Estimating the mean and standard deviation of concentration distributions using censored samples

Environmental data sets of pollutant concentrations in air, water, and soil frequently include unquantified sample values reported only as being below the analytical method detection limit. These values, referred to as censored values, should be considered in the estimation of distribution parameters as each represents some value of pollutant concentration between zero and the detection limit. Most of the currently accepted methods for estimating the population parameters of environmental data sets containing censored values rely upon the assumption of an underlying normal (or transformed normal) distribution. This assumption can result in unacceptable levels of error in parameter estimation due to the unbounded left tail of the normal distribution. With the beta distribution, which is bounded by the same range of a distribution of concentrations, $\rm\lbrack0\le x\le1\rbrack,$ parameter estimation errors resulting from improper distribution bounds are avoided. This work developed a method that uses the beta distribution to estimate population parameters from censored environmental data sets and evaluated its performance in comparison to currently accepted methods that rely upon an underlying normal (or transformed normal) distribution. Data sets were generated assuming typical values encountered in environmental pollutant evaluation for mean, standard deviation, and number of variates. For each set of model values, data sets were generated assuming that the data was distributed either normally, lognormally, or according to a beta distribution. For varying levels of censoring, two established methods of parameter estimation, regression on normal ordered statistics, and regression on lognormal ordered statistics, were used to estimate the known mean and standard deviation of each data set. The method developed for this study, employing a beta distribution assumption, was also used to estimate parameters and the relative accuracy of all three methods were compared. For data sets of all three distribution types, and for censoring levels up to 50%, the performance of the new method equaled, if not exceeded, the performance of the two established methods. Because of its robustness in parameter estimation regardless of distribution type or censoring level, the method employing the beta distribution should be considered for full development in estimating parameters for censored environmental data sets. ^

Pathway analysis of genome-wide association study data in primary biliary cirrhosisa

Genome-wide association studies (GWAS) have successfully identified several genetic loci associated with inherited predisposition to primary biliary cirrhosis (PBC), the most common autoimmune disease of the liver. Pathway-based tests constitute a novel paradigm for GWAS analysis. By evaluating genetic variation across a biological pathway (gene set), these tests have the potential to determine the collective impact of variants with subtle effects that are individually too weak to be detected in traditional single variant GWAS analysis. To identify biological pathways associated with the risk of development of PBC, GWAS of PBC from Italy (449 cases and 940 controls) and Canada (530 cases and 398 controls) were independently analyzed. The linear combination test (LCT), a recently developed pathway-level statistical method was used for this analysis. For additional validation, pathways that were replicated at the P <0.05 level of significance in both GWAS on LCT analysis were also tested for association with PBC in each dataset using two complementary GWAS pathway approaches. The complementary approaches included a modification of the gene set enrichment analysis algorithm (i-GSEA4GWAS) and Fisher's exact test for pathway enrichment ratios. Twenty-five pathways were associated with PBC risk on LCT analysis in the Italian dataset at P<0.05, of which eight had an FDR<0.25. The top pathway in the Italian dataset was the TNF/stress related signaling pathway (p=7.38×10 -4, FDR=0.18). Twenty-six pathways were associated with PBC at the P<0.05 level using the LCT in the Canadian dataset with the regulation and function of ChREBP in liver pathway (p=5.68×10-4, FDR=0.285) emerging as the most significant pathway. Two pathways, phosphatidylinositol signaling system (Italian: p=0.016, FDR=0.436; Canadian: p=0.034, FDR=0.693) and hedgehog signaling (Italian: p=0.044, FDR=0.636; Canadian: p=0.041, FDR=0.693), were replicated at LCT P<0.05 in both datasets. Statistically significant association of both pathways with PBC genetic susceptibility was confirmed in the Italian dataset on i-GSEA4GWAS. Results for the phosphatidylinositol signaling system were also significant in both datasets on applying Fisher's exact test for pathway enrichment ratios. This study identified a combination of known and novel pathway-level associations with PBC risk. If functionally validated, the findings may yield fresh insights into the etiology of this complex autoimmune disease with possible preventive and therapeutic application.^

An examination of the relationship between maternal and neighborhood-level characteristics and intrauterine growth retardation in Harris County, Texas, 1999--2001

The persistence of low birth weight and intrauterine growth retardation (IUGR) in the United States has puzzled researchers for decades. Much of the work that has been conducted on adverse birth outcomes has focused on low birth weight in general and not on IUGR. Studies that have examined IUGR specifically thus far have focused primarily on individual-level maternal risk factors. These risk factors have only been able to explain a small portion of the variance in IUGR. Therefore, recent work has begun to focus on community-level risk factors in addition to the individual-level maternal characteristics. This study uses Social Ecology to examine the relationship of individual and community-level risk factors and IUGR. Logistic regression was used to establish an individual-level model based on 155, 856 births recorded in Harris County, TX during 1999-2001. IUGR was characterized using a fetal growth ratio method with race/ethnic and sex specific mean birth weights calculated from national vital records. The spatial distributions of 114,460 birth records spatially located within the City of Houston were examined using choropleth, probability and density maps. Census tracts with higher than expected rates of IUGR and high levels of neighborhood disadvantage were highlighted. Neighborhood disadvantage was constructed using socioeconomic variables from the 2000 U.S. Census. Factor analysis was used to create a unified single measure. Lastly, a random coefficients model was used to examine the relationship between varying levels of community disadvantage, given the set of individual-level risk factors for 152,997 birth records spatially located within Harris County, TX. Neighborhood disadvantage was measured using three different indices adapted from previous work. The findings show that pregnancy-induced hypertension, previous preterm infant, tobacco use and insufficient weight gain have the highest association with IUGR. Neighborhood disadvantage only slightly further increases the risk of IUGR (OR 1.12 to 1.23). Although community level disadvantage only helped to explain a small proportion of the variance of IUGR, it did have a significant impact. This finding suggests that community level risk factors should be included in future work with IUGR and that more work needs to be conducted. ^