No abstract

We introduce a new adjusted residual maximum likelihood method (REML) in the context of producing an empirical Bayes (EB) confidence interval for a normal mean, a problem of great interest in different small area applications. Like other rival empirical Bayes confidence intervals such as the well-known parametric bootstrap empirical Bayes method, the proposed interval is second-order correct, that is, the proposed interval has a coverage error of order $O(m^{-{3}/{2}})$. Moreover, the proposed interval is carefully constructed so that it always produces an interval shorter than the corresponding direct confidence interval, a property not analytically proved for other competing methods that have the same coverage error of order $O(m^{-{3}/{2}})$. The proposed method is not simulation-based and requires only a fraction of computing time needed for the corresponding parametric bootstrap empirical Bayes confidence interval. A Monte Carlo simulation study demonstrates the superiority of the proposed method over other competing methods.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1219 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

ObjectiveTo track changes in interferon (IFN) production in healthy individuals to shed light on the effect these changes have on the course of healthy ageing.DesignStudy is based on data that were collected over 24 years from a cohort of individuals whose IFN-α production was quantified as a part of their annual routine health check-up.SettingAll individuals in this study underwent regular health check-ups at Louis Pasteur Center for Medical Research.Participants295 healthy individuals (159 males and 136 females) without a history of cancer, autoimmune diseases and hepatitis C virus (HCV) whose IFN-α production was quantified more than five times within 24 years were selected. Finally, 29 males and 4 females whose IFN-α production was quantified more than 25 times were selected and their data were analysed using a mixed model.Main outcome measuresHVJ stimulated IFN-α  production was quantified. Healthy individual's periodical log transformed IFN-α values (y) were plotted versus age (x) and fitted to linear (y=mx+n) and quadratic formula (y=ax2+bx+c) expressions to reveal changes in the IFN-α  production in these healthy individuals.ResultsThe linear expression showed that log (IFN-α) had a slight tendency to decline (3% over 10 years). However, the quadratic formula analysis showed the quadratic expression to be more positive than negative (a concave U-shaped pattern) which means that individuals’ once declining IFN production recovered as they aged.ConclusionsAlthough we observed a marginal decline in IFN-α  production, we also observed that IFN production recovered even in individuals in their mid50s to early 60s. These results combined with our previous cross-sectional studies of patients with various diseases suggest that in healthy individuals, the impairment of IFN production is triggered more by the onset of disease (notwithstanding the cause) rather than by ageing.

Recently, an empirical best linear unbiased predictor is widely used as a practical approach to small area inference. It is also of interest to construct empirical prediction intervals. However, we do not know which method should be used from among the several existing prediction intervals. In this article, we first obtain an empirical prediction interval by using the residual maximum likelihood method for estimating unknown model variance parameters. Then we compare the later with other intervals with the residual maximum likelihood method. Additionally, some different parametric bootstrap methods for constructing empirical prediction intervals are also compared in a simulation study.