Study of the bivariate survival data using frailty models based on Lévy processes

Frailty models allow us to take into account the non-observable inhomogeneity of individual hazard functions. Although models with time-independent frailty have been intensively studied over the last decades and a wide range of applications in survival analysis have been found, the studies based on the models with time-dependent frailty are relatively rare. In this paper, we formulate and prove two propositions related to the identifiability of the bivariate survival models with frailty given by a nonnegative bivariate Lévy process. We discuss parametric and semiparametric procedures for estimating unknown parameters and baseline hazard functions. Numerical experiments with simulated and real data illustrate these procedures. The statements of the propositions can be easily extended to the multivariate case

A frailty model for (interval) censored family survival data, applied to the age at onset of non-physical problems

Family survival data can be used to estimate the degree of genetic and environmental contributions to the age at onset of a disease or of a specific event in life. The data can be modeled with a correlated frailty model in which the frailty variable accounts for the degree of kinship within the family. The heritability (degree of heredity) of the age at a specific event in life (or the onset of a disease) is usually defined as the proportion of variance of the survival age that is associated with genetic effects. If the survival age is (interval) censored, heritability as usually defined cannot be estimated. Instead, it is defined as the proportion of variance of the frailty associated with genetic effects. In this paper we describe a correlated frailty model to estimate the heritability and the degree of environmental effects on the age at which individuals contact a social worker for the first time and to test whether there is a difference between the survival functions of this age for twins and non-twins. © 2009 The Author(s)

The current status of orbital experiments for UHECR studies

Two types of orbital detectors of extreme energy cosmic rays are being developed nowadays: (i) TUS and KLYPVE with reflecting optical systems (mirrors) and (ii) JEM-EUSO with high-transmittance Fresnel lenses. They will cover much larger areas than existing ground-based arrays and almost uniformly monitor the celestial sphere. The TUS detector is the pioneering mission developed in SINP MSU in cooperation with several Russian and foreign institutions. It has relatively small field of view (+/-4.5 deg), which corresponds to a ground area of 6.4x10^3 sq.km. The telescope consists of a Fresnel-type mirror-concentrator (~2 sq.m) and a photo receiver (a matrix of 16x16 photomultiplier tubes). It is to be deployed on the Lomonosov satellite, and is currently at the final stage of preflight tests. Recently, SINP MSU began the KLYPVE project to be installed on board of the Russian segment of the ISS. The optical system of this detector contains a larger primary mirror (10 sq.m), which allows decreasing the energy threshold. The total effective field of view will be at least +/-14 degrees to exceed the annual exposure of the existing ground-based experiments. Several configurations of the detector are being currently considered. Finally, JEM-EUSO is a wide field of view (+/-30 deg) detector. The optics is composed of two curved double-sided Fresnel lenses with 2.65 m external diameter, a precision diffractive middle lens and a pupil. The ultraviolet photons are focused onto the focal surface, which consists of nearly 5000 multi-anode photomultipliers. It is developed by a large international collaboration. All three orbital detectors have multi-purpose character due to continuous monitoring of various atmospheric phenomena. The present status of development of the TUS and KLYPVE missions is reported, and a brief comparison of the projects with JEM-EUSO is given.Comment: 18 pages; based on the rapporteur talk given by M.I. Panasyuk at ECRS-2014; v2: a few minor language issues fixed thanks to the editor; to be published in the proceeding