The left (right) graph is the histogram of lifespan for WL-HF (EO-HF) group in the data from Vasselli et al

[].<p><b>Copyright information:</b></p><p>Taken from "Testing for differences in distribution tails to test for differences in 'maximum' lifespan"</p><p>http://www.biomedcentral.com/1471-2288/8/49</p><p>BMC Medical Research Methodology 2008;8():49-49.</p><p>Published online 25 Jul 2008</p><p>PMCID:PMC2529340.</p><p></p

The left (right) graph is the histogram of lifespan for group with genotype ' / ' ('-/-') in the data from Redmann & Argyropoulos

<p><b>Copyright information:</b></p><p>Taken from "Testing for differences in distribution tails to test for differences in 'maximum' lifespan"</p><p>http://www.biomedcentral.com/1471-2288/8/49</p><p>BMC Medical Research Methodology 2008;8():49-49.</p><p>Published online 25 Jul 2008</p><p>PMCID:PMC2529340.</p><p></p

A proposed metric for assessing the measurement quality of individual microarrays-1

<p><b>Copyright information:</b></p><p>Taken from "A proposed metric for assessing the measurement quality of individual microarrays"</p><p>BMC Bioinformatics 2006;7():35-35.</p><p>Published online 23 Jan 2006</p><p>PMCID:PMC1373606.</p><p>Copyright © 2006 Kim et al; licensee BioMed Central Ltd.</p>t corner of chip 12 is shown enlarged

A proposed metric for assessing the measurement quality of individual microarrays-0

<p><b>Copyright information:</b></p><p>Taken from "A proposed metric for assessing the measurement quality of individual microarrays"</p><p>BMC Bioinformatics 2006;7():35-35.</p><p>Published online 23 Jan 2006</p><p>PMCID:PMC1373606.</p><p>Copyright © 2006 Kim et al; licensee BioMed Central Ltd.</p>and model (2), respectively. Black rectangles and white diamonds represent GEODEX computed by model (2), using measurements in the log scale on base 2 and trimmed measurements after removing four blocks on the corners, respectively. b. For comparisons between different measures of gene expression, black circles, white circles, and black upper triangles represent GEODEX of difference (PM-MM) measurements of pairs of the perfect match (PM) and mismatch (MM) probes, of PM-only measurements, and of MM-only measurements, respectively. GEODEX were computed by model (2) (N= 36). X-axis indicates a chip identification number and Y-axis indicates the degree of GEODEX

A proposed metric for assessing the measurement quality of individual microarrays-3

<p><b>Copyright information:</b></p><p>Taken from "A proposed metric for assessing the measurement quality of individual microarrays"</p><p>BMC Bioinformatics 2006;7():35-35.</p><p>Published online 23 Jan 2006</p><p>PMCID:PMC1373606.</p><p>Copyright © 2006 Kim et al; licensee BioMed Central Ltd.</p>riation (CV) of measurements for experiment A (a simulation study). Scatter plot b (d) presents the relationship between pairwise GEODEX computed by equation (5) and the degree of inter-chip discrepancy computed by equation (4) for every pair of technical replicates for biological samples in experiment A (for every pair of the sample array and simulated replicates for a simulation study). GEODEX was computed by model (2)

A proposed metric for assessing the measurement quality of individual microarrays-2

<p><b>Copyright information:</b></p><p>Taken from "A proposed metric for assessing the measurement quality of individual microarrays"</p><p>BMC Bioinformatics 2006;7():35-35.</p><p>Published online 23 Jan 2006</p><p>PMCID:PMC1373606.</p><p>Copyright © 2006 Kim et al; licensee BioMed Central Ltd.</p>36 blocks per chip (i.e., N= 36). The X-axis indicates a chip identification number. b. A boxplot of 36 blocks: Each box shows the distribution of blockwise GEODEX for 25 chips per block. The X-axis indicates a block identification number within the chip. Crosses represent outliers

Path Diagram Illustrating the Relationship between Admixture, Ancestry, and Phenotype

<p>This figure was created based on the rules of path diagrams outlined in [<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.0020137#pgen-0020137-b065" target="_blank">65</a>] with minor modifications. We wish to explore the association of the putative QTL with a given phenotype. However, as illustrated, this zero-order (i.e., unadjusted) association may be affected by relationships with other factors. The rectangles and ellipses in the path diagram represent observable and latent (unobservable) variables, respectively. The dashed ellipses indicate variables potentially capable of influencing the phenotype. Sources of error from random variation introduced by the meiosis process or measurement error are indicated for observable and unobservable variables. The variable <i>v</i>_i, <i>i</i> = 1,2 denotes the number of alleles inherited from a specific parental population at the i^th QTL (the putative QTL, QTL 1, is observed, whereas QTL 2 is unobserved). Note that for a specific QTL, only two possible values of <i>V</i>_i, <i>i</i> = 1,2 are considered in the model; the third possible value will serve as a reference. <i>P</i>_i, <i>i</i> = 1,2 represents the ancestry of each parent for a sampled individual. The objective is to test for association between the putative QTL and the observed phenotype. Observed association may simply result from unaccounted correlation among the putative QTL, the phenotype, and individual ancestry. The association can be further confounded by the presence of unobserved factors, such as QTL 2. Controlling for parental and individual ancestry would break this confounding pathway. Because ancestry is not directly observable, individual admixture estimates are used as surrogates. These estimates, obtainable through existing software, can be seen as error-contaminated measurements of the true individual ancestry values. Hence, the measurement error problem must be addressed when including these estimates in the model. Hoggart et al. [<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.0020137#pgen-0020137-b007" target="_blank">7</a>] offer a figure similar to the one presented here.</p

Power improvement of alpha-spending p-values with respect to the ordinary t-test

<p><b>Copyright information:</b></p><p>Taken from "An adaptive alpha spending algorithm improves the power of statistical inference in microarray data analysis"</p><p>Bioinformation 2007;1(10):384-389.</p><p>Published online 10 Apr 2007</p><p>PMCID:PMC1896052.</p><p></p> The results are from the partial null hypothesis simulations with 20% of the genes differentially expressed and correlated with the same correlation coefficient and 80% of the genes non-differentially expressed and uncorrelated. For = 700 , the 700 = 7x100 simulated data sets per plot were obtained by independently generating 100 data sets for each of seven different values of the population mean differential expression Δ . These seven values of Δ = Δ(1– ) were obtained such that the corresponding power of the ordinary t-test in detecting the differentially expressed genes was varied by1– = 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8 . For = 2000 the 30 simulated data sets correspond to 1– = 0.5 only. The situation = 2000 is simulated for = 4, 6 but not for =1

Conditioning on Individual Ancestry and the Product of Parental Ancestries Is Necessary and Sufficient to Control for Confounding

<div><p>A dataset was simulated from idealized circumstances for the purposes of illustration. The dataset contained 1,000 individuals that were admixed from parental populations <i>V</i> and <i>V</i>. For each individual, both parents had the same amount of <i>V</i> ancestry. The <i>V</i> ancestry proportion of each individual was drawn from a beta distribution (Beta [0.3771, 0.8341]). These parameter values were based on estimates of African ancestry proportions from a sample of 479 individuals recruited from different previously described studies in New York City, New York, and Birmingham, Alabama [<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.0020137#pgen-0020137-b066" target="_blank">66</a>–<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.0020137#pgen-0020137-b068" target="_blank">68</a>]. We simulated a trait-influencing diallelic QTL (G1) that had alleles G and g with frequencies 0.2 and 0.8, respectively, in population <i>V</i> and frequencies 0.8 and 0.2, respectively, in population <i>V</i>. We simulated a phenotype, Y, that was a function of G1 and a random normal deviate. Finally, we simulated a marker (G2) that had alleles with frequencies 0.2 and 0.8 in population <i>V</i> and complementary frequencies in population <i>V</i>. Alleles at G2 did not influence Y and G2 was unlinked to G1. However, G1, G2, and Y are all correlated with ancestry. However, the association between G2 and Y is spurious. We then test for association between Y and G2 by regressing Y on two dummy codes for the genotypes at G2 [<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.0020137#pgen-0020137-b069" target="_blank">69</a>] and conducting a two degrees of freedom (df) test under the following scenarios: (1) without any type of control (i.e., no covariates); (2) controlling for linear term of true individual ancestry when the alleles at G1 act in an additive fashion; (3) controlling for linear term of true individual ancestry when the alleles at G1 act in an overdominant fashion; and (4) controlling for linear and quadratic term of true individual ancestry when the alleles at G1 act in an overdominant fashion. Because we imposed the simplifying condition that for each individual, both parents had the same amount of <i>V</i> ancestry, the square of individual ancestry is equivalent to the product of parental ancestries. Since alleles at G2 do not cause variation in Y nor is G2 linked to a gene that causes variation in Y, every significant association found under any of the above scenarios constitutes a false positive. The graphs in this panel were created by simulating 1,000 independent replicate datasets. The dots on each graph located on the left portion of each panel represent the observed <i>p</i> values (expressed on a −log₁₀ scale) for the test for the effect of G2 for each dataset. The bar plot of the right section of each panel represents the observed ratio of the empirical to the nominal type I error for each simulation.</p><p>(A) Not controlling for ancestry leads to inflated type I error. The degree of type 1 error rate inflation increases with smaller α levels.</p><p>(B) Controlling for only the linear term of individual ancestry is sufficient only when the confounding QTL affects the phenotype only in an additive fashion. In this case, there was no excess of type 1 errors.</p><p>(C) When the QTL affects the phenotype in a nonadditive fashion (in this case, through overdominance), controlling for the linear term of ancestry is insufficient to remove the confounding effect. The type I error rates remain quite inflated even after including true individual ancestry in the model.</p><p>(D) When the QTL affects the phenotype in an overdominant fashion, controlling for true individual ancestry and the product of parental ancestries effectively eliminates the confounding. In this case, the ratios of empirical to nominal α levels are within sampling error of 1.0.</p></div

Reliability of Individual Admixture Estimates Used as Estimates of Individual Ancestry

<p>We simulated a randomly mating population or organisms based upon the “island model” or intermixture admixture process [<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.0020137#pgen-0020137-b016" target="_blank">16</a>]. Because the data are simulated, true individual ancestry and true individual admixture are known for each individual. True individual ancestry is displayed on each abscissa. The top four panels each contain data from a simulation of 500 admixed individuals five generations after the admixture event. Two hundred ancestry informative markers are genotyped with an average allele frequency difference between the original parental populations of 0.3. Founders (250 from each parental population) were simulated for use in the procedures that estimated individual admixture. The bottom four panels also each contain data from a simulation of 500 admixed individuals five generations after the admixture event. However, here only 50 ancestry informative markers are genotyped with an average allele frequency difference between the original parental populations of only 0.2 and only 40 founders (20 from each parental population) were simulated for use in the procedures that estimated individual admixture. Maximum likelihood estimates were calculated using Tang et al.'s [<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.0020137#pgen-0020137-b010" target="_blank">10</a>] method. Structure estimates were produced using software described here [<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.0020137#pgen-0020137-b008" target="_blank">8</a>,<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.0020137#pgen-0020137-b064" target="_blank">64</a>]. Several points are noteworthy. First, our results in the top and bottom rightmost panels recapitulate results obtained by Tang et al. [<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.0020137#pgen-0020137-b010" target="_blank">10</a>] and Zhu et al. [<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.0020137#pgen-0020137-b016" target="_blank">16</a>]. However, our results also show that even though two methods of estimating individual admixture may produce correlations very close to 1.0, the correlation of these estimates with true ancestry may be far lower (only ~.80 in our upper row and only ~.50 in our lower row). Finally, the two leftmost figures highlight the fact that there are important differences between true admixture and true ancestry.</p