Generalized Linear Models

The importance of random number generators has increased over the years. This follows from the fact that contemporary research methods rely more and more on simulation and the increased importance of encryption technology. The output of a random number generator is created by either an algorithm or a physical device. The most popular method for random number generation is through the use of an algorithm. This article presents a new category of physical random bit generator that is packaged by several manufacturers. A statistical analysis of the output from the generators is given.     

On computer generation of gamma random variables by rejection and composition procedures 2

The paper presents various algorithms for generating gamma random variables, by combining rejection and composition procedures. Two efficient algorithms are given for the case when the parameter of the gamma distribution is 0<v<l. For the case vl, several algorithms are given but they (except one), work reliably only for small values of v. Results of some computer tests together with FORTRAN subroutines are also presented.     

Dependence Estimation Over a Finite Bivariate Failure Time Region

This articleconcerns nonparametric estimation of association between bivariatefailure times. In the presence of independent right censoring,the support for failure time variates may be restricted and measuresof dependence over a finite failure time region may be of particularinterest. To this end, the reciprocal cross ratio function, weightedby the bivariate failure time density, is proposed as a summarymeasure of dependence over a failure time region. This `relativerisk' estimator is shown to be consistent and asymptoticallynormally distributed, with consistent bootstrap variance estimator.A finite-region version of Kendall's tau, which is suitable forcensored failure time data, is also proposed, and correspondingasymptotic distribution theory is noted. The accuracy of theseasymptotic approximations is studied in simulations and an illustrationis provided.     

Bayesian Estimation of Survival Functions under Stochastic Precedence

When estimating the distributions of two random variables, X and Y, investigators often have prior information that Y tends to be bigger than X. To formalize this prior belief, one could potentially assume stochastic ordering between X and Y, which implies Pr(X < or = z) > or = Pr(Y < or = z) for all z in the domain of X and Y. Stochastic ordering is quite restrictive, though, and this article focuses instead on Bayesian estimation of the distribution functions of X and Y under the weaker stochastic precedence constraint, Pr(X < or = Y) > or = 0.5. We consider the case where both X and Y are categorical variables with common support and develop a Gibbs sampling algorithm for posterior computation. The method is then generalized to the case where X and Y are survival times. The proposed approach is illustrated using data on survival after tumor removal for patients with malignant melanoma.     

Regression Analysis of Restricted Mean Survival Time Based on Pseudo-Observations

Regression models for survival data are often specified from the hazard function while classical regression analysis of quantitative outcomes focuses on the mean value (possibly after suitable transformations). Methods for regression analysis of mean survival time and the related quantity, the restricted mean survival time, are reviewed and compared to a method based on pseudo-observations. Both Monte Carlo simulations and two real data sets are studied. It is concluded that while existing methods may be superior for analysis of the mean, pseudo-observations seem well suited when the restricted mean is studied.     

Optimal estimation of a finite population mean under generalized random permutation models

Employing certain generalized random permutation models and a general class of linear estimators of a finite population mean, it is shown that many of the conventional estimators are “optimal” in the sense of minimum average mean square error. Simple proofs are provided by using a well-known theorem on UMV estimation. The results also cover certain simple response error situations.     

Estimation of a Change Point in a Hazard Function Based on Censored Data

The hazard function plays an important role in reliability or survival studies since it describes the instantaneous risk of failure of items at a time point, given that they have not failed before. In some real life applications, abrupt changes in the hazard function are observed due to overhauls, major operations or specific maintenance activities. In such situations it is of interest to detect the location where such a change occurs and estimate the size of the change. In this paper we consider the problem of estimating a single change point in a piecewise constant hazard function when the observed variables are subject to random censoring. We suggest an estimation procedure that is based on certain structural properties and on least squares ideas. A simulation study is carried out to compare the performance of this estimator with two estimators available in the literature: an estimator based on a functional of the Nelson-Aalen estimator and a maximum likelihood estimator. The proposed least squares estimator tums out to be less biased than the other two estimators, but has a larger variance. We illustrate the estimation method on some real data sets.     

A joint modelling approach for clustered recurrent events and death events

In dental implant research studies, events such as implant complications including pain or infection may be observed recurrently before failure events, i.e. the death of implants. It is natural to assume that recurrent events and failure events are correlated to each other, since they happen on the same implant (subject) and complication times have strong effects on the implant survival time. On the other hand, each patient may have more than one implant. Therefore these recurrent events or failure events are clustered since implant complication times or failure times within the same patient (cluster) are likely to be correlated. The overall implant survival times and recurrent complication times are both interesting to us. In this paper, a joint modelling approach is proposed for modelling complication events and dental implant survival times simultaneously. The proposed method uses a frailty process to model the correlation within cluster and the correlation within subjects. We use Bayesian methods to obtain estimates of the parameters. Performance of the joint models are shown via simulation studies and data analysis.     

Asymptotic Distributions of Unit-Root Tests When the Process Is Nearly Stationary

Several test criteria are available for testing the hypothesis that the autoregressive polynomial of an autoregressive moving average process has a single unit root. Schwert (1989), using a Monte Carlo study, investigated the performance of some of the available test criteria. He concluded that the actual levels of the test criteria considered in his study are far from the specified levels when the moving average polynomial also has a root close to 1. This article studies the asymptotic null distribution of the test statistics for testing p = 1 in the model Y_t = pY _t-1 + e _t – 0e _t-1 as 0 approaches 1. It is shown that the test statistics differ from one another in their asymptotic properties depending on the rate at which 0 converges to 1.     

Multivariate forests with missing mixed outcomes

In this article, we propose a multivariate random forest method for multiple responses of mixed types with missing responses. Imputation is performed for each bootstrap sample used to build the individual trees that form the forest. The individual trees are built using a weighted splitting rule allowing downweighting of imputed observations. A simulation study shows the benefits of this approach over complete case analysis when missing responses are missing completely at random and missing at random (MAR). In particular, the gain in prediction accuracy of the proposed method is larger in the MAR case and also increases as the proportion of missing increases.