Table 2 Benchmarks

Algorithm	GCTA	pylmm	FaST-LMM	FEATHER (Deriv. Based)	FEATHER (SAMC)
No. of perm. used p = 10⁻⁴	10⁶	10⁶	10⁶	10⁶	10⁶
Total time used p = 10⁻⁴	>8 months	∼1.8 days	∼13 h	∼23 min	∼16 min
No. of perm. used p = 10⁻⁷	10⁹	10⁹	10⁹	10⁹	10⁶
Total time used p = 10⁻⁷		>4 years	∼1.4 years	∼16 days	∼16 min
No. of perm. used p = 10⁻⁹	10¹¹	10¹¹	10¹¹	10¹¹	10⁶
Total time used p = 10⁻⁹				>4 years	∼16 min

The running time of permutation tests, as calculated by GCTA²⁹, pylmm³⁷ and FaST-LMM³⁸ (performing full estimation for each permutation), vs. the derivative-based approach, with and without SAMC, on a single site from the KORA dataset, with 1799 individuals. Benchmarks are shown for the cases where the true p-value is 10⁻⁴, 10⁻⁷, or 10⁻⁹. The number of permutations required for the non-SAMC methods is assumed to be p/100 (see Methods). For these p-values, SAMC converged after 10⁶ permutations (see Results). Per permutation, the derivative-based approaches have a speed up of two orders of magnitude compared to the best full estimation permutation test program. The usage of SAMC for small p-values introduces an additional speed up of up to 6 orders of magnitude. Expected computation times for several sites are multiplied by the number of examined sites

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