On Estimating Survival and Hazard Ratios Using One Time-Scale When Cohort Data Have Multiple Time-Scales: A Simulation Study
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Abstract Background : When estimating survival functions and hazard ratios during theanalysis of cohort data, we often choose one time-scale, such as time-on-study, asthe primary time-scale, and include a xed covariate, such as age at entry, in themodel. However, we rarely consider the possibility of simultaneous effects ofmultiple time-scales on the hazard function. Methods : In a simulation study, within the framework of exible parametricmodels, we investigate whether relying on one time-scale and xed covariate asproxy for the second time-scale is sucient in capturing the true survivalfunctions and hazard ratios when there are actually two underlying time-scales. Result : We demonstrate that the one-time-scale survival models appeared toapproximate well the survival proportions, however, large bias was observed in thelog hazard ratios if the covariate of interest had interactions with the secondtime-scale or with both time-scales. Conclusion : We recommend to exercise caution and encourage tting modelswith multiple time-scales if it is suspected that the cohort data have underlyingnon-proportional hazards on the second time-scale or both time-scales.Keywords:
Survival function
Abstract For the past two decades the Cox proportional hazards model has been used extensively to examine the covariate effects on the hazard function for the failure time variable. On the other hand, the accelerated failure time model, which simply regresses the logarithm of the survival time over the covariates, has seldom been utilized in the analysis of censored survival data. In this article, we review some newly developed linear regression methods for analysing failure time observations. These procedures have sound theoretical justification and can be implemented with an efficient numerical method. The accelerated failure time model has an intuitive physical interpretation and would be a useful alternative to the Cox model in survival analysis.
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Proportional Hazards models have been widely used to analyze survival data. In many cases survival data do not verify the assumption of proportional hazards. An alternative to the PH models with more relaxed conditions are Accelerated Failure Time models. These models are fairly commonly used in the field of manufacturing, but they are more and more frequent for modeling clinical trial data. They focus on the direct effect of the explanatory variables on the survival function allowing an easier interpretation of the effect of the corresponding covariates on the survival time. Optimal experimental designs are computed in this framework for Type I and random arrival. The results are applied to clinical models used to prevent tuberculosis in Ugandan adults infected with HIV.
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Abstract Graphical representation of statistical results is often used to assist readers in the interpretation of the findings. This is especially true for survival analysis where there is an interest in explaining the patterns of survival over time for specific covariates. For fixed categorical covariates, such as a group membership indicator, Kaplan‐Meier estimates (1958) can be used to display the curves. For time‐dependent covariates this method may not be adequate. Simon and Makuch (1984) proposed a technique that evaluates the covariate status of the individuals remaining at risk at each event time. The method takes into account the change in an individual's covariate status over time. The survival computations are the same as the Kaplan‐Meier method, in that the conditional survival estimates are the function of the ratio of the number of events to the number at risk at each event time. The difference between the two methods is that the individuals at risk within each level defined by the covariate is not fixed at time 0 in the Simon and Makuch method as it is with the Kaplan‐Meier method. Examples of how the two methods can differ for time dependent covariates in Cox proportional hazards regression analysis are presented. Copyright © 2002 Whurr Publishers Ltd.
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Extensions of the Kaplan-Meier estimator have been developed to illustrate the relationship between a time-varying covariate of interest and survival. In particular, Snapinn et al and Xu et al developed estimators to display survival for patients who always have a certain value of a time-varying covariate. These estimators properly handle time-varying covariates, but their clinical interpretation is limited. It is of greater clinical interest to display survival for patients whose covariates lie along certain defined paths. In this article, we propose extensions of Snapinn et al and Xu et al's estimators, providing crude and covariate-adjusted estimates of the survival function for patients defined by covariate paths. We also derive analytical variance estimators. We demonstrate the utility of these estimators with medical examples and a simulation study.
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The restricted mean survival time is a clinically easy-to-interpret measure that does not require any assumption of proportional hazards. We focus on two ways to directly model the survival time and adjust the covariates. One is to calculate the pseudo-survival time for each subject using leave-one-out, and then perform a model analysis using all pseudo-values to adjust for covariates. The pseudo-survival time is used to reflect information of censored subjects in the model analysis. The other method adjusts for covariates using subjects for whom the time-to-event was observed while adjusting for the censored subjects using the inverse probability of censoring weighting (IPCW). This paper evaluates the performance of these two methods in terms of the power to detect group differences through a simple example dataset and computer simulations. The simple example illustrates the intuitive behavior of the two methods. With the method using pseudo-survival times, it is difficult to interpret the pseudo-values. We confirm that the pseudo-survival times are different from the actual data obtained in a primary biliary cholangitis clinical trial because of the many censored data. In the simulations, the method using IPCW is found to be more powerful. Even in the case of group differences with respect to the censor incidence rates and covariates, the method using IPCW maintains a nominal significance level for the type-1 error rate. We conclude that the IPCW method should be used to estimate the restricted mean survival time when adjusting the covariates.
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This research aimed to estimate the effects of prognostic factors on chest cancer survival, the research studied two models in survival analysis; the Cox-Proportional Hazard (PH) model is most usable method in present time of survival data in the occurrence covariate or prognosticates aspects, and the Accelerated Failure Time (AFT) model is another substitute way for analysis of survival data. Kaplan-Meier method has been applied to survival function and hazard function for estimation, the log-rank test was used to test the differences in the survival analysis. The data was obtained from Nanakali Hospital in the period from 1 st January 2013 to 31 st December 2017 with follow up period until 1 st April 2018. The results for Kaplan-Meier and log-rank test showed the significant difference in survival or death by chest cancer for all presented related prognostic factors. The Cox-PH and AFT model does not identify the same prognostic factors that influenced in chest cancer survival. The Cox Proportional Hazards model displays a significant lack of fit while the accelerated failure time model describes the data well. AFT with Weibull distribution was chosen to be the best model for our data by using Tow model selection criterion; Akaike Information Criterion (AIC) and Bayesian information criterion (BIC). Also, the results performed by the statistical package in Mat-lab, Stat-graphic and SPSS, which was used to analyze the data. Key words: Survival Analysis, Cox-proportional hazard, Accelerated Failure Time, Kaplan Meier , Log-Rank test , Chest Cancer. .
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The analysis of time-to-event data, often referred to as survival data or in some circumstances failure time data, refers to the study of durations, whether that is a duration of a lifetime or more generally the time until an event of interest occurs. This chapter discusses regression analysis of time-to-event data. It provides a discussion of the two commonly-used summaries of the distribution of survival data, the survival function and the hazard function. The chapter discusses accelerated failure time models, which are the natural generalization of the regression models. It reviews parametric models, in which the relationship between expected survival time and the predictors and the distribution of survival times are explicitly specified, taking potential censoring into account. Adaptation of the Kaplan-Meier estimator and the Cox proportional hazards model to left-truncated/right-censored data is straightforward, involving two modifications.
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Survival or failure time traits such as herd life and days open are both important economically and pose a number of challenges to an analysis based on linear mixed models. The main features of a survival trait are that it is the time until some event occurs, and some of the observations are censored. Survival models and the associated estimation procedures provide a flexible means of modeling survival traits. In this paper I will discuss the application of survival analysis based on the Weibull distribution. The components that make up a survival model will be presented along with their interpretation. Issues related to the model construction and estimation will be presented.
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The prelims comprise: Analyzing the time to an event Survival data Censoring Survivor and hazard functions Setting up a survival data set in Stata Kaplan–Meier nonparametric method Comparing survival outcomes: Kaplan–Meier method Cox semiparametric method, and a brief mention of parametric methods Survival analysis:summary and comparison to logistic regression
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