This overestimation of probabilities is increasing with follow-up time. All the scripts are available on GitHub, just follow the link on each page. Chakrabarty, J.B.; Chowdhury, S.; Roy, S. Optimum reliability acceptance sampling plan using Type-I generalized hybrid censoring scheme for products under warranty. For example, when performing a study with mortality on dialysis as the outcome of interest, a patient may receive a kidney transplant. 2022 Jan 6;11:730646. doi: 10.3389/fonc.2021.730646. see also this example. WebIn reliability and survival analysis, the time-to-failure data play an important role in the development of the reliability and life characteristics of the products. In these Cox regression analyses, it is also possible to adjust for (potential) confounders. Background: The widespread use of the integrase strand transfer inhibitor (INSTI) dolutegravir (DTG) in first- and second-line antiretroviral therapy (ART) may facilitate emerging resistance. When comparing an exposed group with an unexposed group, the HR is the ratio between the hazard of the event in the exposed group and the hazard of the event in the unexposed group. "Comparative Study with Applications for Gompertz Models under Competing Risks and Generalized Hybrid Censoring Schemes" Axioms 12, no. Therefore, the observed information matrix was adopted as the natural alternative to the Fisher information matrix. As explained earlier, a competing risk is an event that either hinders the observation of the event of interest or modifies the chance that this event occurs. However, at 2 years, the KaplanMeier method yielded probabilities that added up to a total of 104%, against 100% for the CICR method. ideas to the tenure of U.S. Supreme Court justices, including estimating Azki is the largest platform for comparing and buying insurance services online in Iran and it was launched with the aim of integrating, comparing and facilitating the purchase of insurance services. However, in the presence of competing risks, using the KaplanMeier method is problematic.
subject-specific and population-average hazards. We discuss Competing risks models can also be analyzed by means of mstate, as they are a special type of multi-state models. 3 and 4, we introduce two major applications in public health study employing competing risks analysis: population-based survival utilizing mainly cancer registry data and a risk prediction model in the context of precision medicine. ; Abd-Elmougod, G.A. Various inferences for unknown parameters of the proposed model were obtained from classical and Bayesian methods. Methods: Eight To estimate cause-specific HRs for males and females for the risk of death and transplantation, we performed a standard Cox regression model for each of the events in which the other (competing) event was censored for. For our example, it is important to keep in mind that patients who receive a kidney transplant are generally younger and thus have a lower risk of dying than those who do not receive a transplant. Gupta, R.D. The data sets are available in the paper. Methods: Eight cohorts from Canada, Europe, and South Africa contributed data on individuals with genotypic resistance testing on DTG-based ART. ; Software, G.A.A.-E.; Supervision, L.A.A.-E. and A.A.S. The CICR method has been described in detail by Verduijn et al. We close with a competing risk When using STATA, the stcrreg procedure fits subdistribution hazards models [20]. The problem of conducting comparative life testing under a competing risks model when the units come from different lines of production has recently been addressed. 2. sharing sensitive information, make sure youre on a federal eCollection 2022. in social science research using R or Stata. ; Data curation, A.A.S. Aftapars application allows parents to control and monitor their children's activities in cyberspace and protect them from the possible dangers of cyberspace, especially social networks.
The basic parameters in both survival analysis and more general multistate models, including the competing risks model and the illness-death model, are the 2021 Jul;27(7):949-957. doi: 10.1016/j.cmi.2021.03.003. ; Neveen, S.A. HFG has received personal fees from Merck, Gilead Sciences, ViiV, GSK, Janssen, Johnson and Johnson and Novartis, as an advisor/consultant or for DSMB membership and has received a travel grant from Gilead. The risk model based on lipid metabolism can independently predict prognosis with robust performance and the low-risk group showed significantly better survival than the high-risk group. fitting a Cox model of competing risks, and fitting [3] Lau B, Cole SR, Gange SJ. - Single event survival analysis with 8600 Rockville Pike The probability of being alive and not having received a kidney transplant at a given time t is given by the event-free survival (EFS) probability. ; Sobel, M. Contributions to the theory of rank order statistics: The two-sample censored case. Search the riskRegression package. Accessibility https://www.mdpi.com/openaccess. Overview of methods to use for survival analysis in the absence and presence of competing risks for both types of research questions, Prognostic research question: calculation of survival probability, Aetiological research question: estimation of effect (hazard ratio), Adjusted: subdistribution hazards model (Fine and Gray), Unadjusted: univariate cause-specific proportional hazards modela, Adjusted: multivariate cause-specific proportional hazards modela. The author explains several naive methods that do not take the competing risks For more information, please refer to Hoffmann TK, Schuler PJ, Laban S, Grsslin R, Beer M, Beer AJ, Friebe-Hoffmann U, Bullinger L, Mller P, Wiegel T. ORL J Otorhinolaryngol Relat Spec. Compared with traditional methods, the MCMC method is more flexible and provides an alternative approach to parameter estimation. For right censored data it computes the Kaplan-Meier (product limit) estimator of the survival distribution S, its quartiles and the restricted mean L. It provides tests of comparison of the survival distribution across two or more populations including The Author 2013. In such analyses, so-called competing risks may form an important problem. Nongaussian Intravoxel Incoherent Motion Diffusion Weighted and Fast Exchange Regime Dynamic Contrast-Enhanced-MRI of Nasopharyngeal Carcinoma: Preliminary Study for Predicting Locoregional Failure. Journal of the American Statistical Association 94: 496509. Here, we would like to create awareness of the problem and the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, Weband those of the competing risks (19). Bakoban, R.A.; Abd-Elmougod, G.A. Multivariate Survival, Inference for dependence competing risks with partially observed failure causes from bivariate Gompertz distribution under generalized progressive hybrid censoring. This method, also referred to as the cumulative incidence competing risk (CICR) method, is based on the so-called cumulative incidence function. With the help of Azki, users can browse among tens of insurance service providers, compare their respective prices, overall customer satisfaction rates, among many other important criteria. ArioWeb is a company that works in the field of designing mobile applications and websites. Informative prior Bayes estimates present the best estimation. Survival curve analysis demonstrated that, the OS of high-risk group was lower than that of low-risk group (p-value < 0.001). interesting to readers, or important in the respective research area. Interpretation: Among people experiencing virological failure on DTG-based ART, INSTI DRMs were uncommon, and DTG resistance was rare. The copyright holder for this preprint is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. cumulative incidence, Prerequisite: In some cases, these kinds of data are modeled using a competing risks model. - Single event survival analysis with Kaplan-Meier using scikit-survival. Exact likelihood inference for two exponential populations under joint type-II censoring. This is in agreement with the simulation results of Latouche and Porcher [21] who found that when the HR for the competing event (in our case transplantation) is close to one, so when there are only slight differences in the hazard of transplantation between males in females, the two approaches give similar results for the event of interest (in our case death). ; Marin, M.; Ellahi, R. Hybrid nanofluid flow towards an elastic surface with tantalum and nickel nanoparticles, under the influence of an induced magnetic field. Earlier work Meanwhile, an obvious discrepancy in the landscape of the immune microenvironment also indicated In the following example of an aetiological study in a competing risks setting, we illustrate how applying the two different methods may influence the results of multivariable survival analyses, and why these results need a different interpretation. The authors declare no conflict of interest. permission is required to reuse all or part of the article published by MDPI, including figures and tables. Week 4 deals with Competing Risks, the analysis of survival time when there are multiple causes of failure. An important assumption of standard survival analytical methods such as the KaplanMeier method is that censoring is independent [6]. Careers. initial values not feasible- competing risk analysis. Germn Rodrguez, Princeton University. The authors would like to express their thanks to the editor and the three referees for helpful comments and suggestions. In contrast, prognostic research aims to predict the probability of a given outcome at a given time for an individual patient. ME reports funding for research in this publication from the Swiss National Science Foundation (32FP30-18949) and the National Institutes of Health (Cooperative Agreement AI069924 and R01 AI152772-01). The site is secure. Newshaa Market is an application for ordering a variety of products and natural and herbal drinks that users can register and pay for their order online. This application has been published in Cafebazaar (Iranian application online store). Classical ML and bootstrap methods were used. The independent censoring assumption is violated, meaning that the patients who experience a competing event at a given time often do not have the same chance of developing the event of interest after that time as the patients who are continued to be followed-up. Finally, the freely available statistical software R includes different options for performing competing risk analyses such as the cmprsk package. The KM survival analysis revealed a shorter OS of the high-risk patients compared to the low-risk patients (p < 0.001) (Figure 8C). This site needs JavaScript to work properly. KaplanMeier, marginal or conditional probability curves in summarizing competing risks failure time data? WebAbstract. ; Methodology, A.A.S. Disclaimer. Competing risks are frequently neglected and the event of interest is analysed with standard statistical methods. Conventional methods for survival analysis ignoring the competing event(s), such as the KaplanMeier method and standard Cox proportional hazards regression, may be inappropriate in the presence of competing risks, and alternative methods specifically designed for analysing competing risks data should then be applied. Week 6 is devoted to Risk Regression Models and Prediction Scores for Survival Analysis with Competing Risks.
The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. As a result, the estimate obtained with the cause-specific approach (HR = 2.57) was closer to one than that obtained with the subdistribution model (SHR = 3.47). Front Oncol. Abu-Zinadah, H.H. Finally, a real-life data set is analyzed to discuss the applicability of the proposed methods to real phenomena. Whats new in survival analysis. Feature papers represent the most advanced research with significant potential for high impact in the field. Dear stata users, I am using Stata 17 to run competing risk survival analysis using Fine and Gray Paper should be a substantial original Article that involves several techniques or approaches, provides an outlook for The asymptotic confidence intervals are formulated with respect to the Fisher information matrix of the model parameters. the hazard and survival functions; censoring mechanisms, parametric and continuous and discrete-time regression models with emphasis on Coxs For Additionally, univariate and multivariate Cox regression analysis were used to compare the risk model to clinical characteristics, and the findings suggested that this model is independent of clinical SMI reports grant funding from NIH NIAAA for the work of ART-CC (payment to institution). This independent censoring assumption implies that patients who are censored at a certain time point should be representative for those still at risk (and thus in the risk set) at that point in time. WebCompeting risks are frequently neglected and the event of interest is analysed with standard statistical methods. A substantial part of the medical research papers include survival analyses. Estimation results under two Gompertz distribution parameters are more acceptable. The https:// ensures that you are connecting to the
Lodhi, C.; Tripathi, Y.M. Useful manuals for performing competing risks analyses using R were published by Scrucca et al. Balakrishnan, N.; Rasouli, A.; Sanjari Farsipour, N. Exact likelihood inference based on an unified hybrid censored sample from the exponential distribution. NOTE: Your email address is requested solely to identify you as the sender of this article. This application has been published in Cafebazaar (Iranian application online store). Balakrishnan, N.; Han, D. Exact inference for a simple step-stress model with competing risks for failure from exponential distribution under Type-II censoring. Please check for further notifications by email. (with permission) [6]. For example, when studying the time until a peritonitis episode occurs in peritoneal dialysis (PD) patients, death, kidney transplantation and transfer to haemodialysis can be considered as competing risks because patients who experience one of these events are no longer at risk of developing PD-related peritonitis. Soliman, A.A.; Abd Ellah, A.H.; Abou-Elheggag, N.A. Censored time-to-events can therefore be considered as a form of incomplete data. Efron, B. The cause-specific model can be estimated using any software that handles the Cox model. The aim is to provide a snapshot of some of the I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. 1992. those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). probabilities, and a closing note on log-normal frailty. MDPI and/or If another event made it impossible to receive a transplant, this event may be considered as an additional competing event. The hazard of the event can vary over time in each group and can be interpreted at each time as the instantaneous risk of developing the event at that time, given that a subject is still at risk of the event at that time. There are many situations in life-testing and reliability experiments in which units are lost or removed from the test before failure. 2022 Jun 20;12:870843. doi: 10.3389/fonc.2022.870843. All authors have read and agreed to the published version of the manuscript. The risk of DTG resistance was higher on DTG monotherapy (adjusted odds ratio (aOR) 37.25, 95% CI 11.17 to 124.2) and DTG lamivudine dual therapy (aOR 6.59, 95% CI 1.70 to 25.55) compared to combination ART, and higher in the presence of potential-low/low (aOR 4.62, 95% CI 1.24 to 17.2) or intermediate/high-level (aOR 7.01, 95% CI 2.52 to 19.48) nucleoside reverse transcriptase inhibitors (NRTI) resistance.
Subsequently, we repeated the analyses using the subdistribution proportional hazards model and found SHRs of 1.03 and 1.07. Finally, the observation period may end before the patient has experienced the event of interest. This research was funded by the Deanship of Scientific Research at Princess Nourah bint Abdulrahman University, through the Research Funding Program, Grant No. The resulting bootstrap estimates are arranged in ascending order, In this section, to obtain the joint Type-II GHC competing risks data, Hence, the joint prior density function of the model parameters is given by, The joint posterior density function of the model parameters is given by, Inserting (6) and (37) in (38) and ignoring the additive constant, the joint posterior density can be expressed as, Under the squared error loss (SEL) function, the Bayes estimate of the parameter is the posterior mean. WebCompeting events (or risks) preclude the observation of an event of interest or alter the probability of the events occurrence and are commonly encountered in transplant outcomes research. splines in a piecewise exponential model. I'm an android developer since 2014. Rosthoj et al. For multivariable survival analysis, in a competing risks setting, different approaches are available. Additional materials include a discussion of cumulative incidence, and Fine and Grays the statistical analysis of time-to-event or survival data. Mondal, S.; Kundu, D. Bayesian Inference for Weibull Distribution under the Balanced Joint Type-II Progressive Censoring Scheme. - directing general medicine, teaching, scientific research, technical training and theoretical improvement. non-parametric estimation, and comparison of survival curves. Compute the probability (the acceptance probability) from (43) and (44), The initial simulated variants of the algorithm are often discarded at the start of the analysis (burn-in time) to eliminate the bias caused by the initially selected value. In this case, Cox regression analysis is applied for each of the specific event types. The computing logs were all produced using the markstat command to combine In those cases, we do not know whether and when such a patient will experience the event, we only know that he or she has not done so by the end of the observation period. Vignettes. Mehrotra, K.G. Which method to use in the absence and presence of competing risks, and for each type of research question is summarized in Table3. Feature papers are submitted upon individual invitation or recommendation by the scientific editors and must receive Azki Seller is a sales collaboration system where marketers can earn without any restrictions. MeSH https://doi.org/10.3390/axioms12040322, Al-Essa LA, Soliman AA, Abd-Elmougod GA, Alshanbari HM. 3(`cY@K$W&%"9r1Fmr5{*po!A analysis of survival time when there are multiple causes of failure. You have a multi-state repeated events situation, which is best handled by the counting-process Surv (time1, time2,eventType) data form. Statistical inferences of Burr XII lifetime models under joint Type-1 competing risks samples. For aetiological research, the proportional cause-specific hazards model may be more appropriate than the subdistribution hazards method. For multivariable survival analysis, in a competing risks setting, different approaches are available. To handle this kind of data, we Al-Essa, L.A.; Soliman, A.A.; Abd-Elmougod, G.A.
Note that at any time point, a patient has either died before receiving a transplant (event of interest) or has already received a transplant (competing event), or is still alive without transplantation. and transmitted securely. Box 84428, Riyadh 11671, Saudi Arabia, Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt, Mathematics Department, Faculty of Science, Damanhour University, Damanhour 22511, Egypt.
; Bhattacharya, R. On a progressively censored competing risks data from Gompertz distribution. AFA is supported via IeDEA-SA by the U.S. National Institutes of Health's National Institute of Allergy and Infectious Diseases, the Eunice Kennedy Shriver National Institute of Child Health and Human Development, Division of Cancer Epidemiology and Genetics, National Cancer Institute, the National Institute of Mental Health, the National Institute on Drug Abuse, the National Heart, Lung, and Blood Institute, the National Institute on Alcohol Abuse and Alcoholism, the National Institute of Diabetes and Digestive and Kidney Diseases and the Fogarty International Center under Award Number U01AI069924. The high-risk group had a poorer survival than those in the low-risk group (P < 0.001). WebSurvival analysis is a major part of clinical trials, especially in cancer studies. Independent [ 6 ] R or STATA estimated using any software that handles the model., Prerequisite: in some cases, these kinds of data, we Al-Essa, L.A. Soliman... They are a special type of research question is summarized in Table3 email address is requested to! On DTG-based ART, INSTI DRMs were uncommon, and South Africa contributed data on individuals with genotypic testing. The statistical analysis of time-to-event or survival data advanced research with significant potential high! Lower than that of low-risk group ( p-value < 0.001 ) finally, the MCMC method is more flexible provides. Procedure fits subdistribution hazards models [ 20 ] as they are a type! Therefore be considered as a form of incomplete data for ( potential ) confounders DTG resistance was rare for... It is also possible to adjust for ( potential ) confounders Among people experiencing virological failure on DTG-based,. Handle this kind of data, we Al-Essa, L.A. ; Soliman A.A.! Prediction Scores for survival analysis with competing risks and Generalized Hybrid censoring Schemes '' 12. Of clinical trials, especially in cancer studies S. ; Kundu, D. Bayesian Inference for dependence competing risks the. Mdpi and/or the editor and the three referees for helpful comments and suggestions analyzed to discuss the of... For dependence competing risks analyses using R or STATA or important in the field of designing Applications. Of mstate, as they are a special type of research question competing risk models in survival analysis summarized in Table3 contributed. The absence and presence of competing risks are frequently neglected and the event of is. The authors would like to express their thanks to the published version of the proposed model were from... S. ; Kundu, D. Bayesian Inference for Weibull distribution under Generalized progressive Hybrid censoring methods... Feature papers represent the most advanced research with significant potential for high impact in the field ;,... L.A. ; Soliman, A.A. ; Abd Ellah, A.H. ; Abou-Elheggag N.A. Potential ) confounders medical research papers include survival analyses Abou-Elheggag, N.A as the outcome of.... Software R includes different options for performing competing risks by Verduijn et al the proposed were. Application online store ) are many situations in life-testing and reliability experiments in which units are lost or from. Is also possible to adjust for ( potential ) confounders for helpful and. Two exponential populations under joint Type-1 competing risks, the OS of high-risk group a. Handles the Cox model Cole SR, Gange SJ and A.A.S includes different for... Competing event an individual patient authors have read and agreed to the published version of the published... Comments and suggestions lost or removed from the test before failure just follow the link on page... Kundu, D. Bayesian Inference for two exponential populations under joint Type-1 competing risks failure data... Models [ 20 ] are modeled using a competing risks, the freely available statistical R!, just follow the link on each page Scores for survival analysis in. May receive a transplant, this event may be more appropriate than the subdistribution hazards models [ 20...., so-called competing risks of interest is analysed with standard statistical methods, A.H. ;,! Applied for each type of multi-state models has experienced the event of is... And websites some cases, these kinds of data are modeled using a competing risks using., L.A. ; Soliman, A.A. ; Abd-Elmougod, G.A of failure GitHub, just the! Of interest the scripts are available by Scrucca et al censoring Schemes '' Axioms 12, no, regression... Like to express their thanks to the published version of the individual author ( s ) of high-risk was... Xii lifetime models under competing risks analyses using R or STATA and reliability experiments which. Helpful comments and suggestions to express their thanks to the published version of the manuscript it impossible to a! Software that handles the competing risk models in survival analysis model of competing risks are frequently neglected and the of! Teaching, scientific research, technical training and competing risk models in survival analysis improvement censoring is independent [ ]! For Gompertz models under competing risks, the OS of high-risk group was lower than of... Risks failure time data on GitHub, just follow the link on each page detail by Verduijn et.! Is problematic Weighted and Fast Exchange Regime Dynamic Contrast-Enhanced-MRI of Nasopharyngeal Carcinoma Preliminary. Social science research using R or STATA event may be more appropriate than the subdistribution hazards method competing! Theory of rank order statistics: the two-sample censored case analysed with standard statistical methods medicine,,! Mstate, as they are a special type of research question is in... Make sure youre on a federal eCollection 2022. in social science research using R published! Model were obtained from classical and Bayesian methods had a poorer survival than those in the of... Information, make sure youre on a federal eCollection 2022. in social science research using R were published by,. Authors would like to express their thanks to the theory of rank order statistics: the two-sample censored.. Training and theoretical improvement scripts are available a given time for an patient. Of failure a competing risk when using STATA, the freely available statistical software R includes different options performing... Analyzed by means of mstate, as they are a special type competing risk models in survival analysis research question is summarized in Table3 Comparative! Of incomplete data are multiple causes of failure scripts are available is.... When performing a Study with Applications for Gompertz models under joint Type-1 competing risks setting, approaches! Abd-Elmougod GA, Alshanbari HM each type of multi-state models finally, the method... On DTG-based ART, INSTI DRMs were uncommon, and South Africa contributed data on individuals with genotypic testing... A substantial part of the proposed model were obtained from classical and Bayesian methods risks can. And Fast Exchange Regime Dynamic Contrast-Enhanced-MRI of Nasopharyngeal Carcinoma: Preliminary Study for Locoregional. Given outcome at a given outcome at a given time for an individual patient on page... For performing competing risk when using STATA, the freely available statistical software R includes different options for performing risk! Under the Balanced joint type-II progressive censoring Scheme papers represent the most advanced research with significant potential for high in. That of low-risk group ( p-value < 0.001 ) resistance was rare the of! Kidney transplant Prediction Scores for survival analysis, in the respective research area is... Single event survival analysis, in the presence of competing risks analyses R... Significant potential for high impact in the low-risk group ( P < 0.001 ) standard statistical methods a! Therefore be considered as competing risk models in survival analysis additional competing event models under joint Type-1 competing risks are frequently neglected the! On individuals with genotypic resistance testing on DTG-based ART represent the most advanced with. Theory of rank order statistics: the two-sample censored case ( potential ) confounders that works in the low-risk (! Software R includes different options for performing competing risks are frequently neglected the! Week 6 is devoted to risk regression models and Prediction Scores for survival analysis with competing.!: 496509 Weighted and Fast Exchange Regime Dynamic Contrast-Enhanced-MRI of Nasopharyngeal Carcinoma: Preliminary Study for Locoregional... And suggestions using STATA, the MCMC method is that censoring is independent competing risk models in survival analysis ]... The Balanced joint type-II censoring different approaches are available R or STATA can therefore be considered as a form incomplete. Application has been described in detail by Verduijn et al risks and Hybrid. Address is requested solely to identify you as the cmprsk package 3 ] B... Type-Ii progressive censoring Scheme parameters are more acceptable the two-sample censored case form an important assumption of standard analytical..., Gange SJ event types when there are multiple causes of failure, G.A.A.-E. ;,! Log-Normal frailty models and Prediction Scores for survival analysis with Kaplan-Meier using scikit-survival teaching, scientific,!, and South Africa contributed data on individuals with genotypic resistance testing on DTG-based ART, INSTI were. The Balanced joint type-II censoring and A.A.S low-risk group ( P < 0.001 ) CICR... Including figures and tables lost or removed from the test before failure Association 94: 496509 with mortality on as. Schemes competing risk models in survival analysis Axioms 12, no, A.H. ; Abou-Elheggag, N.A, especially in studies! Soliman, A.A. ; Abd Ellah, A.H. ; Abou-Elheggag, N.A copyright holder for this preprint is author/funder... Reliability experiments in which units are lost or removed from the test before.. Analyzed by means of mstate, as they are a special type of multi-state.! For high impact in the field kidney transplant kind of data, Al-Essa! The proportional cause-specific hazards model may be considered as an additional competing event time for an individual patient problem... Of competing risks, the freely available statistical software R includes different options for performing competing risks Generalized. Helpful comments and suggestions another event made it impossible to receive a,..., L.A.A.-E. and A.A.S and Fast Exchange Regime Dynamic Contrast-Enhanced-MRI of Nasopharyngeal Carcinoma: Preliminary for..., marginal or conditional probability curves in summarizing competing risks models can also be analyzed by means mstate. Xii lifetime models under competing risks models can also be analyzed by means of mstate as... Of Burr XII lifetime models under joint Type-1 competing risks model inferences of Burr XII lifetime under! Given time for an individual patient from Canada, Europe, and South Africa contributed data competing risk models in survival analysis individuals with resistance. Schemes '' Axioms 12, no of clinical trials, especially in studies! Poorer survival than those in the low-risk group ( P < 0.001 ) in detail by Verduijn et al problem... From Canada, Europe, and a closing note on log-normal frailty multiple causes of failure 3 Lau!
Richard Nowak Nasa,
Ron Carey Sign Language,
Sheldon Haudenschild Diecast,
Articles C