The thermoelastic Hertzian contact problem

AbstractA numerical solution is obtained for the steady-state thermoelastic contact problem in which heat is conducted between two elastic bodies of dissimilar materials at different temperatures with arbitrary quadratic profiles. Thermoelastic deformation causes the initially elliptical contact area to be reduced in size and to become more nearly circular as the temperature difference is increased. There is also a small but identifiable deviation from exact ellipticity at intermediate temperature differences. An approximate analytical solution is obtained, based on approximating the contact area by an ellipse

Sample size estimation for recurrent event data using multifrailty and multilevel survival models

In epidemiology and clinical research, recurrent events refer to individuals who are likely to experience transient clinical events repeatedly over an observation period. Examples include hospitalizations in patients with heart failure, fractures in osteoporosis studies and the occurrence of new lesions in oncology. We provided an in-depth analysis of the sample size required for the analysis of recurrent time-to-event data using multifrailty or multilevel survival models. We covered the topic from the simple shared frailty model to models with hierarchical or joint frailties. We relied on a Wald-type test statistic to estimate the sample size assuming either a single or multiple endpoints. Simulations revealed that the sample size increased as heterogeneity increased. We also observed that it was more attractive to include more patients and reduce the duration of follow-up than to include fewer patients and increase the duration of follow-up to obtain the number of events required. Each model investigated can address the question of the number of subjects for recurrent events. However, depending on the research question, one model will be more suitable than another. We illustrated our methodology with the AFFIRM-AHF trial investigating the effect of intravenous ferric carboxymaltose in patients hospitalised for acute heart failure.</p

Effect and 95% CIs of a 10-μg/m increase in air pollution on death using a Cox proportional hazards model with a second-degree polynomial–distributed lag model, adjusted for meteorologic variables

<p><b>Copyright information:</b></p><p>Taken from "Survival Analysis to Estimate Association between Short-Term Mortality and Air Pollution"</p><p>Environmental Health Perspectives 2005;114(2):242-247.</p><p>Published online 3 Oct 2005</p><p>PMCID:PMC1367838.</p><p>This is an Open Access article: verbatim copying and redistribution of this article are permitted in all media for any purpose, provided this notice is preserved along with the article's original DOI.</p