Flexible two-piece distributions for right censored survival data.

An important complexity in censored data is that only partial information on the variables of interest is observed. In recent years, a large family of asymmetric distributions and maximum likelihood estimation for the parameters in that family has been studied, in the complete data case. In this paper, we exploit the appealing family of quantile-based asymmetric distributions to obtain flexible distributions for modelling right censored survival data. The flexible distributions can be generated using a variety of symmetric distributions and monotonic link functions. The interesting feature of this family is that the location parameter coincides with an index-parameter quantile of the distribution. This family is also suitable to characterize different shapes of the hazard function (constant, increasing, decreasing, bathtub and upside-down bathtub or unimodal shapes). Statistical inference is done for the whole family of distributions. The parameter estimation is carried out by optimizing a non-differentiable likelihood function. The asymptotic properties of the estimators are established. The finite-sample performance of the proposed method and the impact of censorship are investigated via simulations. Finally, the methodology is illustrated on two real data examples (times to weaning in breast-fed data and German Breast Cancer data).

Distributions of Aß42 and Aß42/40 in the Cerebrospinal Fluid in View of the Probability Theory.

Amyloid ß 42/40 concentration quotient has been empirically shown to improve accuracy of the neurochemical diagnostics of Alzheimer's Disease (AD) compared to the Aß42 concentration alone, but this improvement in diagnostic performance has not been backed up by a theoretical argumentation so far. In this report we show that better accuracy of Aß42/40 compared to Aß1-42 is granted by fundamental laws of probability. In particular, it can be shown that the dispersion of a distribution of a quotient of two random variables (Aß42/40) is smaller than the dispersion of the random variable in the numerator (Aß42), provided that the two variables are proportional. Further, this concept predicts and explains presence of outlying observations, i.e., AD patients with falsely negatively high Aß42/40 ratio, and non-AD subjects with extremely low, falsely positive, Aß42/40 ratio.

Conditional Sure Independence Screening.

Independence screening is powerful for variable selection when the number of variables is massive. Commonly used independence screening methods are based on marginal correlations or its variants. When some prior knowledge on a certain important set of variables is available, a natural assessment on the relative importance of the other predictors is their conditional contributions to the response given the known set of variables. This results in conditional sure independence screening (CSIS). CSIS produces a rich family of alternative screening methods by different choices of the conditioning set and can help reduce the number of false positive and false negative selections when covariates are highly correlated. This paper proposes and studies CSIS in generalized linear models. We give conditions under which sure screening is possible and derive an upper bound on the number of selected variables. We also spell out the situation under which CSIS yields model selection consistency and the properties of CSIS when a data-driven conditioning set is used. Moreover, we provide two data-driven methods to select the thresholding parameter of conditional screening. The utility of the procedure is illustrated by simulation studies and analysis of two real datasets.