Paul Janssen

Evolution of recurrent asthma event rate over time in frailty models

Summary. To model the time evolution of the event rate in recurrent event data a crucial role is played by the timescale that is used. Depending on the timescale selected the interpretation of the time evolution will be entirely different, both in parametric and semiparametric frailty models. The gap timescale is more appropriate when studying the recurrent event rate as a function of time since the last event, whereas the calendar timescale keeps track of actual time. We show both timescales in action on data from an asthma prevention trial in young children. The frailty model is further extended to include both timescales simultaneously as this might be most relevant in practice.

Glivenko-Cantelli properties of some generalized empirical DF's and strong convergence of generalized L-statistics

SummaryWe study a nonclassical form of empirical df Hnwhich is of U-statistic structure and extend to Hnthe classical exponential probability inequalities and Glivenko-Cantelli convergence properties known for the usual empirical df. An important class of statistics is given byT(Hn), where T(·) is a generalized form of L-functional. For such statisticswe prove almost sure convergence using an approach which separates the functional-analytic and stochastic components of the problem and handles the latter component by application of Glivenko-Cantelli type properties.Classical results for U-statistics and L-statistics are obtained as special cases without addition of unnecessary restrictions.Many important new types of statistics of current interest are covered as well by our result.

The shared frailty model and the power for heterogeneity tests in multicenter trials

Heterogeneity between centers in multicenter trials with time to event outcome can be modeled by the frailty proportional hazards model. The majority of the different approaches that have been used to fit frailty models assume either the gamma or the lognormal frailty density and are based on similar log likelihood expressions. These approaches are briefly reviewed and their specific features described; simulations further demonstrate that the different techniques lead to virtually the same estimates for the heterogeneity parameter. An important issue is the relationship between the size of a multicenter trial, in terms of number of centers and number of patients per center, and the bias and the spread of estimates of the heterogeneity parameter around its true value. Based on simulation results (restricted to constant hazard rate and the gamma frailty density), it becomes clear how the number of centers and the number of patients per center influence the quality of the estimates in the particular setting of breast cancer clinical trials. This insight is important in treatment outcome research, where one tries to relate differences with respect to clinical practice to differences in outcome in the various centers.

RESAMPLING FROM CENTERED DATA IN THE TWO-SAMPLE PROBLEM*

Abstract Bootstrap and permutation approximations to the distribution of U-statistics are shown to be valid when the resampling is from residuals in the two-sample problem. The motivation for using residuals comes from testing for homogeneity of scale in the presence of nuisance location parameters. New asymptotic results for U-statistics with estimated parameters are key tools in the proofs.

Presmoothed Kaplan–Meier and Nelson–Aalen estimators

In this article, a modification of the Kaplan–Meier and Nelson–Aalen estimators in the right random censorship model is studied. The new estimators are obtained by replacing the censoring indicator variables in the classical definitions by values of a nonparametric regression estimator. Asymptotic normality is obtained and it is shown that this presmoothing idea leads to a gain in asymptotic mean squared error. A local plug-in bandwidth selector is introduced and the problem of optimal pilot bandwidth selection for this estimator is studied. The gain of the presmoothed estimators with automatic plug-in bandwidth selector is demonstrated in a simulation study.

Smoothing sparse multinomial data using local polynomial fitting

To estimate cell probabilities for sparse multinomial data several smoothing techniques have been investigated. Here we propose local polynomial smoothers as estimators for the cell probabilities and we study their performance. For the mean sum of squared errors we obtain the optimal rate of convergence and we establish a central limit theorem. We show that local polynomial smoothers provide a nice alternative for already existing nonparametric estimators and we discuss interrelations. Some illustrations are also included.

Frailty models and copulas: similarities and differences

Copulas and frailty models are important tools to model bivariate survival data. Equivalence between Archimedean copula models and shared frailty models, e.g. between the Clayton-Oakes copula model and the shared gamma frailty model, has often been claimed in the literature. In this note we show that, in both the models, there is indeed a well-known equivalence between the copula functions; the modeling of the marginal survival functions, however, is quite different. The latter fact leads to different joint survival functions.

Comparison of different estimation procedures for proportional hazards model with random effects

Proportional hazards models with multivariate random effects (frailties) acting multiplicatively on the baseline hazard are a topic of intensive research. Several estimation procedures have been proposed to deal with this type of models. Four procedures used to fit these models are compared in two real-life datasets and in a simulation study. The performance of the four methods is investigated in terms of the bias of point estimates, their empirical variability and the bias of the estimation of the variability.

Survival of Red Maasai, Dorper and crossbred lambs in the sub-humid tropics

Univ Nairobi, Nairobi, Kenya. Limburgs Univ Ctr, B-3590 Diepenbeek, Belgium. ILRI, Nairobi, Kenya.Nguti, R, Univ Nairobi, POB 30197, Nairobi, Kenya.L.Baker@cgiar.org

Understanding Heterogeneity in Generalized Mixed and Frailty Models

Variance components are useful parameters to quantify the different sources of randomness in hierarchical models. Interpreting the variance components in generalized mixed and frailty models is not straightforward because the variance is not directly related to quantities with a biologicalmeaning. We therefore investigate how the estimated values of the variance components affect the variability of specific quantities of interest such as the prevalence or the median time to event. We discuss two examples from veterinary science with clustering between animals and show for theseexamples how variance components can be interpreted in the case of a binary and time-to-event response variable.