Searching for missing heritability: Designing rare variant association studies

Or Zuk; Stephen F. Schaffner; Kaitlin Samocha; Ron Do; Eliana Hechter; Sekar Kathiresan; Mark J. Daly; Benjamin M. Neale; Shamil R. Sunyaev; Eric S. Lander

doi:10.1073/pnas.1322563111

New Research In

Contributed by Eric S. Lander, December 10, 2013 (sent for review September 23, 2013)

Significance

Discovering the genetic basis of common diseases, such as diabetes, heart disease, and schizophrenia, is a key goal in biomedicine. Genomic studies have revealed thousands of common genetic variants underlying disease, but these variants explain only a portion of the heritability. Rare variants are also likely to play an important role, but few examples are known thus far, and initial discovery efforts with small sample sizes have had only limited success. In this paper, we describe an analytical framework for the design of rare variant association studies of disease. It provides guidance with respect to sample size, as well as the roles of selection, disruptive and missense alleles, gene-specific allele frequency thresholds, isolated populations, gene sets, and coding vs. noncoding regions.

Abstract

Genetic studies have revealed thousands of loci predisposing to hundreds of human diseases and traits, revealing important biological pathways and defining novel therapeutic hypotheses. However, the genes discovered to date typically explain less than half of the apparent heritability. Because efforts have largely focused on common genetic variants, one hypothesis is that much of the missing heritability is due to rare genetic variants. Studies of common variants are typically referred to as genomewide association studies, whereas studies of rare variants are often simply called sequencing studies. Because they are actually closely related, we use the terms common variant association study (CVAS) and rare variant association study (RVAS). In this paper, we outline the similarities and differences between RVAS and CVAS and describe a conceptual framework for the design of RVAS. We apply the framework to address key questions about the sample sizes needed to detect association, the relative merits of testing disruptive alleles vs. missense alleles, frequency thresholds for filtering alleles, the value of predictors of the functional impact of missense alleles, the potential utility of isolated populations, the value of gene-set analysis, and the utility of de novo mutations. The optimal design depends critically on the selection coefficient against deleterious alleles and thus varies across genes. The analysis shows that common variant and rare variant studies require similarly large sample collections. In particular, a well-powered RVAS should involve discovery sets with at least 25,000 cases, together with a substantial replication set.

Footnotes

↵¹Present address: Department of Statistics, The Hebrew University of Jerusalem, Mt. Scopus, Jerusalem 91905, Israel.
↵²To whom correspondence should be addressed. E-mail: lander{at}broadinstitute.org.

Author contributions: O.Z., E.H., M.J.D., B.M.N., S.R.S., and E.S.L. designed research; O.Z., S.F.S., K.S., R.D., E.H., B.M.N., S.R.S., and E.S.L. performed research; K.S., R.D., and S.K. contributed new reagents/analytic tools; O.Z., S.F.S., K.S., E.H., M.J.D., B.M.N., S.R.S., and E.S.L. analyzed data; and O.Z., M.J.D., B.M.N., S.R.S., and E.S.L. wrote the paper.
The authors declare no conflict of interest.
^†We focus on risk to heterozygous carriers. Our calculations implicitly assume that the risk to individuals carrying two null alleles (λ_C*) is the same as the risk to heterozygous carriers (λ_C). Although such individuals may well have higher risk, they are much rarer than heterozygous carriers (because f_C is small) and thus their impact on RVAS is typically negligible. [The effective relative risk is increased by f_C(λ_C*/λ_C), which is ≪1 unless λ_C*/λ_C is huge; this case would essentially be a monogenic recessive trait.]
^‡We focus on the number n of cases needed when the frequency f_C in the population is known perfectly based on an (infinitely) large population survey. We make this assumption in the belief that very large datasets will become available in the coming years and that shared population controls can be used across studies. In the meanwhile, one can estimate f_D within a study based on the frequency in either unaffected or random individuals. If a study involves cases and unaffecteds in proportion r and 1 − r, one requires approximately n/(1 − r) cases and n/r controls to detect association, where n is the number of cases given in Eq. 1 (SI Appendix, Section 3.3). For a balanced design, this corresponds to 2n cases and 2n controls.
^§g(λ)=[(λ+1)ln(1+λ)−λ], which is approximately λ2/2 for small λ (0 ≤ λ< 1) and cλln(λ) for larger λ (with c in the range 0.7–0.8 for 2<λ<100).
^¶The expected CAF for new neutral alleles born in a given generation is μ_C and thus the increase in the expected CAF over k generations cannot exceed kμ_C (and will be lower because many newborn alleles are lost). It follows that the collection of neutral alleles born since the onset of human population cannot increase the CAF of neutral alleles by more than 5% (= kμ_C/4μ_CN_eq, where k =1,000 and N_eq = 10,000). The actual increase is typically much smaller due to loss of newborn alleles.
^||The relevant sampling frame for disease studies involves randomly selecting a chromosome and inspecting it for alleles. Alleles are thus sampled according to their frequency, yielding a frequency-weighted frequency distribution.
**One can also perform an analysis considering only those missense alleles with frequency ≤1% that are predicted to be probably damaging by PolyPhen-2 (that is, RVAS strategy 3). One observes 89 such missense alleles in cases vs. 32 in controls, which corresponds to an apparent excess relative risk λ_{M(1%),PolyPhen2} = 2.5. This result agrees closely with the expectation of λ_{M(1%),PolyPhen2} = 2.3, given the inferred value of s and the frequency threshold of 1%. For this type of analysis (assuming γ_null = 80% and γ_neutral = 20%), the optimal threshold turns out to be T*= 0.15%, which would yield a much higher apparent effect size of λ_{M(T*),PolyPhen2} = 8.2.
^††The paper reports that the best nominal P value observed across the genome is 2.7 × 10⁻⁸ but does not address whether the value is significant. To correct for scanning the entire genome, one can apply extreme value theory for Orenstein-Uhlenbeck diffusions (SI Appendix, Section 11.1). The probability of such a P value arising by chance somewhere in the genome is ∼70%, and thus the observation is not statistically significant. Genomewide significance at the 5% level corresponds to P ∼ 2 × 10⁻⁹ (SI Appendix, Section 11.1).
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