Bayesian methods for a growth-curve degradation model with repeated measures.

The increasing reliability of some manufactured products has led to fewer observed failures in reliability testing. Thus, useful inference on the distribution of failure times is often not possible using traditional survival analysis methods. Partly as a result of this difficulty, there has been increasing interest in inference from degradation measurements made on products prior to failure. In the degradation literature inference is commonly based on large-sample theory and, if the degradation path model is nonlinear, their implementation can be complicated by the need for approximations. In this paper we review existing methods and then describe a fully Bayesian approach which allows approximation-free inference. We focus on predicting the failure time distribution of both future units and those that are currently under test. The methods are illustrated using fatigue crack growth data.

Failure inference from a marker process based on a bivariate Wiener model.

Many models have been proposed that relate failure times and stochastic time-varying covariates. In some of these models, failure occurs when a particular observable marker crosses a threshold level. We are interested in the more difficult, and often more realistic, situation where failure is not related deterministically to an observable marker. In this case, joint models for marker evolution and failure tend to lead to complicated calculations for characteristics such as the marginal distribution of failure time or the joint distribution of failure time and marker value at failure. This paper presents a model based on a bivariate Wiener process in which one component represents the marker and the second, which is latent (unobservable), determines the failure time. In particular, failure occurs when the latent component crosses a threshold level. The model yields reasonably simple expressions for the characteristics mentioned above and is easy to fit to commonly occurring data that involve the marker value at the censoring time for surviving cases and the marker value and failure time for failing cases. Parametric and predictive inference are discussed, as well as model checking. An extension of the model permits the construction of a composite marker from several candidate markers that may be available. The methodology is demonstrated by a simulated example and a case application.

A repeated measurements model with applications in psychology.

The multivariate Burr distribution is discussed in relation to the analysis of repeated measures data in psychology. The ease of coping with censored and missing observations is particularly highlighted. A numerical example involving test scores of low IQ institutional patients is used to illustrate the method.

Effect of vaccination on severity and dissemination of whooping cough.

A study was undertaken in general practice to clarify those factors, especially vaccinations, that influence the clinical picture and infectivity of whooping cough in the community. Although the range of the disease encountered was fairly mild, its duration was notable (mean +/- SD 50.9 +/- 32.1 days). By using multiway contingency table analysis it was found that in the more severe cases of whooping cough vaccination significantly shortened the illness (p less than 0.005) and reduced the number of coughing spasms (p less than 0.025). The protective effect of the vaccine was most notable in modifying infectivity within the family: 19% of vaccinated family contacts of index patients in whom the disease had been confirmed bacteriologically developed the disease when exposed to it compared with 72% of non-vaccinated contacts (p less than 0.001). These results show that whooping cough vaccination modifies the clinical illness and offers a worthwhile degree of protection to children exposed to the disease.