Analysis of Survival Data with Group Lasso

Identification of influential genes and clinical covariates on the survival of patients is crucial because it can lead us to better understanding of underlying mechanism of diseases and better prediction models. Most of variable selection methods in penalized Cox models cannot deal properly with categorical variables such as gender and family history. The group lasso penalty can combine clinical and genomic covariates effectively. In this article, we introduce an optimization algorithm for Cox regression with group lasso penalty. We compare our method with other methods on simulated and real microarray data sets.     

A Fresh Look at the Running Time Analysis for the Gibbs Sampler

As the Gibbs sampler has become one of the standard tools in computing, the practice of burn-in is almost the default option. Because it takes a certain number of iterations for the initial distribution to reach stationarity, supporters of burn-in will throw away an initial segment of the samples and argue that such a practice ensures unbiasedness. Running time analysis studies the question of how many samples to be thrown away. Basically, it equates the number of iterations to stationarity with the number of initial samples to be discarded. However, many practitioners have found that burn-in wastes potentially useful samples and the practice is inefficient, and thus unnecessary. For the example considered, a single chain without burn-in offers both efficiency and accuracy superior to multiple chains with burn-in. We show that the Gibbs sampler uses odds to generate samples. Because the correct odds are used from the onset of the iterative process, the observations generated by the Gibbs sampler are identically distributed as the target distribution; thus throwing away those valid samples is wasteful. When the chain of distributions and the trajectory (sample path) of the chain are considered based on their separate merits, the disagreement can be settled. We advocate carefully choosing the initial state, but without burn-in to quicken the formation of the stationary distribution.     

Approximate mrpp p-values obtained from four exact moments

A F0RTRAN-77 subroutine for a general version of multi-response permutation procedures (MRPP) is described. The exact four moments are employed in conjunction with the Pearson type I, type III, and type VI distributions to calculate the associated P-values.     

Recurrence relations for the moments of truncated multinormal distribution

In this paper some recurrence relations of moments of doubly truncated multivariate normal distribution are obtained. The bivariate case is given as an example and some applications are indicated.     

Multiple comparisons of matched proportions

It is well known (see, e.g., Scheffé (1959)) that if confidence intervals are desired for several treatment comparisons of interest, especially after a preliminary test of significance, then the appropriate technique is to consider simultaneous confidence intervals with a certain joint confidence coefficient. Goodman (1964) derived such simultaneous confidence intervals for contrasts among several multinomial populations, each with the same number, say J, of classes. The special case involving simultaneous confidence intervals for contrasts among several binomial populations on the basis of independent samples follows simply by taking J=2. This paper now deals with the problem of construction of simultaneous confidence intervals among probabilities of ‘success’ on the basis of matched samples.     

On Mixture Failure Rates Ordering

Mixtures of increasing failure rate distributions (IFR) can decrease at least in some intervals of time. Usually, this property can be observed asymptotically as t → ∞. This is due to the fact that the mixture failure rate is “bent down” compared with the corresponding unconditional expectation of the baseline failure rate, which was proved previously for some specific cases. We generalize this result and discuss the “weakest populations are dying first” property, which leads to the change in the failure rate shape. We also consider the problem of mixture failure rate ordering for the ordered mixing distributions. Two types of stochastic ordering are analyzed: ordering in the likelihood ratio sense and ordering in variances when the means are equal.     

Methods for Bivariate Survival Data with Mismeasured Covariates Under an Accelerated Failure Time Model

Accelerated failure time models are useful in survival data analysis, but such models have received little attention in the context of measurement error. In this paper we discuss an accelerated failure time model for bivariate survival data with covariates subject to measurement error. In particular, methods based on the marginal and joint models are considered. Consistency and efficiency of the resultant estimators are investigated. Simulation studies are carried out to evaluate the performance of the estimators as well as the impact of ignoring the measurement error of covariates. As an illustration we apply the proposed methods to analyze a data set arising from the Busselton Health Study (Knuiman et al., 1994 Knuiman , M. W. , Cullent , K. J. , Bulsara , M. K. , Welborn , T. A. , Hobbs , M. S. T. ( 1994 ). Mortality trends, 1965 to 1989, in Busselton, the site of repeated health surveys and interventions . Austral. J. Public Health 18 : 129 – 135 . [CSA] [Crossref], [PubMed] , [Google Scholar]).     

Gaussian Hypergeometric Probability Distributions for Fitting Discrete Data

The distributions generated by the Gaussian hypergeometric function compose a tetraparametric family that includes many of the most common discrete distributions in the literature. In this article, probability aspects related to the whole family are reviewed and methods of estimation for fitting them to real data are developed. Several applied examples are also provided to illustrate the procedures and compare the methods of estimation.     

Convex Ordering for Bivariate Distributions

An attempt is made to extend well-known univariate notion of convex ordering to bivariate case. A convex ordered family for bivariate distributions is then introduced and its properties are examined.     

Sample Entropy Statistics and Testing for Order in Complex Physiological Signals

Sample Entropy (SampEn) statistics have provided insight into the amount of order present in several types of complex physiological time series, particularly the heart rate dynamics of premature infants. Very little, however, is known of SampEn's statistical properties and this has hindered strategies for optimization and significance testing. This article shows that SampEn statistics are asymptotically Gaussian under general conditions. A straightforward point estimate of the statistic's variance is developed and compared to empirical results obtained from complex surrogate data. Statistical tests are developed to quantify the amount and scale of order detected in a signal. These tests are used to show that significant order is, in fact, being detected in the heart rate dynamics of neonates, and to suggest strategies for optimizing the analysis parameters.