ON THE EXPECTED VALUES OF SEQUENCES OF FUNCTIONS

We prove new extensions to lemmas about combinations of convergent sequences of distribution functions and absolutely continuous bounded functions. New lemma one, a generalized Helly theorem, allows computing the limit of the expected value of a sequence of functions with respect to a sequence of measures. Previously published results allow either the function or the measure to be a sequence, but not both. Lemma two allows computing the expected value of an absolutely continuous monotone function by integrating the probabilities of the inverse function values. Previous results were restricted to the identity function. Lemma three gives a computationally and analytically convenient form for the limit of the expected value of a sequence of functions of a sequence of random variables. This is a new result that follows directly from the first two lemmas. Although the lemmas resemble standard results and seem obviously true, we have found only similar looking and related but quite distinct results in the literature. We provide examples which highlight the value of the new results

Adjusting power for a baseline covariate in linear models

The analysis of covariance provides a common approach to adjusting for a baseline covariate in medical research. With Gaussian errors, adding random covariates does not change either the theory or the computations of general linear model data analysis. However, adding random covariates does change the theory and computation of power analysis. Many data analysts fail to fully account for this complication in planning a study. We present our results in five parts. (i) A review of published results helps document the importance of the problem and the limitations of available methods. (ii) A taxonomy for general linear multivariate models and hypotheses allows identifying a particular problem. (iii) We describe how random covariates introduce the need to consider quantiles and conditional values of power. (iv) We provide new exact and approximate methods for power analysis of a range of multivariate models with a Gaussian baseline covariate, for both small and large samples. The new results apply to the Hotelling-Lawley test and the four tests in the “univariate” approach to repeated measures (unadjusted, Huynh-Feldt, Geisser-Greenhouse, Box). The techniques allow rapid calculation and an interactive, graphical approach to sample size choice. (v) Calculating power for a clinical trial of a treatment for increasing bone density illustrates the new methods. We particularly recommend using quantile power with a new Satterthwaite-style approximation

Childhood adiposity and adolescent sex steroids in the Exploring Perinatal Outcomes among Children study

ObjectiveIt is unclear how childhood adipose tissue deposition influences sex hormone profiles in later adolescence.DesignProspective cohort study.ParticipantsChildren (n = 418) with a mean age of 10.5 (1.5) years at visit 1 and 16.7 (1.2) at visit 2 in the Exploring Perinatal Outcomes among Children (EPOCH) Study.MeasurementsWe used reverse‐scale Cox proportional hazard models to assess associations between pubertal dehydroepiandrosterone (DHEA), testosterone (T), and oestradiol (E2) and childhood‐to‐puberty rate of change in visceral (VAT) and subcutaneous adipose tissue (SAT). Models stratified by sex and adjusted for childhood adiposity, maternal factors, birthweight and pubertal onset, and then further adjusted for insulin, luteinizing hormone (LH), leptin and hepatic fat fraction.ResultsAmong boys, more rapid accumulation of either VAT or SAT was associated with lower testosterone at visit 2 (HR 0.86, and .96, respectively, both P < .0001), independently of race/ethnicity, LH, leptin and hepatic fat fraction. Among boys, more childhood VAT was associated with lower testosterone in adolescence (HR 0.98, P = .003), but this association did not persist after adjustment for leptin or insulin. No associations were observed between either fat measure and oestradiol or DHEA in boys. In girls, no associations between childhood fat or fat accumulation and sex hormones were observed.ConclusionsMore rapid accumulation of fat is associated with lower testosterone in boys. These associations suggest that fat growth influences androgen profiles in adolescent boys. Since fat accumulation is a modifiable risk factor, the study results provide a possible intervention target and time period for improving adult health.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151892/1/cen14058_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151892/2/cen14058.pd

Recommendations for choosing an analysis method that controls Type I error for unbalanced cluster sample designs with Gaussian outcomes: J. L. JOHNSONET AL.

We used theoretical and simulation-based approaches to study Type I error rates for one-stage and two-stage analytic methods for cluster-randomized designs. The one-stage approach uses the observed data as outcomes, and accounts for within cluster correlation using a general linear mixed model. The two-stage model uses the cluster specific means as the outcomes in a general linear univariate model. We demonstrate analytically that both one-stage and two-stage models achieve exact Type I error rates when cluster sizes are equal. With unbalanced data, an exact size α test does not exist and Type I error inflation may occur. Via simulation, we compare the Type I error rates for four one-stage and six two-stage hypothesis testing approaches for unbalanced data. With unbalanced data, the two-stage model, weighted by the inverse of the estimated theoretical variance of the cluster means, and with variance constrained to be positive, provided the best Type I error control for studies having at least 6 clusters per arm. The one-stage model with Kenward-Roger degrees of freedom and unconstrained variance performed well for studies having at least 14 clusters per arm. The popular analytic method of using a one-stage model with denominator degrees of freedom appropriate for balanced data performed poorly for small sample sizes and low intracluster correlation. Since small sample sizes and low intracluster correlation are common features of cluster-randomized trials, the Kenward-Roger method is the preferred one-stage approach

Maternal dietary intake during pregnancy and offspring body composition: The Healthy Start Study

Consistent evidence of an influence of maternal dietary intake during pregnancy on infant body size and composition in human populations is lacking, despite robust evidence in animal models

Two-Modality Mammography May Confer an Advantage Over Either Full-Field Digital Mammography or Screen-Film Mammography

To compare the cancer detection rate and ROC area under the curve of full-field digital mammography, screen-film mammography, and a combined technique that allowed diagnosis if a finding was suspicious on film, on digital, or both

An Assessment of Oral Health on the Pine Ridge Indian Reservation

An assessment on the oral health of 292 Oglala Lakota residents of the Pine Ridge Indian Reservation in South Dakota looks at dental issues, periodontal disease, oral lesions and need for dental care. The research was conducted by the University of Colorado, Center for Native Oral Health Research and funded by the W.K. Kellogg Foundation

Analysis of human immunodeficiency virus type 1 nef gene sequences present in vivo.

The nef genes of the human immunodeficiency viruses type 1 and 2 (HIV-1 and HIV-2) and the related simian immunodeficiency viruses (SIVs) encode a protein (Nef) whose role in virus replication and cytopathicity remains uncertain. As an attempt to elucidate the function of nef, we characterized the nucleotide and corresponding protein sequences of naturally occurring nef genes obtained from several HIV-1-infected individuals. A consensus Nef sequence was derived and used to identify several features that were highly conserved among the Nef sequences. These features included a nearly invariant myristylation signal, regions of sequence polymorphism and variable duplication, a region with an acidic charge, a (Pxx)4 repeat sequence, and a potential protein kinase C phosphorylation site. Clustering of premature stop codons at position 124 was noted in 6 of the 54 Nef sequences. Further analysis revealed four stretches of residues that were highly conserved not only among the patient-derived HIV-1 Nef sequences, but also among the Nef sequences of HIV-2 and the SIVs, suggesting that Nef proteins expressed by these retroviruses are functionally equivalent. The "Nef-defining" sequences were used to evaluate the sequence alignments of known proteins reported to share sequence similarity with Nef sequences and to conduct additional computer-based searches for similar protein sequences. A gene encoding the consensus Nef sequence was also generated. This gene encodes a full-length Nef protein that should be a valuable tool in further studies of Nef function

Associations of maternal BMI and gestational weight gain with neonatal adiposity in the Healthy Start study

Background: Maternal obesity and weight gain during pregnancy are risk factors for child obesity. Associations may be attributable to causal effects of the intrauterine environment or genetic and postnatal environmental factors