Catálogo de publicaciones - libros

Consider a chronic disease process which is beginning to be observed at a point in chronological time. The backward recurrence and forward recurrence times are defined for prevalent cases as the time with disease and the time to leave the disease state respectively, where the reference point is the point in time at which the disease process is being observed. In this setting the incidence of disease affects the recurrence time distributions. In addition, the survival of prevalent cases will tend to be greater than the population with disease due to length biased sampling. A similar problem arises in models for the early detection of disease. In this case the backward recurrence time is how long an individual has had disease before detection and the forward recurrence time is the time gained by early diagnosis; i.e. until the disease becomes clinical by exhibiting signs or symptoms. In these examples the incidence of disease may be age related resulting in a non-stationary process. The resulting recurrence time distributions are derived as well as some generalization of length-biased sampling.

Age patterns of male and female cancer incidence rate do not look similar. This is because of the biologically based difference in susceptibility to cancer of different sites. This argument, however, does not clarify how age patterns of male and female cancer incidence rate must look like. The analysis of epidemiological data on cancer in different countries and in different years shows that male and female cancer incidence rates intersect around the age of female climacteric. We explain the observed pattern using the difference in ontogenetic components of aging between males and females. The explanation requires a new model of carcinogenesis, which takes this difference into account. Application to data on cancer incidence in Japan (Miyagi prefecture) illustrates the model.

The paper considers the analysis of disablement process of the elderly using the general path model with noise. The impact of dementia and sex on degradation is analysed. These joint model for survival and longitudinal data is discussed.

We consider a semi-Markov chain, with a finite state space. Taking a censored history, we obtain empirical estimators for the discrete semi-Markov kernel, renewal function and semi-Markov transition function. We propose estimators for two different failure rate functions: the usual failure rate, BMP-failure rate, defined by [BMP63], and the new introduced failure rate, RG-failure rate, proposed by [RG92]. We study the strong consistency and the asymptotic normality for each estimator and we construct the confidence intervals. We illustrate our results by a numerical example.

Markov chain proportional hazard regression model provides a powerful tool for analysis of multiple event times. We discuss estimation in absorbing Markov chains with missing covariates. We consider a MAR model assuming that the missing data mechanism depends on the observed covariates, as well as the number of events observed in a given time period, their types and times of their occurrence. For estimation purposes we use a piecewise constant intensity regression model.

Let Z = Z _1, …, Z _n be an i.i.d. sample from the distribution F ( z ) = P ( Z ≤ z ) and density f ( z ) = d/dz F ( z ). Let Z _1, n < … < Z _n,n be the order statistics generated by Z _1, …, Z _n. Let Z _0, n = a = inf{ z : F ( z ) > 0} and Z _ n +1, n = b = sup{ z : F ( z ) < 1} denote the end-points of the common distribution of these observations, and assume that f is continuous and positive on ( a; b ). We establish the asymptotic normality of the sum of logarithms of the spacings Z _i,n − Z_ i −1, n , for i = 1, …, n + 1, under minimal additional conditions on f . Our results largely extend previous results in the literature due to Blumenthal [Blu68] and other authors.

An impact of environment on mortality, similar to survival analysis, is often modelled by the proportional hazards model, which assumes the corresponding comparison with a baseline environment. This model describes the memory-less property, when the mortality rate at a given instant of time depends only on the environment at this instant of time and does not depend on the history. In the presence of degradation the assumption of this kind is usually unrealistic and history-dependent models should be considered. The simplest stochastic degradation model is the accelerated life model. We discuss these models for the cohort setting and apply the developed approach to the period setting for the case when environment (stress) is modelled by the functions with switching points (jumps in the level of the stress).