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</o:shapelayout></xml><![endif]--></head><body lang=NL link="#0563C1" vlink="#954F72"><div class=WordSection1><p class=MsoNormal><span lang=EN-US>Hi,<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US>We are a group of geneticists using meta-regression for genome-wide meta-analysis and encountered a hidden thorny issue.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US>We use metafor rma.mv models to meta-analyse:<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><ul style='margin-top:0cm' type=disc><li class=MsoListParagraph style='margin-left:0cm;mso-list:l1 level1 lfo1'><span lang=EN-US>130 correlated input statistics <o:p></o:p></span></li><li class=MsoListParagraph style='margin-left:0cm;mso-list:l1 level1 lfo1'><span lang=EN-US>each statistics has BETAs for 8 million variants (reflecting genetic association effects) <o:p></o:p></span></li></ul><p class=MsoListParagraph><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US>capturing:<o:p></o:p></span></p><ul style='margin-top:0cm' type=disc><li class=MsoListParagraph style='margin-left:0cm;mso-list:l0 level1 lfo2'><span lang=EN-US>70000 individuals<o:p></o:p></span></li><li class=MsoListParagraph style='margin-left:0cm;mso-list:l0 level1 lfo2'><span lang=EN-US>400000 repeat observations<o:p></o:p></span></li></ul><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US>from<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US>23 cohorts.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US>Across the 8 million variants, the following model fits quite well for each variant, based on a (fairly) well-known phenotypic correlation matrix for sample overlap (Vsampoverlap) scaled to the SE of each BETA.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-family:"Courier New"'>model_cov <- rma.mv(yi = BETA, V = Vsampoverlap, mods = COV1+ COV2+COV3, random= list(~ 1|COHORT/VAR), data = df)}, silent = F)<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US>where VAR specifies the input statistics, COHORT represents cohorts, and COV represents fixed effects.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US>However, when predicting BETAs for each of the 8 million variants across a grid of fixed effect predictors (COV1, COV2, COV3) we note that, on average, derived genome-wide Z-scores based on predicted BETAs and SEs are too conservative and deviate from the expected null distribution in a quantile-quantile plot, affecting all predictions. We can also quantify this deviation from a null distribution across all 8 million variants using the LDSC intercept (i.e. the Linkage disequilibrium Score regression intercept for a variant-based heritability estimation; Bullik-Sullivan 2015: <a href="https://pubmed.ncbi.nlm.nih.gov/25642630/">https://pubmed.ncbi.nlm.nih.gov/25642630/</a>), which should be one if unbiased, but we observe ~0.9(SE=0.005). Note that the intercept would be above one, if test statistics were inflated.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US>Thus, we think we subtly over-correct for relatedness and quench the power of our analysis. Would there be any thoughts within the group as to how to relax the adjustment for relatedness in metafor?<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US>Thanks so much for any input,<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US>Beate<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US>PS: Note to random geneticists in the group: If we could, we would replace the phenotypic correlation matrix with the non-genetic part of the phenotypic correlation matrix, but such an estimation is unreliable given the small sample size of most cohorts.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><pre style='background:#002240;word-break:break-all'><span class=gnd-iwgdh3b><span lang=EN-US style='font-size:8.0pt;font-family:"Lucida Console";color:white;border:none windowtext 1.0pt;padding:0cm'>R version 4.1.3 (2022-03-10)<o:p></o:p></span></span></pre><pre style='background:#002240;word-break:break-all'><span class=gnd-iwgdh3b><span lang=EN-US style='font-size:8.0pt;font-family:"Lucida Console";color:white;border:none windowtext 1.0pt;padding:0cm'>Platform: x86_64-w64-mingw32/x64 (64-bit)<o:p></o:p></span></span></pre><pre style='background:#002240;word-break:break-all'><span class=gnd-iwgdh3b><span lang=EN-US style='font-size:8.0pt;font-family:"Lucida Console";color:white;border:none windowtext 1.0pt;padding:0cm'>Running under: Windows 10 x64 (build 19045)<o:p></o:p></span></span></pre><pre style='background:#002240;word-break:break-all'><span class=gnd-iwgdh3b><span lang=EN-US style='font-size:8.0pt;font-family:"Lucida Console";color:white;border:none windowtext 1.0pt;padding:0cm'><o:p> </o:p></span></span></pre><pre style='background:#002240;word-break:break-all'><span class=gnd-iwgdh3b><span lang=EN-US style='font-size:8.0pt;font-family:"Lucida Console";color:white;border:none windowtext 1.0pt;padding:0cm'>Matrix products: default<o:p></o:p></span></span></pre><pre style='background:#002240;word-break:break-all'><span class=gnd-iwgdh3b><span lang=EN-US style='font-size:8.0pt;font-family:"Lucida Console";color:white;border:none windowtext 1.0pt;padding:0cm'><o:p> </o:p></span></span></pre><pre style='background:#002240;word-break:break-all'><span class=gnd-iwgdh3b><span lang=EN-US style='font-size:8.0pt;font-family:"Lucida Console";color:white;border:none windowtext 1.0pt;padding:0cm'>locale:<o:p></o:p></span></span></pre><pre style='background:#002240;word-break:break-all'><span class=gnd-iwgdh3b><span lang=EN-US style='font-size:8.0pt;font-family:"Lucida Console";color:white;border:none windowtext 1.0pt;padding:0cm'>[1] LC_COLLATE=English_Europe.1252 LC_CTYPE=English_Europe.1252 LC_MONETARY=English_Europe.1252 LC_NUMERIC=C <o:p></o:p></span></span></pre><pre style='background:#002240;word-break:break-all'><span class=gnd-iwgdh3b><span lang=EN-US style='font-size:8.0pt;font-family:"Lucida Console";color:white;border:none windowtext 1.0pt;padding:0cm'>[5] LC_TIME=English_Europe.1252 <o:p></o:p></span></span></pre><pre style='background:#002240;word-break:break-all'><span class=gnd-iwgdh3b><span lang=EN-US style='font-size:8.0pt;font-family:"Lucida Console";color:white;border:none windowtext 1.0pt;padding:0cm'><o:p> </o:p></span></span></pre><pre style='background:#002240;word-break:break-all'><span class=gnd-iwgdh3b><span lang=EN-US style='font-size:8.0pt;font-family:"Lucida Console";color:white;border:none windowtext 1.0pt;padding:0cm'>attached base packages:<o:p></o:p></span></span></pre><pre style='background:#002240;word-break:break-all'><span class=gnd-iwgdh3b><span lang=EN-US style='font-size:8.0pt;font-family:"Lucida Console";color:white;border:none windowtext 1.0pt;padding:0cm'>[1] parallel stats graphics grDevices utils datasets methods base <o:p></o:p></span></span></pre><pre style='background:#002240;word-break:break-all'><span class=gnd-iwgdh3b><span lang=EN-US style='font-size:8.0pt;font-family:"Lucida Console";color:white;border:none windowtext 1.0pt;padding:0cm'><o:p> </o:p></span></span></pre><pre style='background:#002240;word-break:break-all'><span class=gnd-iwgdh3b><span lang=EN-US style='font-size:8.0pt;font-family:"Lucida Console";color:white;border:none windowtext 1.0pt;padding:0cm'>other attached packages:<o:p></o:p></span></span></pre><pre style='background:#002240;word-break:break-all'><span class=gnd-iwgdh3b><span lang=EN-US style='font-size:8.0pt;font-family:"Lucida Console";color:white;border:none windowtext 1.0pt;padding:0cm'>[1] data.table_1.14.2 metafor_4.4-0 numDeriv_2016.8-1.1 metadat_1.2-0 Matrix_1.4-0 </span></span><span lang=EN-US><o:p></o:p></span></pre><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><b><span lang=EN-GB style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#4472C4;background:white;mso-fareast-language:EN-GB'>Beate St Pourcain,</span></b><b><span lang=EN-GB style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#4472C4;mso-fareast-language:EN-GB'> PhD<o:p></o:p></span></b></p><p class=MsoNormal><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:black;background:white;mso-fareast-language:EN-GB'>Senior Investigator & Group Leader<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:black;background:white;mso-fareast-language:EN-GB'>Room A207<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:black;background:white;mso-fareast-language:EN-GB'>Max Planck Institute for Psycholinguistics</span><span lang=EN-GB style='font-family:"Arial",sans-serif;mso-fareast-language:EN-GB'> </span><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:black;mso-fareast-language:EN-GB'>| </span><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:black;background:white;mso-fareast-language:EN-GB'>Wundtlaan 1</span><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:black;mso-fareast-language:EN-GB'> | 6525 XD Nijmegen | The Netherlands</span><span lang=en-150 style='font-size:8.0pt;font-family:"Arial",sans-serif;color:black;mso-fareast-language:EN-GB'><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:black;mso-fareast-language:EN-GB'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:black;mso-fareast-language:EN-GB'><o:p> </o:p></span></p><p class=MsoNormal><b><span lang=en-150 style='font-size:8.0pt;font-family:"Arial",sans-serif;color:#4472C4;background:white;mso-fareast-language:EN-GB'>@bstpourcain</span></b><b><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:#4472C4;mso-fareast-language:EN-GB'><o:p></o:p></span></b></p><p class=MsoNormal><b><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:#4472C4;mso-fareast-language:EN-GB'>T</span></b><b><span lang=en-150 style='font-size:8.0pt;font-family:"Arial",sans-serif;color:#4472C4;mso-fareast-language:EN-GB'>el</span></b><b><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:#4472C4;mso-fareast-language:EN-GB'>:</span></b><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;mso-fareast-language:EN-GB'> </span><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:black;mso-fareast-language:EN-GB'><a href="tel:+31%2024%20352%201964" target="_blank"><span style='color:black;background:white;text-decoration:none'>+31 24 3521964</span></a></span><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;mso-fareast-language:EN-GB'><o:p></o:p></span></p><p class=MsoNormal><b><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:#4472C4;background:white;mso-fareast-language:EN-GB'>F</span></b><b><span lang=en-150 style='font-size:8.0pt;font-family:"Arial",sans-serif;color:#4472C4;background:white;mso-fareast-language:EN-GB'>ax</span></b><b><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:#4472C4;background:white;mso-fareast-language:EN-GB'>:</span></b><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;background:white;mso-fareast-language:EN-GB'> </span><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:black;mso-fareast-language:EN-GB'><a href="tel:+31%2024%20352%201213" target="_blank"><span style='color:black;background:white;text-decoration:none'>+31 24 3521213</span></a><o:p></o:p></span></p><p class=MsoNormal><b><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:#4472C4;mso-fareast-language:EN-GB'>ORCID:</span></b><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:black;mso-fareast-language:EN-GB'> <a href="https://orcid.org/0000-0002-4680-3517"><span style='color:black;text-decoration:none'>https://orcid.org/0000-0002-4680-3517</span></a><o:p></o:p></span></p><p class=MsoNormal><b><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:#4472C4;mso-fareast-language:EN-GB'>W</span></b><b><span lang=en-150 style='font-size:8.0pt;font-family:"Arial",sans-serif;color:#4472C4;mso-fareast-language:EN-GB'>eb</span></b><b><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:#4472C4;mso-fareast-language:EN-GB'>:</span></b><b><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;mso-fareast-language:EN-GB'> </span></b><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:black;background:white;mso-fareast-language:EN-GB'><a href="https://www.mpi.nl/departments/language-and-genetics/projects/population-variation-and-human-communication/"><span style='color:blue'>https://www.mpi.nl/departments/language-and-genetics/projects/population-variation-and-human-communication/</span></a><o:p></o:p></span></p><p class=MsoNormal><b><span lang=en-150 style='font-size:8.0pt;font-family:"Arial",sans-serif;color:#4F81BD;mso-fareast-language:EN-GB'>Further </span></b><b><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:#4F81BD;mso-fareast-language:EN-GB'>affiliations</span></b><b><span lang=en-150 style='font-size:8.0pt;font-family:"Arial",sans-serif;color:#4F81BD;mso-fareast-language:EN-GB'> with:</span></b><span lang=en-150 style='color:black;mso-fareast-language:EN-GB'><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:black;mso-fareast-language:EN-GB'>MRC Integrative Epidemiology Unit </span><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:black;mso-fareast-language:EN-GB'>| </span><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:black;mso-fareast-language:EN-GB'>University of Bristol </span><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:black;mso-fareast-language:EN-GB'>|</span><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:black;mso-fareast-language:EN-GB'> UK<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:black;mso-fareast-language:EN-GB'>Donders Institute for Brain, Cognition and Behaviour </span><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:black;mso-fareast-language:EN-GB'>|</span><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:black;mso-fareast-language:EN-GB'> Radboud University </span><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:black;mso-fareast-language:EN-GB'>|</span><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:black;mso-fareast-language:EN-GB'> The Netherlands<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:black;mso-fareast-language:EN-GB'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-GB style='font-size:8.0pt;font-family:"Arial",sans-serif;color:black;mso-fareast-language:EN-GB'>My working hours may not be your working hours. Please do not feel obligated to reply outside of your normal working schedule.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p></div></body></html>