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

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

End-digits preference for self-reported height depends on language

BACKGROUND: When individuals report figures, they often prefer to round to specific end-digits (e.g. zero). Such preference has been found in reports of body weight, cigarette consumption or blood pressure measurements. Very little is known about self-reported body height. End-digit preference can distort estimates of prevalence and other statistical parameters. This study examines end-digit preference for self-reported height and how it relates with sex, age, educational level or cultural affiliation. METHODS: We analysed reports of height of 47,192 individuals (aged 15 years or older) living in Switzerland and participating in one of the three population-based Swiss Health Surveys carried out in 1992/93, 1997 and 2002 respectively. Digit preferences were analysed by sex, age group, educational level, survey, smoking status, interview language (only for Swiss nationals) and nationality. Adjusted odds ratios (OR) with 95% confidence interval were calculated by using multivariate logistic regression. RESULTS: Italian and French nationals (44.1% and 40.6%) and Italian and French Swiss (39.6% and 35.3%) more strongly preferred zero and five than Germans and German Swiss (29.2% and 30.3%). Two, four, six and eight were more popular in Germans and German Swiss (both 44.4%). Compared to German Swiss (OR = 1), for the end-digits zero and five, the OR were 1.50 (1.38-1.63) for Italian Swiss and 1.24 (1.18-1.30) for French Swiss; 1.73 (1.58-1.89) for Italian nationals and 1.61 (1.33-1.95) for French nationals. The end-digits two, four, six and eight showed an opposite pattern. CONCLUSION: Different preferences for end-digits depending on language and nationality could be observed consistently in all three national health surveys. The patterns were strikingly similar in Swiss and foreign nationals speaking the same language, suggesting that preferences were specific to language rather than to nationality. Taking into account rounding preferences could allow more valid comparisons in analyses of self-reported data originating from different cultures

Limiting weight gain in overweight and obese women during pregnancy to improve health outcomes: the LIMIT randomised controlled trial

Extent: 5p.Background: Obesity is a significant global health problem, with the proportion of women entering pregnancy with a body mass index greater than or equal to 25 kg/m2 approaching 50%. Obesity during pregnancy is associated with a well-recognised increased risk of adverse health outcomes both for the woman and her infant, however there is more limited information available regarding effective interventions to improve health outcomes. The aims of this randomised controlled trial are to assess whether the implementation of a package of dietary and lifestyle advice to overweight and obese women during pregnancy to limit gestational weight gain is effective in improving maternal, fetal and infant health outcomes. Methods/Design: Design: Multicentred randomised, controlled trial. Inclusion Criteria: Women with a singleton, live gestation between 10+0-20+0 weeks who are obese or overweight (defined as body mass index greater than or equal to 25 kg/m2), at the first antenatal visit. Trial Entry & Randomisation: Eligible, consenting women will be randomised between 10+0 and 20+0 weeks gestation using a central telephone randomisation service, and randomisation schedule prepared by non-clinical research staff with balanced variable blocks. Stratification will be according to maternal BMI at trial entry, parity, and centre where planned to give birth. Treatment Schedules: Women randomised to the Dietary and Lifestyle Advice Group will receive a series of inputs from research assistants and research dietician to limit gestational weight gain, and will include a combination of dietary, exercise and behavioural strategies. Women randomised to the Standard Care Group will continue to receive their pregnancy care according to local hospital guidelines, which does not currently include routine provision of dietary, lifestyle and behavioural advice. Outcome assessors will be blinded to the allocated treatment group. Primary Study Outcome: infant large for gestational age (defined as infant birth weight ≥ 90th centile for gestational age). Sample Size: 2,180 women to detect a 30% reduction in large for gestational age infants from 14.40% (p = 0.05, 80% power, two-tailed). Discussion This is a protocol for a randomised trial. The findings will contribute to the development of evidence based clinical practice guidelines.Jodie M Dodd, Deborah A Turnbull, Andrew J McPhee, Gary Wittert, Caroline A Crowther and Jeffrey S Robinso