Incorporating prior knowledge to facilitate discoveries in a genome-wide association study on age-related macular degeneration

Substantial genotyping data produced by current high-throughput technologies have brought opportunities and difficulties. High-density genotyping platforms have been developed in a hope that underlying disease-associated genes can be identified through denser and denser collections of single-nucleotide polymorphism (SNP) data. However with the number of SNPs going into millions comes the harsh challenge of multiple-testing adjustment. To counteract multiple-testing penalty incurred by testing such a large number of SNPs, some genome-wide association studies (GWASs) responded by taking a large sample size--with the number of study subjects soaring into thousands, tens of thousands, or even more [1].

There are two approaches for multiple-testing adjustments. One is controlling the family-wise error rate (FWER), the other is controlling the false discovery rate (FDR) [2, 3]. The FWER is defined as the probability of at least one type I error. Among methods for controlling FWER, the Bonferroni correction is the best known approach, although it is very conservative. Holm's step-down procedure [4] is less conservative than the classical Bonferroni correction. The FWER can also be controlled by the resampling-based P-value adjustment procedure. Compared with controlling the FWER, controlling the FDR is usually a more powerful approach. However, even with the FDR approach, a GWAS may still fall short of discovering any true positive gene, particularly when it has a relatively small sample size. When testing simultaneously for a huge number of SNPs, even true positive SNPs would have difficulty in standing out among all the noise, based on a straight (and brutal) comparison of their p values. GWAS on age-related macular degeneration (AMD) is a good example, and we will show this in this paper.

The above simple FDR approach has been further extended to dependent tests and to tests with prior information [5]. The false discovery control with P-value weighting [5, 6] can improve power when the assignment of weights (based on previous linkage evidence [6]) is adequate, but there is some power loss when the weights are poorly assigned. Sun et al.'s [7] stratified false discovery control is another approach. They partitioned all SNPs into two subsets based on minor-allele frequencies (MAFs), and then the FDR control is applied to the two subsets respectively. However, as pointed out by Li et al. [8], MAFs have little relevance with biological information and thus partitioning SNPs based on MAFs probably may not improve much power. To address this issue, Li et al. [8] proposed a 'prioritized subset analysis' (PSA). The PSA makes clever use of available prior knowledge, either of the linkage information, the biological information or both. We will show that the PSA can greatly facilitate discoveries in GWASs, with a demonstration on an AMD data.

Prior information can come from a researcher's biological knowledge, or findings of data other than that provided in the current study. But one should not 'snoop' his/her data at hand for the prior knowledge. If one naively prioritizes those SNPs with the smallest p values in the study data, the actual overall FDR would no longer be properly controlled. To avoid such bias, we searched findings of other data to build our 'prior knowledge', before seeing the analysis results of individual SNPs in the current AMD data set. At that time, we did know that rs380390 is a significant SNP in the AMD data set which can withstand a FWER control of 0.05 [9]. But the chromosomal region around rs380390 had already been replicated by many previous linkage studies [10–15] (all published before Klein et al. [9]). And so, prioritizing chromosomal region around rs380390 won't constitute an act of data snooping.

Around a particular gene, how large a chromosomal region should be prioritized is also an issue. Because of the consistent findings in the CFH gene, both from genome-wide linkage analyses [10–15] and case-control studies [19–21], we prioritized SNPs within 1 Mb from the CFH gene. Other evidence of linkage and associations are relatively unconfirmed by prior studies, so we prioritized SNPs within 500 kb and 50 kb, respectively. Because linkage is a coarse mapping whereas association is a fine mapping, in general a wider region of SNPs should be prioritized for a linkage peak. Admittedly, there is no absolute criterion for choosing the sizes of prioritized regions. No matter how large a chromosomal region is prioritized, the FDR within subsets should be controlled at the desired level, and this can be verified by estimating the permutation-based FDR [29].

In recent GWASs, a commonly used approach to incorporate prior knowledge is to calculate the Bayes factors [1, 30]. However, to estimate the Bayes factors, the prior distributions and the effect sizes should be carefully specified [30]. This may limit its applicability. By contrast, the PSA method used in this paper can feed on prior knowledge that is only rudimentary (we need only to decide beforehand whether a particular SNP is more likely a true positive or a true negative, but don't need to know exactly how likely). And there is almost no penalty for poor guessing [8]. In this paper, we demonstrated that such a simple dichotomization followed by a simple PSA can greatly facilitate discoveries in a GWAS on AMD.

Note that we did not recruit any more subjects or type any more SNPs beyond what Klein et al. [9] had done. The only thing we did is to incorporate prior knowledge about AMD into the analysis. And we see this input of knowledge is rather powerful (six/two additional significant SNPs/genes were identified in the same AMD case-control data). One may question that our input of knowledge and the subsequent partition of SNPs into two subsets to be tested separately and harvested combinedly are making easier (and perhaps too easier) for the SNPs to come out. But we should emphasize that we did not loosen our FDR control in any way. The total seven significant SNPs found in this re-analysis have an overall 0.05 FDR attached to them, much the same way with the one SNP rs380390 originally found in Klein et al. [9] had a 0.05 FDR attached to it. And we believe that researchers will find no difficulties to choose seven SNPs or just one--that is, under the same FDR criteria.

The PSA approach is rather powerful and is easy to implement. Based on the success of our re-analysis of Klein et al's GWAS on AMD, we advocate using PSA to facilitate discoveries in future GWASs.