Estimation of Sample Size and Power For Quantile Regression

Quantile regression (QR) was first introduced by Roger Koenker and Gilbert Bassett in 1978. It is robust to outliers which affect least squares estimator on a large scale in linear regression. Instead of modeling mean of the response, QR provides an alternative way to model the relationship between quantiles of the response and covariates. Therefore, QR can be widely used to solve problems in econometrics, environmental sciences and health sciences. Sample size is an important factor in the planning stage of experimental design and observational studies. In ordinary linear regression, sample size may be determined based on either precision analysis or power analysis with closed form formulas. There are also methods that calculate sample size based on precision analysis for QR like C.Jennen-Steinmetz and S.Wellek (2005). A method to estimate sample size for QR based on power analysis was proposed by Shao and Wang (2009). In this paper, a new method is proposed to calculate sample size based on power analysis under hypothesis test of covariate effects. Even though error distribution assumption is not necessary for QR analysis itself, researchers have to make assumptions of error distribution and covariate structure in the planning stage of a study to obtain a reasonable estimate of sample size. In this project, both parametric and nonparametric methods are provided to estimate error distribution. Since the method proposed can be implemented in R, user is able to choose either parametric distribution or nonparametric kernel density estimation for error distribution. User also needs to specify the covariate structure and effect size to carry out sample size and power calculation. The performance of the method proposed is further evaluated using numerical simulation. The results suggest that the sample sizes obtained from our method provide empirical powers that are closed to the nominal power level, for example, 80%.

IMMUNE-ANGIOGENESIS MECHANISMS ASSOCIATED WITH PORCINE PREGNANCY SUCCESS AND FAILURE

Spontaneous fetal loss (25-40%) leading to decrease in litter size is a significant concern to the pork industry. A deficit in the placental vasculature has emerged as one of the important factors associated with fetal loss. During early pig pregnancy, the endometrium becomes enriched with immune cells recruited by conceptus-derived signals including specific chemokine stimuli. These immune cells assist in various aspects of placental development and angiogenesis. Recent evidence suggests that microRNAs (miRNAs: small non-coding RNAs that regulate gene expression) regulate immune cell development and their functions. In addition, intercellular communication including exchange of biomolecules (e.g. miRNAs) between the conceptus and endometrium regulate key developmental processes during pregnancy. To understand the biological significance of immune cell enrichment, regulation of their functions by miRNAs and transfer of miRNAs across the maternal fetal-interface, we screened specific sets of chemokines and pro- and anti-angiogenic miRNAs in endometrial lymphocytes (ENDO LY), endometrium, and chorioallantoic membrane (CAM) isolated from conceptus attachment sites (CAS) during early, gestation day (gd)20 and mid-pregnancy (gd50). We report increased expression of selected chemokines including CXCR3 and CCR5 in ENDO LY and CXCL10, CXCR3, CCL5, CCR5 in endometrium associated with arresting CAS at gd20. Some of these differences were also noted at the protein level (CXCL10, CXCR3, CCL5, and CCR5) in endometrium and CAM. We report for the first time significant differences for miRNAs involved in immune cell-derived angiogenesis (miR-296-5P, miR-150, miR-17P-5P, miR-18a, and miR-19a) between ENDO LY associated with healthy and arresting CAS. Significant differences were also found in endometrium and CAM for some miRNAs (miR-17-5P, miR-18a, miR-15b-5P, and miR-222). Finally, we confirm that placenta specific-exosomes contain proteins and 14 select miRNAs including miR-126-5P, miR-296-5P, miR-16, and miR-17-5P that are of relevance to early implantation events. We further demonstrated the bidirectional exosome shuttling between porcine trophectoderm cells (PTr2) and porcine aortic endothelial cells (PAOEC). PTr2-derived exosomes were able to modulate the endothelial cell proliferation that is crucial for the establishment of pregnancy. Our data unravels the selected chemokines and miRNAs associated with immune cell-regulated angiogenesis and reconfirm that exosome mediated cell-cell communication opens-up new avenues to understand porcine pregnancy.