Assessing the prediction accuracy of cure in the Cox proportional hazards cure model: an application to breast cancer data

A cure rate model is a survival model incorporating the cure rate with the assumption that the population contains both uncured and cured individuals. It is a powerful statistical tool for prognostic studies, especially in cancer. The cure rate is important for making treatment decisions in clinical practice. The proportional hazards (PH) cure model can predict the cure rate for each patient. This contains a logistic regression component for the cure rate and a Cox regression component to estimate the hazard for uncured patients. A measure for quantifying the predictive accuracy of the cure rate estimated by the Cox PH cure model is required, as there has been a lack of previous research in this area. We used the Cox PH cure model for the breast cancer data; however, the area under the receiver operating characteristic curve (AUC) could not be estimated because many patients were censored. In this study, we used imputation‐based AUCs to assess the predictive accuracy of the cure rate from the PH cure model. We examined the precision of these AUCs using simulation studies. The results demonstrated that the imputation‐based AUCs were estimable and their biases were negligibly small in many cases, although ordinary AUC could not be estimated. Additionally, we introduced the bias‐correction method of imputation‐based AUCs and found that the bias‐corrected estimate successfully compensated the overestimation in the simulation studies. We also illustrated the estimation of the imputation‐based AUCs using breast cancer data. Copyright © 2014 John Wiley & Sons, Ltd.     

Analysis of Order Statistics from Distributions with Regularly Varying Tails

In this article, necessary conditions for comparing order statistics from distributions with regularly varying tails are discussed in terms of various stochastic orders. A necessary and sufficient condition for stochastically comparing tail behaviors of order statistics is derived. The main results generalize and recover some results in Kleiber (2002 Kleiber, C. (2002). Variability ordering of heavy-tailed distributions with applications to order statistics. Statist. Probab. Lett. 58:381388.[Crossref], [Web of Science ®] , [Google Scholar], 2004 Kleiber, C. (2004). Lorenz ordering of order statistics from log-logistic and related distributions. J. Statist. Plann. Infer. 120:2004.[Crossref], [Web of Science ®] , [Google Scholar]). Extensions to coherent systems are mentioned as well.     

Do Central Bank Liquidity Facilities Affect Interbank Lending Rates?

In response to the global financial crisis that started in August 2007, central banks provided extraordinary amounts of liquidity to the financial system. To investigate the effect of central bank liquidity facilities on term interbank lending rates near the start of the crisis, we estimate a six-factor arbitrage-free model of U.S. Treasury yields, financial corporate bond yields, and term interbank rates. This model can account for fluctuations in the term structure of credit and liquidity spreads observed in the data. A significant shift in model estimates after the announcement of the liquidity facilities suggests that these central bank actions did help lower the liquidity premium in term interbank rates.     

One-sided trimming in small samples with asymmetric contamination

An estimator for location, given a sample of only four or five observations, is proposed. The underlying distribution on of the sample may (with probability p) be contaminated by an outlier from a rightly-skewed distribution. The estimator minimizes the maximum mean squared error over all values of p. In fact, there exists an estimator which is unbiased in both the outlier - free and extreme-outlier cases, but its mean square error is substantially higher than the mean squared error for the minimax estimator. Mean squared errors for various underlying distributional situations are calculated and compared with those of other location estimators such as the mean and the median.     

Decomposition for multivariate extremal processes

The probability distribution of an extremal process in R^d with independent max-increments is completely determined by its distribution function. The df of an extremal process is similar to the cdf of a random vector. It is a monotone function on (0, ∞) × R^d with values in the interval [0,1]. On the other hand the probability distribution of an extremal process is a probability measure on the space of sample functions. That is the space of all increasing right continuous functions y: (0, ∞) → R^d with the topology of weak convergence. A sequence of extremal processes converges in law if the probability distributions converge weakly. This is shown to be equivalent to weak convergence of the df's.

An extremal process Y: [0, ∞) → R^d is generated by a point process on the space [0, ∞) × [-∞, ∞)^d and has a decomposition Y = X v Z as the maximum of two independent extremal processes with the same lower curve as the original process. The process X is the continuous part and Z contains the fixed discontinuities of the process Y. For a real valued extremal process the decomposition is unique: for a multivariate extremal process uniqueness breaks down due to blotting.     

Sample Attrition and Labor Supply Response in Experimental Panel Data

Sample attrition is a potentially serious problem for analysis of panel data, particularly experimental panel data. In this article, a variety of estimation procedures are used to assess the importance of attrition bias in labor supply response to the Seattle and Denver Income Maintenance Experiments (SIME/DIME). Data from Social Security Administration earnings records and the SIME/DIME public use file are used to test various hypotheses concerning attrition bias. The study differs from previous research in that data on both attriters and nonattriters are used to estimate the experimental labor supply response. Although not conclusive, the analysis suggests that attrition bias is probably not a serious enough problem in the SIME/DIME data to warrant extensive correction procedures. The methodology used in this study could be applied to other panel data sets.     

Computation of the estimated parameters and wald statistic for the generalized growth curve model

Multivariate analysis is difficult when there are missing observations in the response vectors. Kleinbaum (1973) proposed a Wald statistic useful in the analysis of incomplete multivariate data. SUBROUTINE C0EF calculates the estimated parameter matrix g in the generalization of the Potthoff-Roy (1964) growth curve model proposed by Kleinbaum (1973). SUBROUTINE WALD calculates the Wald statistic for hypotheses of the form Hn: H 5 D = 0 as proposed by Kleinbaum (1973).     

Nonparametric Growth Curve Model with Local Linear Approximation

The growth curve model has been developed for longitudinal data, and its time trend is usually described by polynomials. However, it is difficult to interpret each coefficient of the polynomials with higher degrees, even when the number of repetitions is sufficiently large. We propose herein an alternative growth curve model having time-varying coefficients.