Defining the power limits of genome-wide association scan meta-analyses

Abstract

Large-scale meta-analyses of genome-wide association scans (GWAS) have been successful in discovering common risk variants with modest and small effects. The detection of lower frequency signals will undoubtedly require concerted efforts of at least similar scale. We investigate the sample size-dictated power limits of GWAS meta-analyses, in the presence and absence of modest levels of heterogeneity and across a range of different allelic architectures. We find that data combination through large-scale collaboration is vital in the quest for complex trait susceptibility loci, but that effect size heterogeneity across meta-analysed studies drawn from similar populations does not appear to have a profound effect on sample size requirements.

Introduction

The advent of genome-wide association scans (GWAS) has undoubtedly changed the field of complex trait genetics dramatically over the last few years. GWAS became feasible following an alignment of possibilities, including large-scale sample size availability, an improved understanding of human genome sequence variation, advances in high-accuracy, high-throughput genotyping technologies, and a deeper appreciation of analytical considerations for the interpretation of data. The first wave of GWAS led to the successful identification of multiple common variants and, in general, reaped the low-hanging fruit, i.e. variants closely-tagging causal alleles with modest to large effect sizes [WTCCC, 2007]. However, individual studies are limited in power by finite sample sizes. Wide collaborative networks culminated in consortium formation with the purpose of meta-analysing at the genome-wide scale, increasing sample size without the need for de novo genotyping. By synthesizing summary association statistics across multiple GWAS, power is increased and novel discoveries have been made, for example in type 2 diabetes, colorectal cancer, coronary artery disease and fat distribution [Voight et al., 2010; Houlston et al., 2010; Preuss et al., 2010; Heid et al., 2010].

The vast majority of GWAS meta-analyses to date have focused on populations of similar ancestry (primarily European), circumventing the complications of locus heterogeneity that can have profound effects on power when combining data across different genetic architectures. Statistical heterogeneity is a challenge not only for meta-analyses across diverse populations, but also across similar-ancestry datasets when effect sizes are dissimilar. Allelic heterogeneity, which is conceivably the case for loci containing multiple low frequency/ rare variants, represents an additional challenge.

The field is poised to continue with ever-increasing large-scale GWAS meta-analyses in parallel to entering the era of next generation association studies involving whole-exome or whole-genome sequencing. In this work, we investigate when GWAS meta-analyses may reach a point of diminishing returns in terms of power to detect disease-associated variants, in the presence and absence of modest levels of heterogeneity and across a range of different allelic architectures.

Replication of findings before declaring success, i.e. before claiming the detection of established disease associations, has become the sine qua non in GWAS. The larger the discovery sample, the smaller the effect sizes that a GWAS meta-analysis can detect. This factor, in combination with winner’s curse (i.e. the fact that the originally identified effect size is likely to be overestimated in comparison to its true value), can translate into a requirement for replication datasets that supersede the discovery set in sample size. For current meta-analysis efforts that involve several tens of thousands of samples (even surpassing 100,000, for example for quantitative anthropometric traits such as height), identifying appropriately sized replication datasets can be extremely challenging. Here we also explore the combined power of the discovery (stage 1) and replication (stage 2) sets to detect associations at genome-wide significance, with a focus on sample size requirements.

Methods

We obtained estimates for the sample sizes required for a range of genetic effect sizes and different risk allele frequencies, keeping power constant at 80%. We investigated different scenarios involving a combination of stage 1 (discovery) and stage 2 (replication) samples, to mimic realistic GWAS meta-analysis studies and their follow-up. We considered a sample of cases and an equal number of controls. This 1:1 ratio was kept constant throughout all simulations for stage 1 and stage 2 and when considering the effects of heterogeneity. The disease trait was set to have a population risk of 0.05. We assumed that we were measuring the effect of the causal variant itself and examined power under the additive model in the log-odds ratio of the risk allele.

Stage1 (discovery)

Using the software package Quanto version 1.2.4 [Gauderman, 2002] we estimated the sample sizes required for 12 different ORs ranging from 1.05-3.0 (with increments of 0.05) and 15 different risk allele frequencies ranging from 0.001-0.5 (with initial increments of 0.001, followed by 0.01 then 0.1). We applied 3 different thresholds of significance: p<1×10⁻⁴, p<1×10⁻⁵ and p<5×10⁻⁸ (genome-wide significant) (Figure 1).

Figure 1. Overview of study design.

Stage 1 sample sizes were estimated using the following design parameters: population risk of 0.05, additive inheritance model, case-control ratio of 1:1, 80% power. Replication sample sizes were established using the following design parameters: 80% power to detect 100 signals from a GWAS of 2 million markers, α=5×10⁻⁸.

Stage2 (replication)

Using the software package CaTS [Skol et al., 2006] we assumed that 100 signals (0.005%) from 2 million markers of a GWAS meta-analysis (for example, using HapMap data to impute genotypes at untyped variants) were selected for replication in stage 2. This number of markers is representative of the first follow-up step for most GWAS meta-analysis efforts. The sample size necessary to replicate the stage 1 signals at a final significance threshold of 5×10⁻⁸ in a combined meta-analysis was calculated for each of the scenarios for each of the 3 stage 1 significance thresholds. A combined p-value surpassing genome-wide significance is typically taken as evidence for robust association at disease-associated loci. Sample sizes could not be estimated beyond a threshold of 1,000,000. A total of 540 scenarios were examined.

Heterogeneity

We selected three of the above scenarios for further investigation through simulations incorporating heterogeneity. These were:

1. Allele freq = 0.30, OR = 1.25 (common SNP, moderate effect size)

2. Allele freq = 0.05, OR = 1.25 (low-frequency SNP, moderate effect size)

3. Allele freq = 0.01, OR = 3.0 (low-frequency SNP, large effect size)

Evidence for heterogeneity of genetic effects is commonly investigated using two statistics: Cochran’s Q statistic of homogeneity and the I² measure [Higgins et al., 2003]. We used I² to quantify the effect of heterogeneity. The I² measure has a very intuitive interpretation and allows assessing statistical significance and the extent of heterogeneity simultaneously. Different extents of heterogeneity wereconsidered for each of the 3 scenarios. We assigned adjectives of none, low, moderate and high heterogeneity to I² values less than 15%, between 15% and 35%, between 35% and 70%, and greater than 70%, respectively (calculated as the mean across all simulations carried out for the scenario considered) [Higgins et al., 2003].

For our simulations, we assumed a meta-analysis of 10 studies with equal sample size and with a 1:1 case-control ratio. Disease prevalence was fixed at 0.05 (as above). For a given scenario, the allele frequency was fixed, while the ORs varied across studies to produce the selected, combined meta-analysis OR. The amount of variability depends on the level of heterogeneity considered in the scenario under analysis.

In each scenario, 10,000 replicates of data were simulated. In each replicate, and for each of the 10 studies, the genotypes of the SNP were simulated independently based on the allele frequency considered and assuming Hardy-Weinberg equilibrium. Conditional upon the genotype data, the case-control status was simulated according to the additive model. The association analysis was then performed in a logistic regression modelling framework. Based on this, fixed-effects meta-analysis was carried out, including a test of heterogeneity. Based on these simulations, power to detect association at a significance level of 5×10⁻⁸ was estimated, with mean I² determined to evaluate heterogeneity. These simulations were repeated for different sample sizes in order to verify which would reach a detection power of 80%.

Results

Estimated sample sizes for stage 1 and stage 2 are given for each of the stage 1 significance thresholds of 1×10⁻⁴ (Table 1), 1×10⁻⁵ (Table 2) and 5×10⁻⁸ (Table 3) in the absence of heterogeneity. As expected, the results demonstrate a relationship between sample size, risk allele frequency (RAF), and the size of the genetic effect (Figures 2, 3 and 4). As the genetic variant becomes rarer and the odds ratio becomes smaller, the sample size required to detect the signal becomes increasingly large.

Table 1.

Sample size for stage 1 and stage 2 for a range of RAFs and ORs. Sizes are calculated for detection of 80% power at a significance level of 1×10⁻⁴ for stage 1 and a combined stage 1 and 2 significance level of 5×10⁻⁸. Estimates are based on assumptions of 1:1 case:control ratios and a population risk of 0.05.

OR			RAF
		0.001	0.002	0.003	0.004	0.005	0.01	0.02	0.03	0.04	0.05	0.1	0.2	0.3	0.4	0.5
1.05	stage1	>1000000	>1000000	>1000000	>1000000	>1000000	930100	470000	316700	240100	194200	102700	58000	44400	39000	37600
	stage2						760991	384545	259118	196445	158891	84027	47455	36327	31909	30764
1.1	stage1	>1000000	>1000000	790000	593100	475000	238800	120700	81400	61700	50000	26500	15000	11600	10200	9900
	stage2			646364	485264	388636	195382	98755	66600	50482	40909	21682	12273	9491	8345	8100
1.15	stage1	>1000000	539800	360300	270500	216600	108900	55100	37200	28200	22800	12100	6900	5300	4700	4600
	stage2		441655	294791	221318	177218	89100	45082	30436	23073	18655	9900	5645	4336	3845	3764
1.2	stage1	621900	311300	207800	156000	125000	62900	31800	21500	16300	13200	7000	4000	3100	2800	2700
	stage2	508827	254700	170018	127636	102273	51464	26018	17591	13336	10800	5727	3273	2536	2291	2209
1.25	stage1	407800	204100	136300	102300	82000	41200	20900	14100	10700	8700	4600	2700	2100	1850	1800
	stage2	333655	166991	111518	83700	67091	33709	17100	11536	8755	7118	3764	1800	1400	1514	1473
1.3	stage1	290000	145200	96900	72800	58300	29300	14900	10000	7600	6200	3300	1900	1500	1350	1300
	stage2	237273	118800	79282	59564	47700	23973	9933	8182	6218	4133	2700	1555	1227	900	1064
1.35	stage1	218000	109200	72900	54700	43800	22100	11200	7600	5700	4700	2500	1400	1100	1000	1000
	stage2	178364	89345	48600	36467	29200	14733	7467	5067	4664	3133	1667	1400	1100	1000	818
1.4	stage1	170700	85500	57100	42900	34300	17300	8800	5900	4500	3700	2000	1100	900	800	800
	stage2	139664	69955	38067	28600	22867	11533	5867	3933	3000	2467	1333	1100	600	655	655
1.5	stage1	114200	57200	38200	28700	23000	11600	5900	4000	3000	2700	1300	800	600	550	550
	stage2	93436	38133	25467	19133	15333	7733	3933	2667	2000	1667	1064	431	491	450	450
2	stage1	34700	17400	11600	8700	7000	3500	1800	1200	900	800	400	250	200	200	200
	stage2	23133	11600	7733	5800	4667	2333	1200	800	736	431	327	167	133	108	133
2.5	stage1	18200	9100	6100	4600	3700	1900	950	650	500	400	250	150	100	100	100
	stage2	12133	6067	3285	2477	1992	1023	512	350	269	267	83	64	300	122	300
3	stage1	11800	5900	4000	3000	2400	1200	600	400	350	300	150	100	100	100	100
	stage2	6354	3177	2154	1615	1292	646	400	267	117	100	81	43	18	18	25

Table 2.

Sample size for stage 1 and stage 2 for a range of RAFs and ORs. Sizes are calculated for detection of 80% power at a significance level of 1×10⁻⁵ for stage 1 and a combined stage 1 and 2 significance level of 5×10⁻⁸. Estimates are based on assumptions of 1:1 case:control ratios and a population risk of 0.05.

OR			RAF
		0.001	0.002	0.003	0.004	0.005	0.01	0.02	0.03	0.04	0.05	0.1	0.2	0.3	0.4	0.5
1.05	stage1	>1000000	>1000000	>1000000	>1000000	>1000000	>1000000	580400	391100	296500	239800	126900	71700	54900	48200	46500
	stage2						>1000000	193467	130367	98833	79933	42300	23900	18300	16067	15500
1.1	stage1	>1000000	>1000000	975600	732500	586600	294900	149100	100500	76200	61700	32700	18600	14300	12600	12200
	stage2			325200	244167	195533	98300	49700	33500	25400	20567	10900	6200	4767	4200	4067
1.15	stage1	>1000000	666600	444900	334000	267500	134500	68000	45900	34800	28200	15000	8500	6600	5800	5700
	stage2		222200	148300	111333	89167	44833	22667	15300	11600	9400	5000	2833	2200	1933	1800
1.2	stage1	768000	384400	256600	192700	154300	77600	39300	26500	20100	16300	8700	5000	3900	3400	3350
	stage2	192000	96100	64150	48175	38575	25867	9825	8833	6700	4075	2175	1250	975	1133	1117
1.25	stage1	503600	252100	168300	126400	101200	50900	25800	17400	13200	10700	5700	3300	2600	2300	2250
	stage2	125900	63025	42075	31600	25300	12725	6450	4350	3300	2675	1900	825	650	575	750
1.3	stage1	358100	179300	119700	89900	72000	36200	18300	12400	9400	7600	4100	2400	1800	1650	1600
	stage2	89525	44825	29925	22475	18000	9050	4575	3100	2350	1900	1025	600	600	550	533
1.35	stage1	269300	134800	90000	67600	54100	27200	13800	9300	7100	5800	3100	1800	1400	1250	1250
	stage2	67325	33700	22500	16900	13525	6800	3450	2325	1775	1450	775	450	350	417	313
1.4	stage1	210900	105600	70500	52900	42400	21300	10800	7300	5600	4500	2400	1400	1100	1000	1000
	stage2	52725	26400	17625	13225	10600	5325	2700	1825	1400	1125	600	350	367	250	250
1.5	stage1	141000	70600	47100	35400	28400	14300	7200	4900	3700	3000	1600	1000	750	700	700
	stage2	35250	17650	11775	8850	7100	3575	1800	1225	925	750	533	250	188	175	175
2	stage1	42800	21400	14300	10800	8600	4400	2200	1500	1150	950	500	300	250	250	250
	stage2	10700	5350	3575	2700	2150	1100	550	375	288	238	125	75	63	44	63
2.5	stage1	22400	11200	7500	5700	4500	2300	1200	800	600	500	300	200	150	150	150
	stage2	5600	2800	1875	1006	1125	575	212	141	150	88	33	2	26	17	26
3	stage1	14600	7300	4900	3700	3000	1500	800	550	400	300	200	100	100	100	100
	stage2	2576	1288	865	653	529	265	89	61	71	100	11	43	18	18	25

Table 3.

Sample size requirements for a range of RAFs and ORs. Sizes are calculated for detection of 80% power at a significance level of 5×10⁻⁸ for stage 1. Estimates are based on assumptions of 1:1 case:control ratios and a population risk of 0.05.

OR		RAF
	0.001	0.002	0.003	0.004	0.005	0.01	0.02	0.03	0.04	0.05	0.1	0.2	0.3	0.4	0.5
1.0 5	>100000 0	>100000 0	>100000 0	>100000 0	>100000 0	>100000 0	83110 0	56000 0	42460 0	34340 0	18170 0	10260 0	7850 0	6900 0	6660 0
1.1	>100000 0	>100000 0	>100000 0	>100000 0	>100000 0	422300	21350 0	14390 0	10920 0	88300	46800	26600	2040 0	1800 0	1745 0
1.1 5	>100000 0	954500	637100	478300	383100	192700	97400	65700	49900	40400	21500	12200	9400	8400	8150
1.2	>100000 0	550500	367400	275900	221000	111200	56200	38000	28800	23300	12400	7100	5500	4900	4800
1.2 5	721100	361000	241000	180900	144900	72900	36900	24900	18900	15300	8200	4700	3700	3300	3200
1.3	512800	256700	171400	128700	103100	51900	26300	17700	13500	10900	5800	3400	2600	2400	2300
1.3 5	385600	193000	128900	96800	77500	39000	19800	13400	10200	8200	4400	2600	2000	1800	1800
1.4	301900	151200	100900	75800	60700	30600	15500	10500	8000	6500	3500	2000	1600	1400	1400
1.5	201900	101100	67500	50700	40600	20500	10400	7000	5300	4300	2300	1400	1100	1000	1000
2	61300	30700	20500	15400	12400	6200	3200	2200	1650	1350	750	450	400	350	350
2.5	32100	16100	10800	8100	6500	3300	1700	1150	900	700	400	250	200	200	200
3	20900	10500	7000	5300	4200	2100	1100	800	600	500	300	200	150	150	150

Figure 2.

Sample sizes required to reach 80% power in stage 1 (a) and (c) for a=1×10⁻⁴, and stage 2 (b) and (d) for an overall α=5×10⁻⁸ across a range of ORs and risk allele frequencies. (a) and (b) present results for lower risk allele frequencies (up to 0.05); (c) and (d) present results for common risk allele frequencies (0.05 to 0.5).

Figure 3.

Sample sizes required to reach 80% power in stage 1 (a) and (c) for α=1×10⁻⁵, and stage 2 (b) and (d) for an overall α=5×10⁻⁸ across a range of ORs and risk allele frequencies. (a) and (b) present results for lower risk allele frequencies (up to 0.05); (c) and (d) present results for common risk allele frequencies (0.05 to 0.5).

Figure 4.

Sample sizes required to reach 80% power in stage 1 for α=5×10⁻⁸ across a range of ORs and risk allele frequencies. (a) presents results for lower risk allele frequencies (up to 0.05); (b) presents results for common risk allele frequencies (0.05 to 0.5).

Stage 1

Altering significance levels for declaring success can have profound effects on sample size requirements. As a representative example, at a significance level of 1×10⁻⁴, approximately 120,000 cases are required to detect a risk variant with RAF 0.02 and allelic OR 1.10. This sample size increases to 150,000 when the significance threshold is decreased to 1×10⁻⁵, and to 215,000 when the significance threshold is 5×10⁻⁸. Upholding the genome-wide threshold of significance of 5×10⁻⁸ requires at least 50,000 cases and an equal number of controls to detect ORs of 1.15 and below even for variants with common allele frequencies (>0.05).

Figure 2(a) shows that for low RAFs ranging from 0.001 to 0.005, the number of cases required to detect a signal at p<1×10⁻⁴ is pragmatic (~1,300 cases) for large genetic effects (OR 3.0). The identification of more commonly-encountered ORs in complex traits (1.20-1.30), however, requires between 58,000 and 125,000 cases.

Large-scale consortia are now starting to surpass combined sample sizes of 100,000. Datasets of this size provide adequate power to detect association with low frequency alleles (RAF down to 0.01) and modest effect sizes of at least 1.20 at genome-wide significance thresholds. However, required sample sizes rapidly approach 200,000 cases for RAFs below 0.01. The detection of association with alleles of MAF<0.05 and a small effect size (allelic OR of 1.05) requires samples sizes of over 340,000 cases and an equal number of controls.

Appropriate sample sizes for the detection of association signals at common variants (MAF>0.05) are more readily achievable (Figure 2c), as demonstrated by the success of GWAS meta-analyses to date. The reported median RAF of 531 signals from published GWAS studies of common diseases [Hindorff et al., 2009] was 0.36, interquartile range (IQR) 0.21-0.53, and the median OR was 1.33, IQR 1.12-1.61. The sample sizes required to obtain 80% power at genome-wide significance in order to detect these effects would be 4,118 (RAF 0.36, OR 1.33), 1,460 (RAF 0.53, OR 1.61) and 36,132 (RAF 0.21, OR 1.12) respectively (cases and controls combined).

Stage 2

We estimated replication set sample sizes required to obtain 80% power to detect associations at α=5×10⁻⁸ across the combined stage 1 and stage 2 analysis, i.e. the discovery set and the replication set. When the stage 1 threshold is set to 1×10⁻⁴, an equal number of samples are required in stage 2 to replicate the stage 1 signals for a final genome-wide threshold of 5×10⁻⁸ (Figure 2b and 2d) across all ranges of allele frequencies and ORs.

If the significance threshold for stage 1 is decreased to 1×10⁻⁵, the second stage samples sizes required to obtain a final p-value of 5×10⁻⁸ are lower. However the first stage requires a larger sample size to surpass the initial significance threshold (Figure 3b and 3d) and the combined sample sizes remain similar for both stage 1 thresholds. For example, detection of a signal with OR 1.25 and RAF 0.05 at α=1×10⁻⁵ requires 10,700 cases (and an equal number of controls) in stage 1, and 2,675 cases in stage 2 for a combined α=5×10⁻⁸. If the stage 1 significance threshold were set to 1×10⁻⁴ the respective sample sizes would be 8,700 in stage 1 and 7,118 in stage 2.

Importantly, these calculations were based on the assumption of no heterogeneity between the discovery and replication sets, and we assumed that the replication dataset was drawn from the same population as the stage 1 samples.

Heterogeneity

The relationship between sample size, RAF and OR in the presence of heterogeneity is consistent with that derived from power calculations carried out in the absence of heterogeneity (Table 4). We observe that, as expected, a larger sample size is required as heterogeneity increases. Interestingly, however, the incremental increase needed does not appear to be substantial. For example, in the frequently-encountered scenario of a common variant with a modest effect size (RAF 0.30 and OR 1.25), it is necessary to increase the case sample size by ~600 individuals when heterogeneity levels are high in comparison with that needed when all studies have similar effects. This number decreases to 400 in the presence of more modest levels of heterogeneity.

Table 4.

Total number of samples (across 10 studies with equal sample size, and 1:1 case:control ratio) required at different levels of heterogeneity (measured using I²). Results are based on 10,000 simulations.

Allele Frequency	Meta-analysis OR	Mean I2	Number of cases (*)
0.30	1.25	0.11	3121 (**)
		0.21	3515
		0.45	3639
		0.76	3766
0.05	1.25	0.11	13768 (**)
		0.26	15253
		0.50	15674
		0.82	15971
0.01	3.00	0.05	2314 (**)
		0.17	2455
		0.50	2629
		0.80	2852

^*Number of cases required for 80% power to detect association at a significance level of 5×10⁻⁸.

^**All studies with ORs equal to the meta-analysis OR.

The increase in sample numbers required for lower RAFs (0.05) and the same genetic effect size of 1.25 in the presence of high heterogeneity is more pronounced (additional 2,000 cases needed to achieve the same power). However, this represents a smaller proportional increase in sample size (14%). Overall, the number of additional samples required to overcome loss of power due to heterogeneity is modest.

Discussion

The issue of statistical power and sample size in genetic association studies has previously been addressed in the literature. For example, Fisher and Lewis [2008] found that required sample sizes increase dramatically with decreasing levels of linkage disequilibrium (LD) between the marker and causal variant. Yang and colleagues [2010] demonstrated that when the disease prevalence is low (<0.10), a case-control study design with a 1:1 ratio of cases and controls is more powerful than a quantitative trait association study. Moonesinghe and colleagues [2008] showed that meta-analysis sample size requirements increase steeply when small genetic effects were considered and also in the presence of high levels of between-study heterogeneity. Pereira and colleagues [2009] demonstrated the importance of choosing the correct model for meta-analysis calculations in simulated combinations of several GWAS data sets.

Our findings indicate that, within our simulation framework parameters, the impact of heterogeneity on sample size requirements is not substantial. Whilst, as expected, increased sample sizes are required to counteract the effect of increasing heterogeneity, even with modest ORs of 1.25 and low allele frequencies of 0.05, only approximately 20% more samples are required to maintain the same statistical power for genome-wide significance. This observation may be underpinned by the fact that high levels of heterogeneity in our study were attained by considering a wide range of ORs among the 10 studies contributing to the meta-analysis, including easily-detectable large effect sizes. There are many parameters one can vary in simulation experiments and each can have implications in the downstream results. In our simulations, we assume a meta-analysis of studies with equal sample size. For scenarios in which studies have different sample sizes, results may vary from those presented here. In the presence of high heterogeneity, the number of samples needed is expected to depend on the sample size of the studies with the largest effect sizes. The required sample sizes may increase comparatively to those observed in our simulation study if the sample sizes of the studies with the largest effects decrease.

In the presence of substantial allelic heterogeneity, an alternative approach would be to undertake random-effects analysis which does not make an assumption of homogeneity across studies, in which case the sample sizes required may deviate from the numbers presented here. The level of heterogeneity observed in a meta-analysis should in any case be taken into account, and results interpreted with caution when the observed heterogeneity is high.

Sample size and power have been at the heart of genetic association study design for several decades. Recent advances in the field have made genome-wide scans possible and have ushered in a new era of successful complex disease locus identification. The power constraints of studies conducted thus far have led to the discovery of associations with common-frequency variants of large or modest effect size. Indeed, meta-analyses of GWAS to date have, most probably, identified the vast majority if not all risk variants with moderate effects and common allele frequencies. The formation of large-scale international consortia is now enabling the accrual of sample sizes surpassing 100,000. For example, a recent combined analysis across ~184,000 individuals identified ~180 loci affecting human height variation. As with the vast majority of other complex traits, the proportion of phenotypic variation explained by the combined set of established signals is less than 10% [Lango Allen et al., 2010]. This recurrent observation indicates that further genetic determinants of complex traits remain unidentified. Their allele frequency and effect size spectra could be diverse, with multiple common-frequency variants of small effect size, and/or low-frequency and rare variants of modest/larger effect size contributing towards this missing heritability. Using comprehensive power calculations, we find that the detection and replication of signals within these RAF and OR constraints require large sample sizes (currently achievable through large-scale collaborative efforts) in order to reach genome-wide levels of significance, and that effect size heterogeneity across meta-analysed studies drawn from similar populations does not appear to have a profound effect on sample size requirements.