33 research outputs found

    Standard error of the estimate of genetic correlation from a bivariate analysis of two traits measured on the same or different samples using genome-wide SNP data.

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    <p>Same sample: two traits are measured on the same set of samples. Different sample: two traits are measured on the different sets of samples. : parameter of genetic correlation (i.e. proportion of simulated causal variants shared between the two traits). Est.: estimate of genetic correlation from 100 simulations. SE(Obs.): mean of the observed standard errors from 100 simulations. s.e.m.: standard error of the mean (i.e. SE(Obs.)). SE(Approx.): standard error calculated from our approximation theory.</p

    Statistical power of detecting genetic variance (correlation) under different study designs.

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    <p><b>a</b>) Univarite analysis of a quantitative trait. <b>b</b>) Univariate analysis of a case-control study assuming equal number of cases and controls (<i>v</i> = 0.5) and heritability of liability () of 0.2. <b>c</b>) Bivariate analysis of two quantitative traits measured on the same set of individuals, assuming heritability of 0.2 for both traits. <b>d</b>) Bivariate analysis of two case-control studies on independent sets of samples, assuming equal numbers of cases and controls for each disease, and equal sample size (total number of cases and controls), equal heritability of liability ( = 0.2) and equal prevalence (<i>K</i> = 0.01) for both diseases.</p

    Standard error of the estimate of variance explained by all SNPs vs. sample size.

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    <p>The first three columns are the averaged standard error observed from 100 simulations under three heritability levels. The last column is the predicted standard error from our approximation theory. The plotted data can be found in <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1004269#pgen.1004269.s002" target="_blank">Table S1</a>.</p

    Standard errors of the estimates of variance explained by all SNPs on the observed scale () from published analyses of case-control studies for a number of diseases vs. those predicted from the approximation theory.

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    <p><i>N</i><sub>cases</sub>: number of cases. <i>N</i><sub>controls</sub>: number of controls. SE(Obs.): reported standard error of the estimate of from real data analysis. SE(Approx.): standard error of calculated from our approximation theory. MDD: major depression disorder. ASD: autism spectrum disorders. ADHD: attention-deficit/hyperactivity disorder.</p

    Standard errors of the estimates of genetic correlations from published bivariate analyses of case-control studies for psychiatric diseases [7] vs. those predicted from the approximation theory.

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    <p>SCZ: schizophrenia. BPD: bipolar disorder. MDD: major depression disorder. ASD: autism spectrum disorders. ADHD: attention-deficit/hyperactivity disorder. <i>N</i><sub>cases</sub>: number of cases. <i>N</i><sub>controls</sub>: number of controls. <i>K</i>: disease prevalence. : estimate of variance explained by all SNPs on the observed scale, which was calculated from the reported and disease prevalence in Supplementary <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1004269#pgen-1004269-t001" target="_blank">Table 1</a> of Lee et al. <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1004269#pgen.1004269-Lee3" target="_blank">[7]</a>. : genetic correlation. SE(Obs.): reported standard error of the estimate of from real data analysis. SE(Approx.): standard error of calculated from our approximation theory.</p

    Resolution for varying relatedness using GRM, encGRM and <i>encG-reg</i>.

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    The figure shows the resolution for detecting relatives or overlapping samples with respect to varying number of markers at every row (for better illustration me was twice that of Eq 3) and the degree of relatives to be detected (r = 0, 1, and 2). The y axis is the relatedness calculated from GRM and the x axis is the estimated relatedness calculated from encG-reg (A) and encGRM (B). Each point represents an individual pair between cohort 1 and cohort 2 (there are 200 × 200 = 40,000 pairs in total), given the simulated relatedness. The dotted line indicates the 95% confidence interval of the relatedness directly estimated from the original genotype (blue) and the encrypted genotype (red). The table provides how m and k are estimated. The columns “under minimal me” provide benchmark for a parameter, and it is practically to choose 2×me and then estimate k as shown under the column “practical me”.</p

    Workflow of <i>encG-reg</i> and its practical timeline as exercised in Chinese cohorts.

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    The mathematical details of encG-reg are simply algebraic, but its inter-cohort implementation involves coordination. (A) We illustrate its key steps, the time cost of which was adapted from the present exercise for 9 Chinese datasets (here simplified as three cohorts). Cohort assembly: It took us about a week to call and got positive responses from our collaborators (See Table 3), who agreed with our research plan. Inter-cohort QC: we received allele frequencies reports from each cohort and started to implement inter-cohort QC according to “geo-geno” analysis (see Fig 6). This step took about two weeks. Encrypt genotypes: upon the choice of the exercise, it could be exhaustive design (see UKB example), which may maximize the statistical power but with increased logistics such as generating pairwise Sij; in the Chinese cohorts study we used parsimony design, and generated a unique S given 500 SNPs that were chosen from the 7,009 common SNPs. It took about a week to determine the number of SNPs and the dimension of k according to Eq 3 and 4, and to evaluate the effective number of markers. Perform encG-reg and validation: we conducted inter-cohort encG-reg and validated the results (see Fig 7 and Table 4). It took one week. (B) Two interactions between data owners and central analyst, including example data for exchange and possible attacks and corresponding preventative strategies.</p

    Cohort-level genetic background analyses for Chinese cohorts under parsimony encG-reg analysis.

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    (A) Overview of the intersected SNPs across cohorts, a black dot indicated its corresponding cohort was included. Each row represented one cohort while each column represented one combination of cohorts. Dots linked by lines suggested cohorts in this combination. The height of bars represented the cohort’s SNP numbers (rows) or SNP intersection numbers (columns). Inset histogram plots show the distribution of the 7,009 intersected SNPs and the 500 SNPs randomly chosen from the 7,009 SNPs for encG-reg analysis. (B) 7,009 SNPs were used to estimate fPC from the intersection of SNPs for the 9 cohorts. Each triangle represented one Chinese cohort and was placed according to their first two principal component scores (fPC1 and fPC2) derived from the received allele frequencies. (C) Five private datasets have been pinned onto the base map from GADM (https://gadm.org/data.html) using R language. The size of point indicates the sample size of each dataset. (D) Global fStructure plot indicates global-level Fst-derived genetic composite projected onto the three external reference populations: 1KG-CHN (CHB and CHS), 1KG-EUR (CEU and TSI), and 1KG-AFR (YRI), respectively; 4,296 of the 7,009 SNPs intersected with the three reference populations were used. (E) Within Chinese fStructure plot indicates within-China genetic composite. The three external references are 1KG-CHB (North Chinese), 1KG-CHS (South Chinese), and 1KG-CDX (Southwest minority Chinese Dai), respectively; 4,809 of the 7,009 SNPs intersected with these three reference populations were used. Along x axis are 9 Chinese cohorts and the height of each bar represents its proportional genetic composition of the three reference populations. Cohort codes: YRI, Yoruba in Ibadan representing African samples; CHB, Han Chinese in Beijing; CHS, Southern Han Chinese; CHN, CHB and CHS together; CEU, Utah Residents with Northern and Western European Ancestry; TSI, Tuscani in Italy; CDX, Chinese Dai in Xishuangbanna.</p
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