Adjuvant transarterial chemoembolization timing after radical resection is an independent prognostic factor for patients with hepatocellular carcinoma
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It has been reported that postoperative adjuvant TACE (PA-TACE) treatment decreases recurrence and significantly improves the survival of patients who undergo radical resection of hepatocellular carcinoma (HCC) with high-risk recurrence factors. However, when to perform PA-TACE has not been fully studied.We retrospectively collected the clinicopathologic characteristics of the patients with HCC between October 2013 and June 2020. The optimal cutoff value for PA-TACE time was determined based on the R package "maxstat". Logistic regression and Cox regression analysis were used to determine the effect of the choice of PA-TACE timing on prognosis.The analysis was performed on 789 patients with HCC, and 484 patients were finally involved and were divided into training cohort (378) and validation cohort (106). The PA-TACE timing was found to be associated with survival outcomes. Multivariate logistic analysis found independent predictors of the PA-TACE timing, including gender and history of HBV. Multivariate Cox analysis showed that Ki-67, tumor size, MVI and the PA-TACE timing were independent prognostic factors for RFS in HCC patients.Based on this study, HCC patients with high-risk recurrence factors can receive personalized assistance in undergoing PA-TACE treatment and improve their survival outcomes.Log-rank test
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This article introduces readers to survival (failure-time) models, with a focus on Kaplan-Meier curves, Cox regression and sample size estimation.An example is used to show readers how to calculate a Kaplan-Meier curve from first principles.What makes survival data unique is censoring. Readers should understand censoring before undertaking an analysis of survival data.The Cox model continues to set the standard for survival models, and will continue well into the future.
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Related Article, see p 971KEY POINT: Kaplan-Meier curves, log-rank-test, and Cox proportional hazards regression are common examples of “survival analysis” techniques, which are used to analyze the time until an event of interest occurs.In this issue of Anesthesia & Analgesia, Song et al1 report results of a randomized trial in which they studied the onset of labor analgesia with 3 different epidural puncture and maintenance techniques. These authors compared the techniques on the primary outcome of time until adequate analgesia was reached—defined as a visual analog scale (VAS) score of ≤30 mm—with Kaplan-Meier curves, log-rank tests, and Cox proportional hazards regression. In studies addressing the time until an event of interest occurs, some but not all patients will typically have experienced the event at the end of the follow-up period. Patients in whom the even has not occurred—or who are lost to follow-up during the observation period—are said to be “censored.” It is unknown when and, depending on the event, if the event will occur.2 Simply excluding censored patients from the analysis would bias the analysis results. Specific statistical methods are thus needed that can appropriately account for such censored patient observations. Since the event of interest is often death, these analyses are traditionally termed “survival analyses,” and the time until the event occurs is referred to as the “survival time.” However, as done by Song et al,1 these techniques can also be used for the analysis of the time to any other well-defined event. Among the many available survival analysis methods, Kaplan-Meier curves, log-rank tests to compare these curves, and Cox proportional hazards regression are most commonly used. The Kaplan-Meier method estimates the survival function, which is the probability of “surviving” (ie, the probability that the event has not yet occurred) beyond a certain time point. The corresponding Kaplan-Meier curve is a plot of probability (y-axis) against time (x-axis) (Figure). This curve is a step function in which the estimated survival probability drops vertically whenever one or more outcome events occurred with a horizontal time interval between events. Plotting several Kaplan-Meier curves in 1 figure allows for a visual comparison of estimated survival probabilities between treatment or exposure groups; the curves can formally be compared with a log-rank test. The null hypothesis tested by the log-rank test is that the survival curves are identical over time; it thus compares the entire curves rather than the survival probability at a specific time point.Figure.: Kaplan-Meier plot of the percentage of patients without adequate analgesia, redrawn from Figure 2 in Song et al.1 Note that the original figure plotted the probability of adequate analgesia, as this is easily interpretable for readers in the context of the study research aim. In contrast, we present the figure as conventionally done in a Kaplan-Meier curve or plot, with the estimated probability (here expressed as percentage) of “survival” plotted on the y-axis. Vertical drops in the plot indicate that one or more patients reached the end point of experiencing adequate analgesia at the respective time point. CEI indicates continuous epidural infusion; DPE, dural puncture epidural; EP, conventional epidural; PIEB, programmed intermittent epidural bolus.The log-rank test assesses statistical significance but does not estimate an effect size. Moreover, while there is a stratified log-rank test that can adjust the analysis for a few categorical variables, the log-rank test is essentially not useful to simultaneously analyze the relationships of multiple variables on the survival time. Thus, when researchers either desire (a) to estimate an effect size3 (ie, the magnitude of the difference between groups)—as done in the study by Song et al1—or (b) to test or control for effects of several independent variables on survival time (eg, to adjust for confounding in observational research),4 a Cox proportional hazards model is typically used. The Cox proportional hazards regression5 technique does not actually model the survival time or probability but the so-called hazard function. This function can be thought of as the instantaneous risk of experiencing the event of interest at a certain time point (ie, the probability of experiencing the event during an infinitesimally small time period). The event risk is inversely related to the survival function; thus, “survival” rapidly declines when the hazard rate is high and vice versa. The exponentiated regression coefficients in Cox proportional hazards regression can conveniently be interpreted in terms of a hazard ratio (HR) for a 1-unit increase in the independent variable, for continuous independent variables, or versus a reference category, for categorical independent variables. While the HR is not the same as a relative risk, it can for all practical purposes be interpreted as such by researchers who are not familiar with the intricacies of survival analysis techniques. For those wishing to delve deeper into the details and learn more about survival analysis—including but not limited to the topics that we briefly touch on here—we refer to our tutorial on this topic previously published in Anesthesia & Analgesia.2 Importantly, even though the techniques discussed here do not make assumptions on the distribution of the survival times or survival probabilities, these analysis methods have other important assumptions that must be met for valid inferences, as also discussed in more detail in the previous tutorial.2
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In medical research, analyzing the time it takes for a phenomenon to occur is sometimes crucial. However, various factors can contribute to the length of survival or observation periods, and removing specific data can lead to bias results. In this paper, we discuss the Kaplan-Meier analysis and Cox proportional hazards regression model, which are the most frequently used methods in survival analysis. For the first step, we shall discuss the temporal concepts needed in survival analysis, such as cohort studies and then the basic statistical functions dealt with in survival analysis. After solidifying the concepts, methods of understanding and practical application of the Kaplan-Meier survival analysis is noted. After that, we will discuss the analysis methods for the Cox proportional hazards regression model, which includes multiple covariates. With the interpretation method of Cox proportional hazards regression result, we then discuss methods for checking the assumptions of the Cox proportional hazards regression, such as log minus log plots. Finally, we briefly explain the concept of time-dependent regression analysis. It is our aim that through this paper, readers can obtain an understanding on survival analysis and learn how to perform it.
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Introduction to Survival Analysis.- Kaplan-Meier Survival Curves and the Log-Rank Test.- The Cox Proportional Hazards Model and Its Characteristics.- Evaluating the Proportional Hazards Assumption.- The Stratified Cox Procedure.- Extension of the Cox Proportional Hazards Model for Time-Dependent Variables.- Parametric Survival Models.- Recurrent Events Survival Analysis.- Competing Risks Survival Analysis.
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A common objective in many medical studies is to investigate the survival time of an individual after being diagnosed with a particular disease or health related condition. In most survival analysis studies the analysis is based on modeling the probability of survival. One of the goals in a survival analysis is usually to model the survival function. This chapter presents three different approaches for modeling a survival function. They are the Kaplan–Meier method of modeling a survival function, the Cox proportional hazards model for a survivor function, and the use of logistic regression for modeling a binary survival response variable. It is important to note that the proportional hazards model is based on the actual survival times and the explanatory variables, a proportional hazards model will provide more information about the survival probabilities than will either the Kaplan–Meier model or a logistic regression model.
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Survival analysis of time to an event such as death or sickness. The survivorship function is estimated via the actuarial method and the Kaplan-Meier curve. Both are compared graphically and via the log-rank test. Stratification is needed when confounding is present. The Cox proportional hazard model incorporates covariates into the survival model. Other parametric and non-parametric models are discussed.
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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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Survival analysis is used to analyze data from patients who are followed for different periods of time and in whom the outcome of interest, a dichotomous event, may or may not have occurred at the time the study is halted; data from all patients are used in the analysis, including data from patients who dropped out, regardless of the duration of follow-up. This article discusses basic concepts in survival analysis, explains technical terms such as censoring, and provides reasons why ordinary methods of analysis cannot be applied to such data. The Kaplan-Meier survival curve is described, as is the Cox proportional hazards regression and the hazard ratio. Supplementary information includes a data file, graphs with explanations, and additional discussions; these are provided to enhance the reader's experience and understanding.
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