Accounting for variable sample size.

<p>Effect of missingness on accuracy of imputation of standardised effects, evaluated via simulations where true effect is known. The y-axis is the MSE (on log-scale) between the true standardised effect and the conventional estimate which ignores missingness (<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1007371#pgen.1007371.e003" target="_blank">Eq (1)</a>, grey), our estimate <b><i>D</i></b>^(<i>dep</i>) (<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1007371#pgen.1007371.e029" target="_blank">Eq (10)</a>, green), and our estimate <b><i>D</i></b>^(<i>ind</i>) (<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1007371#pgen.1007371.e030" target="_blank">Eq (11)</a>, blue). The x-axis is the ‘missingness-correlation’ (<i>θ</i>_<i>miss</i>), where a value of 1 means the number of individuals in the samples had maximum overlap with each other, and 0 means they were simulated independently leading to smaller overlap. Each boxplot shows the MSEs across the 40 regions simulated. Top row is where the <b><i>N</i></b>’s (simulated sample sizes) are selected randomly from a study of T2D [<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1007371#pgen.1007371.ref031" target="_blank">31</a>], with sample sizes varying between 13 and 110′219 individuals. Bottom row is based on HDL [<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1007371#pgen.1007371.ref030" target="_blank">30</a>], with sample sizes ranging between 50′000 and 187′167 individuals. All sample sizes are scaled to 0-to-12500 as this is the size of the simulated GWAS.