Abstracts



Cure Models for Survival Data

Ana M. Abreu
CCCEE and CCM, Universidade da Madeira
abreu@uma.pt

 Abstract
Cure models are developed to cover situations where it is plausible to admit that, in the population under study, there are individuals that are cured (or non-susceptible). Although, frequently, the cure is not observable, the suspicion is based in some associated characteristics, namely the existence of many censored observations beyond the last observed survival time. When there are censored observations, usually it is not possible to clearly identify which individuals are cured, which results in incomplete data. Therefore, in the parameter estimation process, the preferred method is the EM algorithm, because it is an iterative method that allows obtaining the parameters maximum likelihood estimates in situations where there are missing observations.
Usually, in a cure model, the aim is to estimate the proportion of cured individuals, the survival function of the susceptible individuals and the effect of the covariates, if they have been included in the model. In this context, the population under study is heterogeneous not only because there are susceptible and cured individuals, but also due to the different values of their covariates.
In this talk, I will describe the general structure of a cure model, point out the main differences that occur when comparing it with the traditional model (the one that doesn’t include a cure fraction), and present some models based in the log-logistic and Chen distributions. Their use is illustrated with the analysis of some leukemia data sets.

Bayesian Modelling of Survival Data with
Genetic, Environmental and Spatial Frailties

Giovani Loiola da Silva
DMIST and CEAUL
http://www.math.ist.utl.pt/~gsilva/

Abstract
In regression analysis for survival data, there are often unobserved heterogeneity when the observed covariates do not fully explain the individual variation. That heterogeneity can be associated with different risk factors. For instance, there may be a tendency for disease occurrence to cluster within families, because of genetic predisposition or shared environmental and spatial factors, and hence the incidence of disease will be higher in families with individuals who are frailest. Frailty survival models have been proposed in order to take into account that kind of heterogeneity. This work aims at presenting a Bayesian analysis of frailty survival models based on counting processes. Fitting these models requires Monte Carlo Markov chain methods. Their illustration is presented through the analysis of two data sets: adoption data (genetic and environmental factors) and coronary artery bypass surgery data (spatial variation). For the latter, we can also produce smoothed maps including spatial effects on disease intensities.

Statistical Considerations in the Use of a Composite
Time-to-Event Endpoint for Comparing Treatment Groups

Guadalupe Gómez1, Stephen W. Lagakos2
1Statistics Dpt., Universitat Politècnica de Catalunya, Spain
2Biostatistics Dpt., Harvard University, USA
gomez@upc.edu

 Abstract
When comparing two treatment groups in a time-to-event analysis, it is common to use a composite outcome event consisting of two or more distinct outcomes, such as the composite of non-fatal MI or revascularization in patients with coronary artery disease, or the composite of clinical progression or death in patients with inoperable cancer. The motivation for using a composite outcome event is sometimes to capture a fuller spectrum of outcomes related to patient population, sometimes to account for a terminating event (such as death), and sometimes to increase the rate of occurrence of the outcome event in hopes of increasing power to detect treatment differences.
There has been considerable debate about the use of composite endpoints as regards the interpretation of results, but very little discussion about the statistical tradeoffs of using a composite endpoint versus an endpoint based on one or a subset of the components in the composite. We investigate this problem by considering the relative efficiency of a logrank test for comparing treatment groups with respect to the endpoint E1 (for example, non-fatal MI) versus the composite endpoint of E1 or E2 (for example, nonfatal MI or revascularization), where E1 and E2 can be either single types of events or composites also see format and style instructions on the webpage.
The relative efficiency of a logrank test based on E1 to a logrank test based on the composite of E1 and E2 depends on the marginal distributions of the times until E1 and E2, the correlation between these times, the treatment group differences with respect to E1 and E2, and the pattern and amount of censoring. We compute this relative efficiency for a variety of settings in order to develop guidelines for deciding whether to expand a study endpoint from E1 to the composite of E1 and E2.