We prove that the slope parameter of the ordinary least squares regression of phylogenetically independent contrasts (PICs) conducted through the origin is identical to the slope parameter of the method of generalized least squares (GLSs) regression under a Brownian motion model of evolution. This equivalence has several implications: 1. Understanding the structure of the linear model for GLS regression provides insight into when and why phylogeny is important in comparative studies. 2. The limitations of the PIC regression analysis are the same as the limitations of the GLS model. In particular, phylogenetic covariance applies only to the response variable in the regression and the explanatory variable should be regarded as fixed. Calculation of PICs for explanatory variables should be treated as a mathematical idiosyncrasy of the PIC regression algorithm. 3. Since the GLS estimator is the best linear unbiased estimator (BLUE), the slope parameter estimated using PICs is also BLUE. 4. If the slope is estimated using different branch lengths for the explanatory and response variables in the PIC algorithm, the estimator is no longer the BLUE, so this is not recommended. Finally, we discuss whether or not and how to accommodate phylogenetic covariance in regression analyses, particularly in relation to the problem of phylogenetic uncertainty. This discussion is from both frequentist and Bayesian perspectives.
Observational studies and randomised controlled studies suggest that vitamin D plays a role in the prevention of acute respiratory tract infection (ARTI); however, findings are inconsistent and the optimal serum 25-hydroxyvitamin D (25(OH)D) concentration remains unclear. To review the link between 25(OH)D concentration and ARTI, we searched PubMed and EMBASE databases to identify observational studies reporting the association between 25(OH)D concentration and risk or severity of ARTI. We used random-effects meta-analysis to pool findings across studies. Twenty-four studies were included in the review, 14 were included in the meta-analysis of ARTI risk and five in the meta-analysis of severity. Serum 25(OH)D concentration was inversely associated with risk and severity of ARTI; pooled odds ratios (95% confidence interval) were 1.83 (1.42–2.37) and 2.46 (1.65–3.66), respectively, comparing the lowest with the highest 25(OH)D category. For each 10 nmol/L decrease in 25(OH)D concentration, the odds of ARTI increased by 1.02 (0.97–1.07). This was a non-linear trend, with the sharpest increase in risk of ARTI occurring at 25(OH)D concentration < 37.5 nmol/L. In conclusion, there is an inverse non-linear association between 25(OH)D concentration and ARTI.
Our previous study reported microorganisms in human follicular fluid. The objective of this study was to test human follicular fluid for the presence of microorganisms and to correlate these findings with the in vitro fertilization (IVF) outcomes. In this study, 263 paired follicular fluids and vaginal swabs were collected from women undergoing IVF cycles, with various causes for infertility, and were cultured to detect microorganisms. The cause of infertility and the IVF outcomes for each woman were correlated with the microorganisms detected within follicular fluid collected at the time of trans-vaginal oocyte retrieval. Microorganisms isolated from follicular fluids were classified as: (1) ‘colonizers’ if microorganisms were detected within the follicular fluid, but not within the vaginal swab (at the time of oocyte retrieval); or (2) ‘contaminants’ if microorganisms detected in the vagina at the time of oocyte retrieval were also detected within the follicular fluid. The presence of Lactobacillus spp. in ovarian follicular fluids was associated with embryo maturation and transfer. This study revealed microorganisms in follicular fluid itself and that the presence of particular microorganisms has an adverse affect on IVF outcomes as seen by an overall decrease in embryo transfer rates and pregnancy rates in both fertile and infertile women, and live birth rates in women with idiopathic infertility. Follicular fluid microorganisms are a potential cause of adverse pregnancy outcomes in IVF in both infertile women and in fertile women with infertile male partners.
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