22 Population stratification is a strong confounding factor in human genetic association studies. In 23 analyses of rare variants, the main correction strategies based on principal components (PC) and linear 24 mixed models (LMM), may yield conflicting conclusions, due to both the specific type of structure 25 induced by rare variants and the particular statistical features of association tests. Studies evaluating 26 these approaches generally focused on specific situations with limited types of simulated structure 27 and large sample sizes. We investigated the properties of several correction methods in the context 28 of a large simulation study using real exome data, and several within-and between-continent 29 stratification scenarios. We also considered different sample sizes, with situations including as few 30 as 50 cases, to account for the analysis of rare disorders. In this context, we focused on a genetic 31 model with a phenotype driven by rare deleterious variants well suited for a burden test. For analyses 32 of large samples, we found that accounting for stratification was more difficult with a continental 33 structure than with a worldwide structure. LMM failed to maintain a correct type I error in many 34 scenarios, whereas PCs based on common variants failed only in the presence of extreme continental 35 stratification. When a sample of 50 cases was considered, an inflation of type I errors was observed 36 with PC for small numbers of controls (≤100), and with LMM for large numbers of controls (≥1000).37 We also tested a promising novel adapted local permutation method (LocPerm), which maintained a 38 correct type I error in all situations. All approaches capable of correcting for stratification properly 39 had similar powers for detecting actual associations pointing out that the key issue is to properly 40 control type I errors. Finally, we found that adding a large panel of external controls (e.g. extracted 41 from publicly available databases) was an efficient way to increase the power of analyses including 42 small numbers of cases, provided an appropriate stratification correction was used. 43 44 3 45 Author Summary 4647 Genetic association studies focusing on rare variants using next generation sequencing (NGS) data 48 have become a common strategy to overcome the shortcomings of classical genome-wide association 49 studies for the analysis of rare and common diseases. The issue of population stratification remains 50 however a substantial question that has not been fully resolved when analyzing NGS data. In this 51 work, we propose a comprehensive evaluation of the main strategies to account for stratification, that 52 are principal components and linear mixed model, along with a novel approach based on local 53 permutations (LocPerm). We compared these correction methods in many different settings, 54 considering several types of population structures, sample sizes or types of variants. Our results 55 highlighted important limitations of some classical methods as those using principal com...