SAMPLE SIZE DETERMINATION IN NON-RADOMIZED SURVIVAL STUDIES WITH NON-CENSORED AND CENSORED DATA
Introduction: In survival analysis, determination of sufficient sample size to achieve suitable statistical power is important .In both parametric and non-parametric methods of classic statistics, randomn selection of samples is a basic condition. practically, in most clinical trials and health surv...
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S FAGHIHZADEH [verfasserIn] M RAHGOZAR [verfasserIn] |
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E-Artikel |
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Englisch |
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2003 |
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In: Journal of Research in Medical Sciences - Wolters Kluwer Medknow Publications, 2005, 8(2003), 2 |
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volume:8 ; year:2003 ; number:2 |
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DOAJ067527094 |
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| 520 | |a Introduction: In survival analysis, determination of sufficient sample size to achieve suitable statistical power is important .In both parametric and non-parametric methods of classic statistics, randomn selection of samples is a basic condition. practically, in most clinical trials and health surveys randomn allocation is impossible. Fixed - effect multiple linear regression analysis covers this need and this feature could be extended to survival regression analysis. This paper is the result of sample size determination in non-randomnized surval analysis with censored and non -censored data. Methods: In non-randomnized survival studies, linear regression with fixed -effect variable could be used. In fact such a regression is conditional expectation of dependent variable, conditioned on independent variable. Likelihood fuction with exponential hazard constructed by considering binary variable for allocation of each subject to one of two comparing groups, stating the variance of coefficient of fixed - effect independent variable by determination coefficient , sample size determination formulas are obtained with both censored and non-cencored data. So estimation of sample size is not based on the relation of a single independent variable but it could be attain the required power for a test adjusted for effect of the other explanatory covariates. Since the asymptotic distribution of the likelihood estimator of parameter is normal, we obtained the variance of the regression coefficient estimator formula then by stating the variance of regression coefficient of fixed-effect variable, by determination coefficient we derived formulas for determination of sample size in both censored and non-censored data. Results: In no-randomnized survival analysis ,to compare hazard rates of two groups without censored data, we obtained an estimation of determination coefficient ,risk ratio and proportion of membership to each group and their variances from likelihood function, when data has censored cases an estimate of the probability of censorship should be considered, after obtaining the varince of maximum likelihood estimator and considering its asymptotic normal distribution and by using coefficient of determination, formulas have been derived. The derived sample size formulas could attain the required power for a test adjuasted for effect of other explanatory covariates. Discussion: application of regression model in non-randomnized survival analysis helps to derive suitable formulas to determin sample size in both randomized and non-randomnized studies in a error level, to attain necessary statistical power. In Coxs semiparametric proportional hazard model ,since the varince of the parameter can not be stated in a simple form ,a simulation model can be used. When the coefficient of determination is partialy large the power bassed on log-rank test overestimates the true value of power, but when coefficient of determination is near to difference between powers decreases zero. By increasing of regression coefficient of determination, the difference between the log-rank test and adjusted coefficient of determination of this paper increases. | ||
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(DE-627)DOAJ067527094 (DE-599)DOAJ5eca91a8a77845d1ba7b5fad8361cfb0 DE-627 ger DE-627 rakwb eng S FAGHIHZADEH verfasserin aut SAMPLE SIZE DETERMINATION IN NON-RADOMIZED SURVIVAL STUDIES WITH NON-CENSORED AND CENSORED DATA 2003 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Introduction: In survival analysis, determination of sufficient sample size to achieve suitable statistical power is important .In both parametric and non-parametric methods of classic statistics, randomn selection of samples is a basic condition. practically, in most clinical trials and health surveys randomn allocation is impossible. Fixed - effect multiple linear regression analysis covers this need and this feature could be extended to survival regression analysis. This paper is the result of sample size determination in non-randomnized surval analysis with censored and non -censored data. Methods: In non-randomnized survival studies, linear regression with fixed -effect variable could be used. In fact such a regression is conditional expectation of dependent variable, conditioned on independent variable. Likelihood fuction with exponential hazard constructed by considering binary variable for allocation of each subject to one of two comparing groups, stating the variance of coefficient of fixed - effect independent variable by determination coefficient , sample size determination formulas are obtained with both censored and non-cencored data. So estimation of sample size is not based on the relation of a single independent variable but it could be attain the required power for a test adjusted for effect of the other explanatory covariates. Since the asymptotic distribution of the likelihood estimator of parameter is normal, we obtained the variance of the regression coefficient estimator formula then by stating the variance of regression coefficient of fixed-effect variable, by determination coefficient we derived formulas for determination of sample size in both censored and non-censored data. Results: In no-randomnized survival analysis ,to compare hazard rates of two groups without censored data, we obtained an estimation of determination coefficient ,risk ratio and proportion of membership to each group and their variances from likelihood function, when data has censored cases an estimate of the probability of censorship should be considered, after obtaining the varince of maximum likelihood estimator and considering its asymptotic normal distribution and by using coefficient of determination, formulas have been derived. The derived sample size formulas could attain the required power for a test adjuasted for effect of other explanatory covariates. Discussion: application of regression model in non-randomnized survival analysis helps to derive suitable formulas to determin sample size in both randomized and non-randomnized studies in a error level, to attain necessary statistical power. In Coxs semiparametric proportional hazard model ,since the varince of the parameter can not be stated in a simple form ,a simulation model can be used. When the coefficient of determination is partialy large the power bassed on log-rank test overestimates the true value of power, but when coefficient of determination is near to difference between powers decreases zero. By increasing of regression coefficient of determination, the difference between the log-rank test and adjusted coefficient of determination of this paper increases. Survival analysis, Sample size determination, non -randomized survival analysis, censored data, non-censored data Medicine R M RAHGOZAR verfasserin aut In Journal of Research in Medical Sciences Wolters Kluwer Medknow Publications, 2005 8(2003), 2 (DE-627)608492930 (DE-600)2513075-4 17357136 nnns volume:8 year:2003 number:2 https://doaj.org/article/5eca91a8a77845d1ba7b5fad8361cfb0 kostenfrei http://journals.mui.ac.ir/jrms/article/view/2994 kostenfrei https://doaj.org/toc/1735-1995 Journal toc kostenfrei https://doaj.org/toc/1735-7136 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ AR 8 2003 2 |
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(DE-627)DOAJ067527094 (DE-599)DOAJ5eca91a8a77845d1ba7b5fad8361cfb0 DE-627 ger DE-627 rakwb eng S FAGHIHZADEH verfasserin aut SAMPLE SIZE DETERMINATION IN NON-RADOMIZED SURVIVAL STUDIES WITH NON-CENSORED AND CENSORED DATA 2003 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Introduction: In survival analysis, determination of sufficient sample size to achieve suitable statistical power is important .In both parametric and non-parametric methods of classic statistics, randomn selection of samples is a basic condition. practically, in most clinical trials and health surveys randomn allocation is impossible. Fixed - effect multiple linear regression analysis covers this need and this feature could be extended to survival regression analysis. This paper is the result of sample size determination in non-randomnized surval analysis with censored and non -censored data. Methods: In non-randomnized survival studies, linear regression with fixed -effect variable could be used. In fact such a regression is conditional expectation of dependent variable, conditioned on independent variable. Likelihood fuction with exponential hazard constructed by considering binary variable for allocation of each subject to one of two comparing groups, stating the variance of coefficient of fixed - effect independent variable by determination coefficient , sample size determination formulas are obtained with both censored and non-cencored data. So estimation of sample size is not based on the relation of a single independent variable but it could be attain the required power for a test adjusted for effect of the other explanatory covariates. Since the asymptotic distribution of the likelihood estimator of parameter is normal, we obtained the variance of the regression coefficient estimator formula then by stating the variance of regression coefficient of fixed-effect variable, by determination coefficient we derived formulas for determination of sample size in both censored and non-censored data. Results: In no-randomnized survival analysis ,to compare hazard rates of two groups without censored data, we obtained an estimation of determination coefficient ,risk ratio and proportion of membership to each group and their variances from likelihood function, when data has censored cases an estimate of the probability of censorship should be considered, after obtaining the varince of maximum likelihood estimator and considering its asymptotic normal distribution and by using coefficient of determination, formulas have been derived. The derived sample size formulas could attain the required power for a test adjuasted for effect of other explanatory covariates. Discussion: application of regression model in non-randomnized survival analysis helps to derive suitable formulas to determin sample size in both randomized and non-randomnized studies in a error level, to attain necessary statistical power. In Coxs semiparametric proportional hazard model ,since the varince of the parameter can not be stated in a simple form ,a simulation model can be used. When the coefficient of determination is partialy large the power bassed on log-rank test overestimates the true value of power, but when coefficient of determination is near to difference between powers decreases zero. By increasing of regression coefficient of determination, the difference between the log-rank test and adjusted coefficient of determination of this paper increases. Survival analysis, Sample size determination, non -randomized survival analysis, censored data, non-censored data Medicine R M RAHGOZAR verfasserin aut In Journal of Research in Medical Sciences Wolters Kluwer Medknow Publications, 2005 8(2003), 2 (DE-627)608492930 (DE-600)2513075-4 17357136 nnns volume:8 year:2003 number:2 https://doaj.org/article/5eca91a8a77845d1ba7b5fad8361cfb0 kostenfrei http://journals.mui.ac.ir/jrms/article/view/2994 kostenfrei https://doaj.org/toc/1735-1995 Journal toc kostenfrei https://doaj.org/toc/1735-7136 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ AR 8 2003 2 |
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(DE-627)DOAJ067527094 (DE-599)DOAJ5eca91a8a77845d1ba7b5fad8361cfb0 DE-627 ger DE-627 rakwb eng S FAGHIHZADEH verfasserin aut SAMPLE SIZE DETERMINATION IN NON-RADOMIZED SURVIVAL STUDIES WITH NON-CENSORED AND CENSORED DATA 2003 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Introduction: In survival analysis, determination of sufficient sample size to achieve suitable statistical power is important .In both parametric and non-parametric methods of classic statistics, randomn selection of samples is a basic condition. practically, in most clinical trials and health surveys randomn allocation is impossible. Fixed - effect multiple linear regression analysis covers this need and this feature could be extended to survival regression analysis. This paper is the result of sample size determination in non-randomnized surval analysis with censored and non -censored data. Methods: In non-randomnized survival studies, linear regression with fixed -effect variable could be used. In fact such a regression is conditional expectation of dependent variable, conditioned on independent variable. Likelihood fuction with exponential hazard constructed by considering binary variable for allocation of each subject to one of two comparing groups, stating the variance of coefficient of fixed - effect independent variable by determination coefficient , sample size determination formulas are obtained with both censored and non-cencored data. So estimation of sample size is not based on the relation of a single independent variable but it could be attain the required power for a test adjusted for effect of the other explanatory covariates. Since the asymptotic distribution of the likelihood estimator of parameter is normal, we obtained the variance of the regression coefficient estimator formula then by stating the variance of regression coefficient of fixed-effect variable, by determination coefficient we derived formulas for determination of sample size in both censored and non-censored data. Results: In no-randomnized survival analysis ,to compare hazard rates of two groups without censored data, we obtained an estimation of determination coefficient ,risk ratio and proportion of membership to each group and their variances from likelihood function, when data has censored cases an estimate of the probability of censorship should be considered, after obtaining the varince of maximum likelihood estimator and considering its asymptotic normal distribution and by using coefficient of determination, formulas have been derived. The derived sample size formulas could attain the required power for a test adjuasted for effect of other explanatory covariates. Discussion: application of regression model in non-randomnized survival analysis helps to derive suitable formulas to determin sample size in both randomized and non-randomnized studies in a error level, to attain necessary statistical power. In Coxs semiparametric proportional hazard model ,since the varince of the parameter can not be stated in a simple form ,a simulation model can be used. When the coefficient of determination is partialy large the power bassed on log-rank test overestimates the true value of power, but when coefficient of determination is near to difference between powers decreases zero. By increasing of regression coefficient of determination, the difference between the log-rank test and adjusted coefficient of determination of this paper increases. Survival analysis, Sample size determination, non -randomized survival analysis, censored data, non-censored data Medicine R M RAHGOZAR verfasserin aut In Journal of Research in Medical Sciences Wolters Kluwer Medknow Publications, 2005 8(2003), 2 (DE-627)608492930 (DE-600)2513075-4 17357136 nnns volume:8 year:2003 number:2 https://doaj.org/article/5eca91a8a77845d1ba7b5fad8361cfb0 kostenfrei http://journals.mui.ac.ir/jrms/article/view/2994 kostenfrei https://doaj.org/toc/1735-1995 Journal toc kostenfrei https://doaj.org/toc/1735-7136 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ AR 8 2003 2 |
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(DE-627)DOAJ067527094 (DE-599)DOAJ5eca91a8a77845d1ba7b5fad8361cfb0 DE-627 ger DE-627 rakwb eng S FAGHIHZADEH verfasserin aut SAMPLE SIZE DETERMINATION IN NON-RADOMIZED SURVIVAL STUDIES WITH NON-CENSORED AND CENSORED DATA 2003 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Introduction: In survival analysis, determination of sufficient sample size to achieve suitable statistical power is important .In both parametric and non-parametric methods of classic statistics, randomn selection of samples is a basic condition. practically, in most clinical trials and health surveys randomn allocation is impossible. Fixed - effect multiple linear regression analysis covers this need and this feature could be extended to survival regression analysis. This paper is the result of sample size determination in non-randomnized surval analysis with censored and non -censored data. Methods: In non-randomnized survival studies, linear regression with fixed -effect variable could be used. In fact such a regression is conditional expectation of dependent variable, conditioned on independent variable. Likelihood fuction with exponential hazard constructed by considering binary variable for allocation of each subject to one of two comparing groups, stating the variance of coefficient of fixed - effect independent variable by determination coefficient , sample size determination formulas are obtained with both censored and non-cencored data. So estimation of sample size is not based on the relation of a single independent variable but it could be attain the required power for a test adjusted for effect of the other explanatory covariates. Since the asymptotic distribution of the likelihood estimator of parameter is normal, we obtained the variance of the regression coefficient estimator formula then by stating the variance of regression coefficient of fixed-effect variable, by determination coefficient we derived formulas for determination of sample size in both censored and non-censored data. Results: In no-randomnized survival analysis ,to compare hazard rates of two groups without censored data, we obtained an estimation of determination coefficient ,risk ratio and proportion of membership to each group and their variances from likelihood function, when data has censored cases an estimate of the probability of censorship should be considered, after obtaining the varince of maximum likelihood estimator and considering its asymptotic normal distribution and by using coefficient of determination, formulas have been derived. The derived sample size formulas could attain the required power for a test adjuasted for effect of other explanatory covariates. Discussion: application of regression model in non-randomnized survival analysis helps to derive suitable formulas to determin sample size in both randomized and non-randomnized studies in a error level, to attain necessary statistical power. In Coxs semiparametric proportional hazard model ,since the varince of the parameter can not be stated in a simple form ,a simulation model can be used. When the coefficient of determination is partialy large the power bassed on log-rank test overestimates the true value of power, but when coefficient of determination is near to difference between powers decreases zero. By increasing of regression coefficient of determination, the difference between the log-rank test and adjusted coefficient of determination of this paper increases. Survival analysis, Sample size determination, non -randomized survival analysis, censored data, non-censored data Medicine R M RAHGOZAR verfasserin aut In Journal of Research in Medical Sciences Wolters Kluwer Medknow Publications, 2005 8(2003), 2 (DE-627)608492930 (DE-600)2513075-4 17357136 nnns volume:8 year:2003 number:2 https://doaj.org/article/5eca91a8a77845d1ba7b5fad8361cfb0 kostenfrei http://journals.mui.ac.ir/jrms/article/view/2994 kostenfrei https://doaj.org/toc/1735-1995 Journal toc kostenfrei https://doaj.org/toc/1735-7136 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ AR 8 2003 2 |
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(DE-627)DOAJ067527094 (DE-599)DOAJ5eca91a8a77845d1ba7b5fad8361cfb0 DE-627 ger DE-627 rakwb eng S FAGHIHZADEH verfasserin aut SAMPLE SIZE DETERMINATION IN NON-RADOMIZED SURVIVAL STUDIES WITH NON-CENSORED AND CENSORED DATA 2003 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Introduction: In survival analysis, determination of sufficient sample size to achieve suitable statistical power is important .In both parametric and non-parametric methods of classic statistics, randomn selection of samples is a basic condition. practically, in most clinical trials and health surveys randomn allocation is impossible. Fixed - effect multiple linear regression analysis covers this need and this feature could be extended to survival regression analysis. This paper is the result of sample size determination in non-randomnized surval analysis with censored and non -censored data. Methods: In non-randomnized survival studies, linear regression with fixed -effect variable could be used. In fact such a regression is conditional expectation of dependent variable, conditioned on independent variable. Likelihood fuction with exponential hazard constructed by considering binary variable for allocation of each subject to one of two comparing groups, stating the variance of coefficient of fixed - effect independent variable by determination coefficient , sample size determination formulas are obtained with both censored and non-cencored data. So estimation of sample size is not based on the relation of a single independent variable but it could be attain the required power for a test adjusted for effect of the other explanatory covariates. Since the asymptotic distribution of the likelihood estimator of parameter is normal, we obtained the variance of the regression coefficient estimator formula then by stating the variance of regression coefficient of fixed-effect variable, by determination coefficient we derived formulas for determination of sample size in both censored and non-censored data. Results: In no-randomnized survival analysis ,to compare hazard rates of two groups without censored data, we obtained an estimation of determination coefficient ,risk ratio and proportion of membership to each group and their variances from likelihood function, when data has censored cases an estimate of the probability of censorship should be considered, after obtaining the varince of maximum likelihood estimator and considering its asymptotic normal distribution and by using coefficient of determination, formulas have been derived. The derived sample size formulas could attain the required power for a test adjuasted for effect of other explanatory covariates. Discussion: application of regression model in non-randomnized survival analysis helps to derive suitable formulas to determin sample size in both randomized and non-randomnized studies in a error level, to attain necessary statistical power. In Coxs semiparametric proportional hazard model ,since the varince of the parameter can not be stated in a simple form ,a simulation model can be used. When the coefficient of determination is partialy large the power bassed on log-rank test overestimates the true value of power, but when coefficient of determination is near to difference between powers decreases zero. By increasing of regression coefficient of determination, the difference between the log-rank test and adjusted coefficient of determination of this paper increases. Survival analysis, Sample size determination, non -randomized survival analysis, censored data, non-censored data Medicine R M RAHGOZAR verfasserin aut In Journal of Research in Medical Sciences Wolters Kluwer Medknow Publications, 2005 8(2003), 2 (DE-627)608492930 (DE-600)2513075-4 17357136 nnns volume:8 year:2003 number:2 https://doaj.org/article/5eca91a8a77845d1ba7b5fad8361cfb0 kostenfrei http://journals.mui.ac.ir/jrms/article/view/2994 kostenfrei https://doaj.org/toc/1735-1995 Journal toc kostenfrei https://doaj.org/toc/1735-7136 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ AR 8 2003 2 |
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Fixed - effect multiple linear regression analysis covers this need and this feature could be extended to survival regression analysis. This paper is the result of sample size determination in non-randomnized surval analysis with censored and non -censored data. Methods: In non-randomnized survival studies, linear regression with fixed -effect variable could be used. In fact such a regression is conditional expectation of dependent variable, conditioned on independent variable. Likelihood fuction with exponential hazard constructed by considering binary variable for allocation of each subject to one of two comparing groups, stating the variance of coefficient of fixed - effect independent variable by determination coefficient , sample size determination formulas are obtained with both censored and non-cencored data. So estimation of sample size is not based on the relation of a single independent variable but it could be attain the required power for a test adjusted for effect of the other explanatory covariates. Since the asymptotic distribution of the likelihood estimator of parameter is normal, we obtained the variance of the regression coefficient estimator formula then by stating the variance of regression coefficient of fixed-effect variable, by determination coefficient we derived formulas for determination of sample size in both censored and non-censored data. Results: In no-randomnized survival analysis ,to compare hazard rates of two groups without censored data, we obtained an estimation of determination coefficient ,risk ratio and proportion of membership to each group and their variances from likelihood function, when data has censored cases an estimate of the probability of censorship should be considered, after obtaining the varince of maximum likelihood estimator and considering its asymptotic normal distribution and by using coefficient of determination, formulas have been derived. The derived sample size formulas could attain the required power for a test adjuasted for effect of other explanatory covariates. Discussion: application of regression model in non-randomnized survival analysis helps to derive suitable formulas to determin sample size in both randomized and non-randomnized studies in a error level, to attain necessary statistical power. In Coxs semiparametric proportional hazard model ,since the varince of the parameter can not be stated in a simple form ,a simulation model can be used. When the coefficient of determination is partialy large the power bassed on log-rank test overestimates the true value of power, but when coefficient of determination is near to difference between powers decreases zero. 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S FAGHIHZADEH misc Survival analysis, Sample size determination, non -randomized survival analysis, censored data, non-censored data misc Medicine misc R SAMPLE SIZE DETERMINATION IN NON-RADOMIZED SURVIVAL STUDIES WITH NON-CENSORED AND CENSORED DATA |
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SAMPLE SIZE DETERMINATION IN NON-RADOMIZED SURVIVAL STUDIES WITH NON-CENSORED AND CENSORED DATA Survival analysis, Sample size determination, non -randomized survival analysis, censored data, non-censored data |
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SAMPLE SIZE DETERMINATION IN NON-RADOMIZED SURVIVAL STUDIES WITH NON-CENSORED AND CENSORED DATA |
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sample size determination in non-radomized survival studies with non-censored and censored data |
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SAMPLE SIZE DETERMINATION IN NON-RADOMIZED SURVIVAL STUDIES WITH NON-CENSORED AND CENSORED DATA |
| abstract |
Introduction: In survival analysis, determination of sufficient sample size to achieve suitable statistical power is important .In both parametric and non-parametric methods of classic statistics, randomn selection of samples is a basic condition. practically, in most clinical trials and health surveys randomn allocation is impossible. Fixed - effect multiple linear regression analysis covers this need and this feature could be extended to survival regression analysis. This paper is the result of sample size determination in non-randomnized surval analysis with censored and non -censored data. Methods: In non-randomnized survival studies, linear regression with fixed -effect variable could be used. In fact such a regression is conditional expectation of dependent variable, conditioned on independent variable. Likelihood fuction with exponential hazard constructed by considering binary variable for allocation of each subject to one of two comparing groups, stating the variance of coefficient of fixed - effect independent variable by determination coefficient , sample size determination formulas are obtained with both censored and non-cencored data. So estimation of sample size is not based on the relation of a single independent variable but it could be attain the required power for a test adjusted for effect of the other explanatory covariates. Since the asymptotic distribution of the likelihood estimator of parameter is normal, we obtained the variance of the regression coefficient estimator formula then by stating the variance of regression coefficient of fixed-effect variable, by determination coefficient we derived formulas for determination of sample size in both censored and non-censored data. Results: In no-randomnized survival analysis ,to compare hazard rates of two groups without censored data, we obtained an estimation of determination coefficient ,risk ratio and proportion of membership to each group and their variances from likelihood function, when data has censored cases an estimate of the probability of censorship should be considered, after obtaining the varince of maximum likelihood estimator and considering its asymptotic normal distribution and by using coefficient of determination, formulas have been derived. The derived sample size formulas could attain the required power for a test adjuasted for effect of other explanatory covariates. Discussion: application of regression model in non-randomnized survival analysis helps to derive suitable formulas to determin sample size in both randomized and non-randomnized studies in a error level, to attain necessary statistical power. In Coxs semiparametric proportional hazard model ,since the varince of the parameter can not be stated in a simple form ,a simulation model can be used. When the coefficient of determination is partialy large the power bassed on log-rank test overestimates the true value of power, but when coefficient of determination is near to difference between powers decreases zero. By increasing of regression coefficient of determination, the difference between the log-rank test and adjusted coefficient of determination of this paper increases. |
| abstractGer |
Introduction: In survival analysis, determination of sufficient sample size to achieve suitable statistical power is important .In both parametric and non-parametric methods of classic statistics, randomn selection of samples is a basic condition. practically, in most clinical trials and health surveys randomn allocation is impossible. Fixed - effect multiple linear regression analysis covers this need and this feature could be extended to survival regression analysis. This paper is the result of sample size determination in non-randomnized surval analysis with censored and non -censored data. Methods: In non-randomnized survival studies, linear regression with fixed -effect variable could be used. In fact such a regression is conditional expectation of dependent variable, conditioned on independent variable. Likelihood fuction with exponential hazard constructed by considering binary variable for allocation of each subject to one of two comparing groups, stating the variance of coefficient of fixed - effect independent variable by determination coefficient , sample size determination formulas are obtained with both censored and non-cencored data. So estimation of sample size is not based on the relation of a single independent variable but it could be attain the required power for a test adjusted for effect of the other explanatory covariates. Since the asymptotic distribution of the likelihood estimator of parameter is normal, we obtained the variance of the regression coefficient estimator formula then by stating the variance of regression coefficient of fixed-effect variable, by determination coefficient we derived formulas for determination of sample size in both censored and non-censored data. Results: In no-randomnized survival analysis ,to compare hazard rates of two groups without censored data, we obtained an estimation of determination coefficient ,risk ratio and proportion of membership to each group and their variances from likelihood function, when data has censored cases an estimate of the probability of censorship should be considered, after obtaining the varince of maximum likelihood estimator and considering its asymptotic normal distribution and by using coefficient of determination, formulas have been derived. The derived sample size formulas could attain the required power for a test adjuasted for effect of other explanatory covariates. Discussion: application of regression model in non-randomnized survival analysis helps to derive suitable formulas to determin sample size in both randomized and non-randomnized studies in a error level, to attain necessary statistical power. In Coxs semiparametric proportional hazard model ,since the varince of the parameter can not be stated in a simple form ,a simulation model can be used. When the coefficient of determination is partialy large the power bassed on log-rank test overestimates the true value of power, but when coefficient of determination is near to difference between powers decreases zero. By increasing of regression coefficient of determination, the difference between the log-rank test and adjusted coefficient of determination of this paper increases. |
| abstract_unstemmed |
Introduction: In survival analysis, determination of sufficient sample size to achieve suitable statistical power is important .In both parametric and non-parametric methods of classic statistics, randomn selection of samples is a basic condition. practically, in most clinical trials and health surveys randomn allocation is impossible. Fixed - effect multiple linear regression analysis covers this need and this feature could be extended to survival regression analysis. This paper is the result of sample size determination in non-randomnized surval analysis with censored and non -censored data. Methods: In non-randomnized survival studies, linear regression with fixed -effect variable could be used. In fact such a regression is conditional expectation of dependent variable, conditioned on independent variable. Likelihood fuction with exponential hazard constructed by considering binary variable for allocation of each subject to one of two comparing groups, stating the variance of coefficient of fixed - effect independent variable by determination coefficient , sample size determination formulas are obtained with both censored and non-cencored data. So estimation of sample size is not based on the relation of a single independent variable but it could be attain the required power for a test adjusted for effect of the other explanatory covariates. Since the asymptotic distribution of the likelihood estimator of parameter is normal, we obtained the variance of the regression coefficient estimator formula then by stating the variance of regression coefficient of fixed-effect variable, by determination coefficient we derived formulas for determination of sample size in both censored and non-censored data. Results: In no-randomnized survival analysis ,to compare hazard rates of two groups without censored data, we obtained an estimation of determination coefficient ,risk ratio and proportion of membership to each group and their variances from likelihood function, when data has censored cases an estimate of the probability of censorship should be considered, after obtaining the varince of maximum likelihood estimator and considering its asymptotic normal distribution and by using coefficient of determination, formulas have been derived. The derived sample size formulas could attain the required power for a test adjuasted for effect of other explanatory covariates. Discussion: application of regression model in non-randomnized survival analysis helps to derive suitable formulas to determin sample size in both randomized and non-randomnized studies in a error level, to attain necessary statistical power. In Coxs semiparametric proportional hazard model ,since the varince of the parameter can not be stated in a simple form ,a simulation model can be used. When the coefficient of determination is partialy large the power bassed on log-rank test overestimates the true value of power, but when coefficient of determination is near to difference between powers decreases zero. By increasing of regression coefficient of determination, the difference between the log-rank test and adjusted coefficient of determination of this paper increases. |
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