A study of R2 measure under the accelerated failure time models

For right-censored data, the accelerated failure time (AFT) model is an alternative to the commonly used proportional hazards regression model. It is a linear model for the (log-transformed) outcome of interest, and is particularly useful for censored outcomes that are not time-to-event, such as laboratory measurements. We provide a general and easily computable definition of the R² measure of explained variation under the AFT model for right-censored data. We study its behavior under different censoring scenarios and under different error distributions; in particular, we also study its robustness when the parametric error distribution is misspecified. Based on Monte Carlo investigation results, we recommend the log-normal distribution as a robust error distribution to be used in practice for the parametric AFT model, when the R² measure is of interest. We apply our methodology to an alcohol consumption during pregnancy data set from Ukraine.     

New regression model with four regression structures and computational aspects

A new general class of exponentiated sinh Cauchy regression models for location, scale, and shape parameters is introduced and studied. It may be applied to censored data and used more effectively in survival analysis when compared with the usual models. For censored data, we employ a frequentist analysis for the parameters of the proposed model. Further, for different parameter settings, sample sizes, and censoring percentages, various simulations are performed. The extended regression model is very useful for the analysis of real data and could give more adequate fits than other special regression models.     

Estimation of coefficient of dispersion using auxiliary information

In this note, we consider the problem of estimation of coefficient of dispersion of a study variable by making use of known value of the coefficient of dispersion of an auxiliary variable. We propose ratio and regression-type estimators. We derive expressions of bias and variance of the proposed estimators to the first order of approximation. The relative efficiencies of the ratio and regression-type estimators with respect to the naïve estimator are investigated through a simulation study.     

Distributions of statistics describing concentration of runs in non homogeneous Markov-dependent trials

In the first n, n ? 3, trials of a non homogeneous zero-one Markov chain of first order, we consider runs of ones of length exceeding a threshold. The article deals with statistics denoting, the length and the position of the shortest segment of the chain in which all such runs of ones are concentrated. The study provides recursive schemes for conditional distributions of these statistics. Numerical examples illustrate the theoretical results.     

Simultaneous estimation of means of two sensitive variables

In this paper, we introduce a new problem of simultaneous estimation of means of two quantitative sensitive variables by using only one randomized response another pseudo response from a respondent in a sample. The proposed estimators are extended to stratified random sampling, and the relative efficiency values are computed for equal, proportional, and optimum allocation with respect to the newly introduced naïve estimators.     

Two multivariate generalized beta families

A multivariate generalized beta distribution is introduced that extends the univariate generalized beta distribution and includes many multivariate distributions, such as the multivariate beta of the first and second kind, the generalized gamma, and the Burr and Dirichlet distributions as special and limiting cases. These interrelationships can be illustrated using a distributional family tree. The corresponding marginal distributions are univariate generalized beta distributions and their special cases. Selected expressions for the moments are reported, and an application to the joint distribution of income and wealth is presented. A simple transformation of the multivariate generalized beta distribution leads to what will be referred to as a multivariate exponential generalized beta distribution, which includes a multivariate form of the logistics and Burr distributions as special cases.     

Computer experiment designs for accurate prediction

Computer experiments using deterministic simulators are sometimes used to replace or supplement physical system experiments. This paper compares designs for an initial computer simulator experiment based on empirical prediction accuracy; it recommends designs for producing accurate predictions. The basis for the majority of the designs compared is the integrated mean squared prediction error (IMSPE) that is computed assuming a Gaussian process model with a Gaussian correlation function. Designs that minimize the IMSPE with respect to a fixed set of correlation parameters as well as designs that minimize a weighted IMSPE over the correlation parameters are studied. These IMSPE-based designs are compared with three widely-used space-filling designs. The designs are used to predict test surfaces representing a range of stationary and non-stationary functions. For the test conditions examined in this paper, the designs constructed under IMSPE-based criteria are shown to outperform space-filling Latin hypercube designs and maximum projection designs when predicting smooth functions of stationary appearance, while space-filling and maximum projection designs are superior for test functions that exhibit strong non-stationarity.     

Fast computation of spatially adaptive kernel estimates

Kernel smoothing of spatial point data can often be improved using an adaptive, spatially varying bandwidth instead of a fixed bandwidth. However, computation with a varying bandwidth is much more demanding, especially when edge correction and bandwidth selection are involved. This paper proposes several new computational methods for adaptive kernel estimation from spatial point pattern data. A key idea is that a variable-bandwidth kernel estimator for d-dimensional spatial data can be represented as a slice of a fixed-bandwidth kernel estimator in \((d+1)\)-dimensional scale space, enabling fast computation using Fourier transforms. Edge correction factors have a similar representation. Different values of global bandwidth correspond to different slices of the scale space, so that bandwidth selection is greatly accelerated. Potential applications include estimation of multivariate probability density and spatial or spatiotemporal point process intensity, relative risk, and regression functions. The new methods perform well in simulations and in two real applications concerning the spatial epidemiology of primary biliary cirrhosis and the alarm calls of capuchin monkeys.     

A joint model of cancer incidence,metastasis, and mortality

Many diseases, especially cancer, are not static, but rather can be summarized by a series of events or stages (e.g. diagnosis, remission, recurrence, metastasis, death). Most available methods to analyze multi-stage data ignore intermediate events and focus on the terminal event or consider (time to) multiple events as independent. Competing-risk or semi-competing-risk models are often deficient in describing the complex relationship between disease progression events which are driven by a shared progression stochastic process. A multi-stage model can only examine two stages at a time and thus fails to capture the effect of one stage on the time spent between other stages. Moreover, most models do not account for latent stages. We propose a semi-parametric joint model of diagnosis, latent metastasis, and cancer death and use nonparametric maximum likelihood to estimate covariate effects on the risks of intermediate events and death and the dependence between them. We illustrate the model with Monte Carlo simulations and analysis of real data on prostate cancer from the SEER database.