival data, Hsieh et al. (2006) stated “No distributional or asymptotic theory is available to date, and even the standard errors (SEs), defined as the standard deviations of the parametric estimators, are difficult to obtain”. The reason behind this difficulty is the estimator of baseline hazard which involves implicit function in the profile likelihood estimation (Hirose and Liu, 2020). Hence finding the estimated SE of the parametric estimators from the Cox PH cure model and joint model using profile likelihood approach is a great challenge. Therefore, bootstrap method has been suggested to get the estimated standard errors while using the profile likelihood approach (Hsieh et al., 2006).</b></p> <p>To solve the difficulty, we have expanded the profile likelihood function directly without assuming the derivative of the profile likelihood score function and obtain the explicit form of the SE estimator using the profile likelihood score function. Our proposed alternative approach gives us not only analytical understanding of the profile likelihood estimation, but also provides closed form formula to compute the standard error of the profile likelihood maximum likelihood estimator in terms of profile likelihood score function. To show the advantage of our proposed approach in medical and clinical studies, we have analysed the simulated and real-life data, and compared our results with the output obtained from the smcure, JM(method: ’Cox-PH-GH’) and joineRML R-packages. The outputs suggest that the bootstrap method and our proposed approach have provided similar and comparable results. In addition, the average computation times of our approach are much less compared to the above mentioned R-packages.</p>

scholarly journals Profile Likelihood Estimation Applied To The Semi-parametric Models With Survival Data

2021 ◽  
Author(s):  
Khandoker Mohammad
Keyword(s):  
Survival Data ◽  
Profile Likelihood ◽  
Bootstrap Method ◽  
Score Function ◽  
Likelihood Estimation ◽  
Joint Model ◽  
Likelihood Score ◽  
Likelihood Approach ◽  
R Packages ◽  
Longitudinal And Survival Data

<p><b>In this thesis, we have investigated the efficiency of profile likelihood in the estimation of parameters from the Cox Proportional Hazards (PH) cure model and joint model of longitudinal and survival data. For the profile likelihood approach in the joint model of longitudinal and survival data, Hsieh et al. (2006) stated “No distributional or asymptotic theory is available to date, and even the standard errors (SEs), defined as the standard deviations of the parametric estimators, are difficult to obtain”. The reason behind this difficulty is the estimator of baseline hazard which involves implicit function in the profile likelihood estimation (Hirose and Liu, 2020). Hence finding the estimated SE of the parametric estimators from the Cox PH cure model and joint model using profile likelihood approach is a great challenge. Therefore, bootstrap method has been suggested to get the estimated standard errors while using the profile likelihood approach (Hsieh et al., 2006).</b></p> <p>To solve the difficulty, we have expanded the profile likelihood function directly without assuming the derivative of the profile likelihood score function and obtain the explicit form of the SE estimator using the profile likelihood score function. Our proposed alternative approach gives us not only analytical understanding of the profile likelihood estimation, but also provides closed form formula to compute the standard error of the profile likelihood maximum likelihood estimator in terms of profile likelihood score function. To show the advantage of our proposed approach in medical and clinical studies, we have analysed the simulated and real-life data, and compared our results with the output obtained from the smcure, JM(method: ’Cox-PH-GH’) and joineRML R-packages. The outputs suggest that the bootstrap method and our proposed approach have provided similar and comparable results. In addition, the average computation times of our approach are much less compared to the above mentioned R-packages.</p>

scholarly journals Statistical Generalized Derivative Applied to the Profile Likelihood Estimation in a Mixture of Semiparametric Models

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 278
Author(s):  
Yuichi Hirose ◽  
Ivy Liu
Keyword(s):  
Standard Error ◽  
Survival Data ◽  
Profile Likelihood ◽  
Score Function ◽  
Likelihood Estimation ◽  
Implicit Function ◽  
Likelihood Estimator ◽  
Generalized Derivative ◽  
Likelihood Score ◽  
Longitudinal And Survival Data

There is a difficulty in finding an estimate of the standard error (SE) of the profile likelihood estimator in the joint model of longitudinal and survival data. The difficulty is on the differentiation of an implicit function that appear in the profile likelihood estimation. We solve the difficulty by introducing the “statistical generalized derivative”. The derivative is used to show the asymptotic normality of the estimator with the SE expressed in terms of the profile likelihood score function.

scholarly journals A new joint model for longitudinal and survival data with a cure fraction

2004 ◽  
Vol 91 (1) ◽  
pp. 18-34 ◽  
Author(s):  
Ming-Hui Chen ◽  
Joseph G Ibrahim ◽  
Debajyoti Sinha
Keyword(s):  
Survival Data ◽  
Joint Model ◽  
Cure Fraction ◽  
Longitudinal And Survival Data

scholarly journals A joint model for mixed and truncated longitudinal data and survival data, with application to HIV vaccine studies

Biostatistics ◽  
2017 ◽  
Vol 19 (3) ◽  
pp. 374-390 ◽  
Author(s):  
Tingting Yu ◽  
Lang Wu ◽  
Peter B Gilbert
Keyword(s):  
Longitudinal Data ◽  
Survival Data ◽  
Joint Model ◽  
Hiv Vaccine ◽  
Likelihood Inference ◽  
Likelihood Method ◽  
Parameter Estimates ◽  
Computationally Efficient ◽  
Approximate Likelihood ◽  
Longitudinal And Survival Data

SUMMARY In HIV vaccine studies, a major research objective is to identify immune response biomarkers measured longitudinally that may be associated with risk of HIV infection. This objective can be assessed via joint modeling of longitudinal and survival data. Joint models for HIV vaccine data are complicated by the following issues: (i) left truncations of some longitudinal data due to lower limits of quantification; (ii) mixed types of longitudinal variables; (iii) measurement errors and missing values in longitudinal measurements; (iv) computational challenges associated with likelihood inference. In this article, we propose a joint model of complex longitudinal and survival data and a computationally efficient method for approximate likelihood inference to address the foregoing issues simultaneously. In particular, our model does not make unverifiable distributional assumptions for truncated values, which is different from methods commonly used in the literature. The parameters are estimated based on the h-likelihood method, which is computationally efficient and offers approximate likelihood inference. Moreover, we propose a new approach to estimate the standard errors of the h-likelihood based parameter estimates by using an adaptive Gauss–Hermite method. Simulation studies show that our methods perform well and are computationally efficient. A comprehensive data analysis is also presented.

scholarly journals Complete Case versus Inverse Probability Weighting Methods of Fitting Incomplete Longitudinal and Survival Data Joint Models

2019 ◽  
pp. 1-10
Author(s):  
D. O. Nyaboga ◽  
A. Mwangi ◽  
D. Lusweti
Keyword(s):  
Missing Data ◽  
Survival Data ◽  
Joint Model ◽  
Information Criteria ◽  
Joint Models ◽  
Full Data ◽  
Complete Case ◽  
Inverse Probability ◽  
Longitudinal And Survival Data ◽  
The Impact

Missing data is a common problem in real word studies especially clinical studies. However, most people working with such data, often drop missing cases from individuals with incomplete observations that occur when patients do not complete the treatment or miss their scheduled visits. This may lead to misleading results and ultimately affect the decision of whether an intervention is good or bad for the patients under treatment. The comparison of Complete Case (CC) and Inverse Probability Weights (IPW) techniques of handling missing data in various models has been addressed, however little has been done to compare these methods when applied to joint models of longitudinal and time to event data. Therefore, this paper seeks to investigate the impact of assuming CC analysis on clinical data with missing cases, comparing it with IPW method when fitting joint models of longitudinal and survival data setting full data model as the baseline model. This paper made use of randomized aids clinical trial data. The model with Deviance Information Criteria (DIC) close to that of full data joint model is considered the best. From the results, joint models from full data, CC and IPW had DIC of 10603.94, 8410.33 and 10600.95 respectively. The joint model obtained from IPW data had a DIC too close to that of full data joint model as compared to model from CC data.

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