Introduction: Cystic fibrosis (CF) has been reported before in Saudi Arabia and the Gulf area. It has been found that screening for 10 most common cystic fibrosis transmembrane conductance regulator (CFTR) mutations can detect 80% of positive CFTR cases. Objectives: To determine the geographic distribution of the most common CFTR variants in 5 regions of Saudi Arabia. Methodology: A retrospective chart review of all CFTR variants conducted from January 1, 1992 to December 1, 2017. Results: The ten most common CFTR mutations in the Saudi population were as follows: p.Gly473GlufsX54 (17%), p.Phe508del (12%), p.Ile1234Val (12%), 3120+1G > A (11%), 711+1G > T (9%), p.His139Leu (6%), p.Gln637Hisfs (5%), p.Ser549Arg (3%), p.N1303K (3%), and delExon19-21 (2%) along with other variants 79 (20%). In terms of the highest frequency, the c.2988+1G > A (3120+1G > A) variant was found in the eastern province (7.3%) of Saudi Arabia, the c.1418delG (p.Gly473GlufsX54) variant in the northern province (6.8%), the c.579+1G > T (711+1G > T) variant in the southern province (4.8%), the c.3700A > G (p.Ile1234Val) variant in the central province (4.8%), and c.1521_1523delCTT (p.Phe508del) variant in the western province (4.3%). Conclusion: The eastern and the northern provinces have the highest prevalence of CF, with the c.2988+1G > A (3120+1G > A) and c.1418delG (p.Gly473GlufsX54) variants showing the highest distribution in the Saudi CF population, which may reflect the effect of consanguinity within the same tribe. Proper family screening and counseling should be emphasized.

Compositional data are positive multivariate data, constrained to lie within the simplex space. Regression analysis of such data has been studied and many regression models have been proposed, but most of them not allowing for zero values. Secondly, the case of compositional data being in the predictor variables side has gained little research interest. Surprisingly enough, the case of both the response and predictor variables being compositional data has not been widely studied. This paper suggests a solution for this last problem. Principal components regression using the-transformation and Kulback-Leibler divergence are the key elements of the proposed approach. An advantage of this approach is that zero values are allowed, in both the response and the predictor variables side. Simulation studies and examples with real data illustrate the performance of our algorithm.

Several methods have been proposed to allow functional genomic information to inform prior distributions in Bayesian fine-mapping case-control association studies. None of these methods allow the inclusion of partially observed functional genomic information. We use functional significance (FS) scores that combine information across multiple bioinformatics sources to inform our effect size prior distributions. These scores are not available for all singlenucleotide polymorphisms (SNPs) but by partitioning SNPs into naturally occurring FS score groups, we show how missing FS scores can easily be accommodated via finite mixtures of elicited priors. Most current approaches adopt a formal Bayesian variable selection approach and either limit the number of causal SNPs allowed or use approximations to avoid the need to explore the vast parameter space. We focus instead on achieving differential shrinkage of the effect sizes through prior scale mixtures of normals and use marginal posterior probability intervals to select candidate causal SNPs. We show via a simulation study how this approach can improve localisation of the causal SNPs compared to existing mutli-SNP fine-mapping methods. We also apply our approach to fine-mapping a region around the CASP8 gene using the iCOGS consortium breast cancer SNP data. K E Y W O R D SBayesian, fine mapping, missing data, prior information, variable selection

The parametric Welch t-test and the non-parametric Wilcoxon-Mann-Whitney test are the most commonly used two independent sample means tests. More recent testing approaches include the nonparametric, empirical likelihood and exponential empirical likelihood. However, the applicability of these non-parametric likelihood testing procedures is limited partially because of their tendency to inflate the type I error in small sized samples. In order to circumvent the type I error problem, we propose simple calibrations using the t distribution and bootstrapping. The two non-parametric likelihood testing procedures, with and without those calibrations, are then compared against the Wilcoxon-Mann-Whitney test and the Welch t-test. The comparisons are implemented via extensive Monte Carlo simulations on the grounds of type I error and power in small/medium sized samples generated from various nonnormal populations. The simulation studies clearly demonstrate that a) the t calibration improves the type I error of the empirical likelihood, b) bootstrap calibration improves the type I error of both nonparametric likelihoods, c) the Welch t-test with or without bootstrap calibration attains the type I error and produces similar levels of power with the former testing procedures, and d) the Wilcoxon-Mann-Whitney test produces inflated type I error while the computation of an exact p-value is not feasible in the presence of ties with discrete data. Further, an application to real gene expression data illustrates the computational high cost and thus the impracticality of the non parametric likelihoods. Overall, the Welch t-test, which is highly computationally efficient and readily interpretable, is shown to be the best method when testing equality of two population means. keywords: Sections; Hypothesis testing; Welch t-test; empirical likelihood; bootstrap amscode: 62G10; 62F40 1 arXiv:1812.11361v2 [stat.ME] 4 Oct 2019 I error, but the simulation study was rather small and narrow. Deriving the Bartlett correction can be challenging and therefore should be estimated via bootstrap [21], and with an increased computational cost. On the same spirit, [17,[22][23][24][25] proposed bootstrap calibration 3 of the EL test statistic directly. In contrast to EL, the EEL, does not admit Bartlett correction [26] and an adjustment was suggested by [27]. This should not be considered as a disadvantage, according to [28], as the Bartlett correction is sometimes ineffective, while EEL shares the same higher order asymptotic properties of the EL [28] as established in [29]. Finally, the non-parametric WMW test is based on ranks and hence unable to capture the differences in the means. The statistic of the WMW without ties is asymptotically normally distributed and although exact p-value computation is possible it becomes difficult as the number of combinations increase. In the presence of ties in small sample sizes, asymptotic normality does not hold and exact p-value computation is not feasible.The parametric Welch t-test is one of the oldest and...