Quasi Markovian behavior in mixing maps

We consider the time dependent probability distribution of a coarse grained observable Y whose evolution is governed by a discrete time map. If the map is mixing, the time dependent one-step transition probabilities converge in the long time limit to yield an ergodic stochastic matrix. The stationary distribution of this matrix is identical to the asymptotic distribution of Y under the exact dynamics. The nth time iterate of the baker map is explicitly computed and used to compare the time evolution of the occupation probabilities with those of the approximating Markov chain. The convergence is found to be at least exponentially fast for all rectangular partitions with Lebesgue measure. In particular, uniform rectangles form a Markov partition for which we find exact agreement.Comment: 16 pages, 1 figure, uses elsart.sty, to be published in Physica D Special Issue on Predictability: Quantifying Uncertainty in Models of Complex Phenomen

Monochorionic-triamniotic triplet pregnancy after intracytoplasmic sperm injection, assisted hatching, and two-embryo transfer: first reported case following IVF

BACKGROUND: We present a case of monochorionic-triamniotic pregnancy that developed after embryo transfer following in vitro fertilization (IVF). METHODS: After controlled ovarian hyperstimulation and transvaginal retrieval of 22 metaphase II oocytes, fertilization was accomplished with intracytoplasmic sperm injection (ICSI). Assisted embryo hatching was performed, and two embryos were transferred in utero. One non-transferred blastocyst was cryopreserved. RESULTS: Fourteen days post-transfer, serum hCG level was 423 mIU/ml and subsequent transvaginal ultrasound revealed a single intrauterine gestational sac with three separate amnion compartments. Three distinct foci of cardiac motion were detected and the diagnosis was revised to monochorionic-triamniotic triplet pregnancy. Antenatal management included cerclage placement at 19 weeks gestation and hospital admission at 28 weeks gestation due to mild preeclampsia. Three viable female infants were delivered via cesarean at 30 5/7 weeks gestation. CONCLUSIONS: The incidence of triplet delivery in humans is approximately 1:6400, and such pregnancies are classified as high-risk for reasons described in this report. We also outline an obstetric management strategy designed to optimize outcomes. The roles of IVF, ICSI, assisted embryo hatching and associated laboratory culture conditions on the subsequent development of monozygotic/monochorionic pregnancy remain controversial. As demonstrated here, even when two-embryo transfer is employed after IVF the statistical probability of monozygotic multiple gestation cannot be reduced to zero. We encourage discussion of this possibility during informed consent for the advanced reproductive technologies

Parents’ experiences of health visiting for children with Down syndrome

© MA Healthcare Limited.Children with Down syndrome have an increased likelihoodof experiencing serious health conditions. Health visitors canhave an important role in monitoring and promoting healthand development for young children with Down syndrome.This study aimed to explore parents’ experiences of healthvisiting services for children with Down syndrome. Twentyfour parents of children with Down syndrome aged 0–5 yearscompleted a brief questionnaire about the number and natureof visits from health visitors in the previous 12 months andtheir support needs. Some parents commented that otherprofessionals met the needs of their child, whereas others saidthat they would like more advice and support from healthvisitors. A further exploration of broader health serviceprovision, including health visiting, for young children withDown syndrome is needed.Peer reviewedFinal Accepted Versio

Analysis of neonatal clinical trials with twin births

<p>Abstract</p> <p>Background</p> <p>In neonatal trials of pre-term or low-birth-weight infants, twins may represent 10–20% of the study sample. Mixed-effects models and generalized estimating equations are common approaches for handling correlated continuous or binary data. However, the operating characteristics of these methods for mixes of correlated and independent data are not well established.</p> <p>Methods</p> <p>Simulation studies were conducted to compare mixed-effects models and generalized estimating equations to linear regression for continuous outcomes. Similarly, mixed-effects models and generalized estimating equations were compared to ordinary logistic regression for binary outcomes. The parameter of interest is the treatment effect in two-armed clinical trials. Data from the National Institute of Child Health & Human Development Neonatal Research Network are used for illustration.</p> <p>Results</p> <p>For continuous outcomes, while the coverage never fell below 0.93, and the type I error rate never exceeded 0.07 for any method, overall linear mixed-effects models performed well with respect to median bias, mean squared error, coverage, and median width. For binary outcomes, the coverage never fell below 0.90, and the type I error rate never exceeded 0.07 for any method. In these analyses, when randomization of twins was to the same treatment group or done independently, ordinary logistic regression performed best. When randomization of twins was to opposite treatment arms, a rare method of randomization in this setting, ordinary logistic regression still performed adequately. Overall, generalized linear mixed models showed the poorest coverage values.</p> <p>Conclusion</p> <p>For continuous outcomes, using linear mixed-effects models for analysis is preferred. For binary outcomes, in this setting where the amount of related data is small, but non-negligible, ordinary logistic regression is recommended.</p