How to use χ2 test correctly——the log-rank test and the implementation of SAS software / 四川精神卫生

The purpose of this article was to introduce the log-rank test and the SAS implementation. There were many different expression forms for the test statistics of the log-rank tests. Among them， there were two most common expression forms： the first was similar to "Pearson΄s goodness-of-fit χ2 test statistic"； the second was similar to "the test statistic of the odds ratio of high-dimensional table data， that was， the Breslow-Day΄s χ2 test statistic". The log-rank test statistic had two distribution types， one was the χ2 distribution， the other was the standard normal distribution. In the process of constructing log-rank test statistics， there were four contents that needed to be paid attention to： ① the sequential multiple four-fold tables formed by stratification or partition after sorting according to the individual "survival time"； ② it was necessary to distinguish whether the "survival time of each individual" was the complete data or the censored data； ③ only the calculation of the "theoretical or expected frequency" on a specific grid ［for example， （1，1） grid］ in each four-fold table data； ④ the method of calculating the theoretical frequency was different from the one in the independent test of the data of the four-fold table. Based on two examples with the different data structures， the paper realized the log-rank tests with the help of the SAS software.

What Should We Consider Carefully When Performing Survival Analysis? / 임상소아혈액종양

The survival data and the survival analysis are the data and analysis methods used to study the probability of survival. The survival data consist of a period from the juncture of a start event to the juncture of the end event (occurrence event). The period is called the survival period or survival time. In this way, the method of analysing the survival time of subjects and appropriately summarizing the degree of survival is called survival analysis. To understand and analyse survival analysis methods, researchers must be aware of some concepts. Concepts to be aware of in the survival analysis include events, censored data, survival period, survival function, survival curve and so on. This review focuses on the terms and concepts used in the survival analysis. It will also cover the types of survival data that should be collected and prepared when using actual survival analysis method and how to prepare them.

Use of interval-censored survival data as an alternative to Kaplan-Meier survival curves: studies of oral lesion occurrence in liver transplants and cancer recurrence

After undergoing liver transplantation, children are susceptible to oral lesions due to immunosuppressant drugs that are needed to maintain the transplant. In this context, it is important to understand how disease characteristics and age at transplantation influence the development of these lesions. Monitoring of lesions begins after transplantation and children are usually observed by a specialist in stomatology at periodic visits. Consequently, lesion development is estimated to occur between two observed times, and this is characterized as interval-censored data. However, in clinical practice, it is common to assume the moment of observation as the time of event occurrence, thereby excluding interval-censored data. Here, we discuss the impact of excluding interval-censored mechanisms in statistical analyses by using simulation studies to consider differences in sample sizes and amplitudes between observed intervals. Then, application studies are presented which use a data set from a prospective study that was conducted to investigate oral lesions in patients after liver transplantation at the A.C.Camargo Cancer Center in Brazil between 2013 and 2016 and a data set involving recurrent ovarian cancer in patients diagnosed with high-grade serous carcinoma at the A.C.Camargo Cancer Center between 2003 and 2016 (AU)

Survival analysis: Part I — analysis of time-to-event / 대한마취과학회지

Length of time is a variable often encountered during data analysis. Survival analysis provides simple, intuitive results concerning time-to-event for events of interest, which are not confined to death. This review introduces methods of analyzing time-to-event. The Kaplan-Meier survival analysis, log-rank test, and Cox proportional hazards regression modeling method are described with examples of hypothetical data.

Processing Methods of Censored Cost Data in Pharmacoeconomics Evaluation / 中国卫生经济

It introduced the types of censored cost data in pharmacoeconomics evaluation,and summarized the methods of recognizing and processing data to provide methodological references for the course of managing censored cost data while implementing pharmacoeconomics evaluation.

Influência de dados censurados no cálculo da concentração média das variáveis de qualidade da água demanda química de oxigênio e fosfato / The influence of censored data on computing mean concentrations of water quality variables chemical oxygen demand and phosphate

Um dos problemas comumente encontrado na análise estatística de dados provenientes do monitoramento da qualidade da água envolve os chamados dados censurados. Este estudo mostra como os valores calculados das concentração médias de amostras que contenham dados censurados são influenciadas pelo tamanho da amostra, percentual de dados censurados e método de cálculo. As concentrações médias foram calculadas com os métodos de substituição e maximum likelihood estimator (MLE) para amostras de demanda química de oxigênio e fosfato. O intervalo de confiança da média foi utilizado como métrica de comparação. Os resultados revelam que as concentrações médias calculadas com o método de substituição simples se posiciona fora do intervalo de confiança. Já o método MLE calcula valores aceitáveis, porém, a eficácia do método depende de um limite de elasticidade do nível de censura e do tamanho da amostra.

One of the most common problems in statistical analysis of data from water quality monitoring programs involves the so-called censored data. This study highlights how the sample mean concentration of chemical oxygen demand and phosphate variables are influenced by the estimation method, sample size and percentage of censored data. The confidence interval was used as a metric for comparison of calculated sample mean concentrations on both simple substitution and maximum likelihood estimator (MLE) methods. The results show that sample mean concentrations calculated by simple substitution method are positioned outside the confidence interval. Otherwise, the MLE method produces acceptable values for sample mean concentration, although the magnitude is constrained by sample size and percentage of censored data. The effectiveness of the method depends on an elastic limit of censoring level and sample size.

Aplicación del análisis estadístico de datos censurados para el manejo de respuestas incompletas en la escala CES-D / Application of censored-data analysis for managing CES-D incomplete responses

Purpose To provide an example of censored data analysis in the management of CED-S missing data, using a data set of a study conducted with Mexican rural women. Material and Methods Data used for this exercise were collected in a cross-sectional study with 416 women in the Mexican region known as the Mixteca Baja. Using a Survival Analysis (SA) focus we present a general description of the scores, along with the estimation of association patterns between those scores and the independent variables departing from Cox's proportional risk model. A comparison is made of these results and those obtained through a regression analysis. Results Using only the information from observations with complete data, the average CES-D score was 11.0 and the prevalence of symptoms above the cut-off point (16) was 23.2%. Twenty-six percent of the women did not respond to at least one item. When conducting the SA, the estimated mean score of the scale was 14.0. Survival above the cut-off point corresponded to an estimated prevalence of 21%. Conclusions SA is useful in the management of data sets with missing data in scales such as the CES-D. In this example, the increased percentage of observations with missing data produced a loss of precision in the estimators. The differences in mean item scores between observation with complete and incomplete data suggested a non-random, no-response pattern, if this is not taken into consideration it could bias the estimation in the scale mean and its association with other variables. Conducting SA we were able to use the information of most women participating in the study, including those who did not respond to all items in the scale.

Objetivo Ejemplificar el uso del análisis de datos censurados en el manejo de datos incompletos de la CES-D utilizando una base de datos de un estudio con mujeres rurales de México. Material y Método Los datos analizados se recogieron en un estudio transversal con 416 mujeres de la Mixteca Baja, al sur de México. Con un enfoque de Análisis de Supervivencia (AS), se presenta una descripción general del comportamiento de las puntuaciones de la CES-D junto con la estimación de patrones de asociación entre esos puntajes y variables independientes a partir del modelo de riesgos proporcionales de Cox, y se hace una comparación entre estos resultados y los obtenidos de un modelo de regresión lineal. Resultados Utilizando sólo la información de las observaciones con datos completos, la puntuación promedio de la CES-D fue de 11.0 y la preva-lencia de síntomas por arriba del punto de corte (16) fue de 23.2%. El 25.2% de las mujeres no contestó al menos un reactivo. Al hacer el AS, el promedio estimado de la puntuación fue de 14.8. La supervivencia por encima del punto de corte corresponde a una prevalencia estimada del 21%. Conclusiones El AS es útil en el manejo de bases que presentan datos faltantes por ejemplo en escalas como CES-D. En nuestro ejemplo, el elevado porcentaje de observaciones con respuestas faltantes ocasionó una pérdida de precisión en los estimadores. Las diferencias de puntuaciones promedio por reactivo entre observaciones con datos perdidos y completos sugieren un patrón de no-respuesta que no es aleatorio, y que de no tomarse en cuenta podría sesgar la estimación, tanto del promedio de la escala como de su asociación con otras variables. El AS utilizó la información de casi la totalidad de las participantes en el estudio incluyendo aquellas que no respondieron todos los reactivos de la escala.