Competing Risk Analysis of Censored Survival Data

A competing risk model is developed to accommodate both planned Type I censoring and random withdrawals. MLE's, their properties, confidence regions for parameters and mean lifetimes are obtained for a model regarding random censoring as a competing risk and compared to those obtained for the model in which withdrawals are regarded as random censoring. Estimated net and crude probabilities are calculated and compared for the two models. The model is developed for two competing risks, one following a Weibull distribution and the other a Rayleigh distribution, and random withdrawals following a Weibull distribution.     

Analysis of Survival Data with Two Dependent Competing Risks

Here we consider a competing risks model where the two risks of interest are not independent. The dependence is due to the additive effect of an independent contaminating risk on two initially independent risks. The problem is identifiable when the three risks fllow independent exponential distributions and also when the two initial risks follow proportional hazards model. Procedures are suggested for estimation and testing hypotheses regarding the parameters of the three exponentials in the first can and the constant of proportionality in the second case, when the information available consists of the times to death and the causes of death of the individuals.     

Estimation of Microorganism Counts in Agglutination and Enzyme Linked Immuno‐Sorbent Assays: Consequences of Ignoring Censored Data

The consequences of ignoring censored data on the estimation of mean microorganism counts using agglutination assays or certain classes of enzyme linked immuno‐sorbent assays are examined. It is shown that both overestimation and underestimation of the maximum likelihood estimate of the mean number of microorganisms per unit volume may occur if censored data are ignored. It is also shown that the asymptotic variance of the maximum likelihood estimate may either be increased or decreased if censored data are ignored. Data from a trial of vaccines against pig pneumonia and data from an equine health certification process are used as illustrations.     

Modeling Familial Association of Ages at Onset of Disease in the Presence of Competing Risk

Summary In genetic family studies, ages at onset of diseases are routinely collected. Often one is interested in assessing the familial association of ages at the onset of a certain disease type. However, when a competing risk is present and is related to the disease of interest, the usual measure of association by treating the competing event as an independent censoring event is biased. We propose a bivariate model that incorporates two types of association: one is between the first event time of paired members, and the other is between the failure types given the first event time. We consider flexible measures for both types of association, and estimate the corresponding association parameters by adopting the two‐stage estimation of Shih and Louis (1995, Biometrics 51, 1384–1399) and Nan et al. (2006, Journal of the American Statistical Association 101, 65–77). The proposed method is illustrated using the kinship data from the Washington Ashkenazi Study.     

混合分布理论及应用

本文介绍了混合分布的历史及其一般理论．在阐述混合分布理论在医学、农业、渔业、地理学等方面的应用以及在统计学其它有关分支中的应用的基础上,还详细讨论了这一理论可能在遗传分析中的作用,并提出一些值得进一步研究的问题．     

Parameter Estimation for Partially Complete Time and Type of Failure Data

The theory of competing risks has been developed to asses a specific risk in presence of other risk factors. In this paper we consider the parametric estimation of different failure modes under partially complete time and type of failure data using latent failure times and cause specific hazard functions models. Uniformly minimum variance unbiased estimators and maximum likelihood estimators are obtained when latent failure times and cause specific hazard functions are exponentially distributed. We also consider the case when they follow Weibull distributions. One data set is used to illustrate the proposed techniques. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling Information Quality Risk for Data Mining in Data Warehouses

Information Quality (IQ) is a critical factor for the success of many activities in the information age, including the development of data warehouses and implementation of data mining. The issue of IQ risk is recognized during the process of data mining; however, there is no formal methodological approach to dealing with such issues.

Consequently, it is essential to measure the risk of IQ in a data warehouse to ensure success in implementing data mining. This article presents a methodology to determine three IQ risk characteristics: accuracy, comprehensiveness, and non-membership. The methodology provides a set of quantitative models to examine how the quality risks of source information affect the quality for information outputs produced using the relational algebra operations: Restriction, Projection, and Cubic product. It can be used to determine how quality risks associated with diverse data sources affect the derived data. The study also develops a data cube model and associated algebra to support IQ risk operations.     

Flood Risk Analysis Based on Information Diffusion Theory

Due to the fact that the flood data series of small drainage basins is relatively short, available data are often not sufficient for flood risk analysis. This presents the problem of risk analysis using very small data samples. One method that can be applied is to regard the available small samples as fuzzy information and optimize them using information diffusion technology to yield analytical results with greater reliability. In this article a risk analysis method based on information diffusion theory is applied to create a new flood risk analysis model. Application of the model is illustrated taking the Jinhuajiang and Qujiang drainage basins as examples. This is a new attempt at applying information diffusion theory in flood risk analysis. Computations based on this analytical flood risk model can yield an estimated flood damage value that is relatively accurate. This study indicates that the aforementioned model exhibits fairly stable analytical results, even when using a small set of sample data. The results also indicate that information diffusion technology is highly capable of extracting useful information and therefore improves system recognition accuracy. This method can be easily applied and the analytical results produced are easy to understand. Results are accurate enough to act as a guide in disaster situations.     

Competing Risks Data Analysis with High-dimensional Covariates:An Application in Bladder Cancer

Analysis of microarray data is associated with the methodological problems of high dimension and small sample size. Various methods have been used for variable selection in highdimension and small sample size cases with a single survival endpoint. However, little effort has been directed toward addressing competing risks where there is more than one failure risks. This study compared three typical variable selection techniques including Lasso, elastic net, and likelihood-based boosting for high-dimensional time-to-event data with competing risks. The performance of these methods was evaluated via a simulation study by analyzing a real dataset related to bladder cancer patients using time-dependent receiver operator characteristic(ROC) curve and bootstrap.632+ prediction error curves. The elastic net penalization method was shown to outperform Lasso and boosting. Based on the elastic net, 33 genes out of 1381 genes related to bladder cancer were selected. By fitting to the Fine and Gray model, eight genes were highly significant(P 0.001). Among them, expression of RTN4, SON, IGF1 R, SNRPE, PTGR1, PLEK, and ETFDH was associated with a decrease in survival time, whereas SMARCAD1 expression was associated with an increase in survival time. This study indicates that the elastic net has a higher capacity than the Lasso and boosting for the prediction of survival time in bladder cancer patients.Moreover, genes selected by all methods improved the predictive power of the model based on only clinical variables, indicating the value of information contained in the microarray features.     

Estimation of Relative Risk in Case Control Studies Through Logistic Regression Analysis

Multiple logistic regression analysis is used to estimate the relative risk in case control studies. The estimators obtained are valid when disease is rare. In this paper an estimator of relative risk in a case control study has been proposed using logistic regression results when the incidence of disease is not small. The bias of the usual estimator through logistic regression as compared to the new estimator has been worked out. The expression of Mean Square Error of proposed estimator has been derived in situations when the incidence of disease is known exactly as well as when estimated through an independent survey. It has been observed that there is a significant bias using the conventional estimator of relative risk when incidence of disease is high. In such situations the proposed estimator can be used with advantage.     

A Study of Log-Logistic Model in Survival Analysis

In survival analysis when the mortality reaches a peak after some finite period and then slowly declines, it is appropriate to use a model which has a nonmonotonic failure rate. In this paper we study the log-logistic model whose failure rate exhibits the above behavior and its mean residual life behaves in the reverse fashion. The maximum likelihood estimation of the parameters is examined and it is proved analytically that unique maximum likelihood estimates exist for the parameters. A lung cancer data set is analyzed. Confidence intervals for the parameters as well as for the critical points of the failure rate and mean residual life functions are obtained for the high performance status (PS) and low PS subgroups, where the term performance status is a measure of general medical status.     

Birnbaum–Saunders frailty regression models: Diagnostics and application to medical data

In survival models, some covariates affecting the lifetime could not be observed or measured. These covariates may correspond to environmental or genetic factors and be considered as a random effect related to a frailty of the individuals explaining their survival times. We propose a methodology based on a Birnbaum–Saunders frailty regression model, which can be applied to censored or uncensored data. Maximum‐likelihood methods are used to estimate the model parameters and to derive local influence techniques. Diagnostic tools are important in regression to detect anomalies, as departures from error assumptions and presence of outliers and influential cases. Normal curvatures for local influence under different perturbations are computed and two types of residuals are introduced. Two examples with uncensored and censored real‐world data illustrate the proposed methodology. Comparison with classical frailty models is carried out in these examples, which shows the superiority of the proposed model.     

删失数据下非线性半参数回归模型中参数的经验似然推断

考察了响应变量在随机删失情形下的非线性半参数回归模型,构造了未知参数的经验对数似然比统计量和调整经验对数似然比统计量,证明在一定条件下,所构造的经验似然比统计量渐近于X~2分布,并由此构造出未知参数的置信域.此外,又构造了未知参数的最小二乘估计量,证明了它的渐近性质.通过模拟研究表明,经验似然方法在置信域的覆盖概率以及精度方面要优于最小二乘法.