Introduction

Up to half of unique genetic variants in evaluations of familial cancer risk are variants of uncertain significance.1,2,3 The number of rare missense variants identified increases linearly, proportionate with the length of DNA sequenced, at a rate of ˜0.008 rare variants identified per kilobase of exonic DNA sequence.4 New next-generation -sequencing–based clinical assays aimed at comprehensive evaluation of cancer risk genes are predicted to identify at least one rare missense variant in more than half of the individuals sequenced.5 These rare variants of uncertain significance can cause confusion and patient anxiety, so definitive classification of these variants is a high priority.6,7,8 Several frameworks have been proposed for classifying novel variants in known cancer genes, with ongoing debate about the level of evidence necessary to classify a novel variant in each category.9,10,11,12,13 For example, the framework outlined by Plon et al. (2008)9 suggests that a variant could be considered pathogenic if combined evidence from multiple sources indicates a 99% or greater probability that the variant causes the phenotype in question, and the Partners Laboratory for Molecular Medicine has multiple criteria for pathogenicity, including LOD score >3 (≥10 meioses).10 Similarly, a variant could be considered likely to be pathogenic if there is greater than 95% probability that the variant is pathogenic or if segregation is seen across more than three meiosis cycles along with other supporting evidence, depending on the classification framework.9,10 Several groups have detailed specific mechanisms that might be used to combine evidence from multiple sources to classify variants.14,15,16,17

Classification is important, but the information about risk of disease is what drives clinical decisions. This risk information intuitively appears implicit in classification; however, classification may or may not facilitate accurate risk prediction. For genes associated with familial cancer risk, understanding novel variants could be seen as a two-step process: (i) categorizing the variant in a broad class and (ii) estimating actual cancer risk conferred by the novel variant. This second step can be more challenging than simply classifying a variant, particularly for missense and splice-site mutations.

In practice, cancer risk is usually inferred from literature based on other variants with the same classification, and many methods for categorizing uncertain variants explicitly assume that risk for novel variants will be identical to that for previously described, highly penetrant variants.6,14 Grouping variants that clearly completely abrogate gene function, such as premature stop codons, early frameshift mutations, and large deletions, appears appropriate for many genes, particularly for highly penetrant cancer risk genes such as BRCA1 (breast cancer 1, early onset) or MLH1 (mutL homolog 1). However, all variants that alter activity, such as missense variants, leaky splice-site variants, or variants that occur near the 3′ end of a gene, may not confer similar risk.18,19,20 In this article, we will first illustrate the level of risk implied by classification groups, acknowledging that there is large uncertainty surrounding this implied risk. Then we will describe the magnitude of effort that would be necessary to better define cancer risk estimates for novel, rare variants in known cancer genes through power calculations of sample sizes necessary to generate minimally useful mutation-specific relative risk (RR) estimates for rare missense variants.

Current practice in risk estimation: implied risk from classification

Variant classification may imply different levels of risk to patients ( Figure 1 ). In the Plon framework,9 as implemented by current classification schemes, the “Definitely Pathogenic” classification implies risk similar to that reported in the literature for pathogenic mutations. For example, pathogenic variants in the most studied breast and colon cancer risk genes eliminate one functional copy of the gene; risk estimates from well defined cases that completely eliminate one functional copy of the gene represent a theoretical upper limit of risk conferred by a heterozygous variant in a specific gene. “Likely Pathogenic” classification implies that there is enough evidence to conclude that the RR of the variant is >1 and suggests that the RR may be similar to the upper limit defined by definitely pathogenic variants. The classification “Uncertain Significance” implies that the RR may be anywhere from slightly >1 to the upper limit of risk seen in pathogenic variants. The classification “Likely Benign” implies that there is enough evidence to conclude that the RR is unlikely to be as great as the risk for pathogenic variants and that the evidence suggests similar risk to that of the general population but that there is not enough evidence to definitively conclude that the risk is similar to the risk of the general population. The term “Benign” implies RR ˜1 (or very slightly <1 because these individuals lack risk conferred by reported variants). Explicitly illustrating this implied risk framework may be useful to genetic counselors for helping patients visualize and understand variant categories ( Figure 1 ).

Figure 1
figure 1

Visualization of current standard-of-care-implied cancer relative risk (RR) from variant classification for dominant diseases with incomplete penetrance. Boxes indicate confidence intervals for RR. Solid vertical lines represent point estimates for RR for which data exist. Dotted vertical lines represent assumed point estimates not supported by independent, variant-specific studies. *High risk is specific to both disease and gene and is defined by variants that completely eliminate one functional copy of the gene; this is the theoretical upper limit of risk conferred by a heterozygous variant in a specific gene.

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This display of implied risk illustrates how simple classification can be suboptimal for patient management because of the high degree of uncertainty in implied risk for missense and splice variants, even those classified as Likely Pathogenic or Likely Benign. Variant-specific RR estimates, beyond helping classification, allow quantitative estimates of outcome probabilities that are necessary for rational medical planning. Current studies indicate that risk conferred by different missense mutations can vary substantially.18,19,20 However, current classification systems often draw from many sources, including sources that provide no information about clinical outcomes or risk, such as in silico protein predictions, in vitro protein function studies, and cross-species sequence conservation.9,10,11 This is likely to lead to overestimates of risk for many rare variants and creates a genetic counseling dilemma because low-frequency missense variants may be grouped into risk categories before population- or family-based RR data are available.9,11 Furthermore, in the setting of novel genes that have been linked with prevalent and less common cancers, RR estimates may be unavailable for any variant, even those classified as known pathogenic. To ascertain the magnitude of this problem, we evaluated the sample sizes that might be necessary to generate a minimally accurate RR estimate for hypothetical rare variants of uncertain significance using the examples of breast and colon cancer risks.

Materials and Methods

Calculation of sample size needed for minimally useful risk estimates

Risk estimates often come from odds ratios (ORs) generated by case–control studies because OR and RR converge for rare diseases. Another strategy to evaluate variants is to use families with the investigated mutation. We modified standard power calculations to explore sample sizes necessary to determine whether the RR for a novel variant is >1.

We used standard formulas for calculating sample size from allele frequency, modified as described by Fleiss et al. to include continuity correction, and in the case of family data, to permit unequal numbers of affected and unaffected individuals.21,22 The R-script that we used for calculations of population- and family-based sample size is included as Supplementary Materials to facilitate additional power calculations across a wider spectrum of allele frequency, RR, desired power, and ascertainment parameters.

We specifically examined variant population frequencies of 0.1, 0.01, and 0.001%. We performed power calculations for population-based case–control studies and family-based linkage studies across several levels of cancer RR. We used RRs of 12, 6, 3, and 1.5 for breast cancer and 20, 10, 5, and 2.5 for colon cancer. From the literature, we identified 12 as the RR for established breast cancer genes (i.e., BRCA1, BRCA2) and 20 as the RR for established colon cancer genes (i.e., MLH1) and then used regular fractions of these to explore sample size over the spectrum of possible risk.23,24,25 We assumed breast cancer cumulative incidence of 0.08 and colon cancer cumulative incidence of 0.03 for individuals between the ages of 40 and 70 years, who were likely to be included in this type of study.

Population-based sample size calculation

Because variants of clinical interest will be in known genes and will presumably have in silico data available, we assume that in silico data in known cancer genes is equivalent to a pretest probability of 0.9, and we use a Bayesian approach to define thresholds for power calculations, similar to approaches used for variant classification in previous studies.14 Hence, we used desired power of 0.8 and an α of 0.1, which would be consistent with a posttest probability of pathogenicity equaling 99% for a pathogenic variant. We used a one-tailed test to calculate sample size because we are assuming that alleles increase cancer risk. We purposefully used these liberal assumptions, which result in low sample size estimates, because we are considering the situation in which we desire definitive classification and a reasonable independent estimate of RR for rare variants in established cancer genes. The estimated RR will have some degree of error. More conservative assumptions would obviously result in larger sample requirements and more precise RR estimates, which may be desirable in certain clinical or research scenarios. If the measured RR is extremely high, this is not a major concern because the practical upper limit of risk is defined by well studied, highly pathogenic variants. Similarly, the statistical lower bound for RR is 0, but the practical lower limit is 1 because only elevated cancer risk is clinically actionable.

Family-based sample size calculation

For family-based variant classification analysis, several strategies have been proposed to generate likelihood ratios that can be used for multifactorial classification of rare variants.26,27,28,29 Variant classification strategies usually favor genotyping individuals with extreme phenotypes such as distant relatives with cancer at a young age. This strategy takes advantage of the fact that identifying a shared rare allele in an unlikely clinical situation can generate very large likelihood ratios with minimal genotyping. Although this strategy may work well for classifying a variant as pathogenic, it does not create information that can be used to define the RR conferred by the variant. Likelihood-based classification studies may dramatically overestimate risk (the winner’s curse). However, for extremely rare variants, it is unlikely that unrelated carriers can be identified. Despite its drawbacks, a family-based approach may be the only way to estimate RR. However, to mitigate the probability of dramatically overestimating risk, studies of families with novel mutations should recruit individuals related to previously identified carriers of variants without regard for disease status. As noted above for population-based studies, extreme overestimates can be avoided by capping risk at the level defined by common, highly pathogenic variants.

One efficient way to gather the most informative individuals for RR estimates in a family would be to iteratively genotype close relatives of individuals carrying the rare allele starting with the proband (but excluding the proband in calculations to avoid ascertainment bias). Case–family and case–family–control methods have been described previously.29,30,31,32 One would recruit all available family members of appropriate age and gender who are likely to carry the variant of interest, regardless of personal cancer history. The strategy would be to ascertain genotype data for all available first- and second-degree relatives of the proband and repeat this process for newly identified carriers, branching to new first- and second-degree relatives while gathering data on disease status but not skewing recruitment based on these data. When a variant is very rare, first-degree relatives have a 50% chance and second-degree relatives have a 25% chance of being carriers. Alternatively, one could recruit only first-degree relatives of identified carriers, which would require additional iterations of testing, or recruit both near and distant relatives, resulting in a lower variant frequency but potentially fewer stages of iterative recruiting. Regardless of strategy, it should be emphasized that for accurate RR estimates, relatives must be recruited without regard for disease status. To calculate RR, one must phenotype enough individuals (i) with and without the variant and (ii) with and without the disease to generate a meaningful risk ratio.

Confidence intervals for the risk estimates could be computed using linear mixed models to account for within-family genotype and environmental cancer risk correlation.29,33,34 For simplicity in our calculations, we assumed that nongenetic factors influencing cancer risk are uncorrelated and that genetic cancer risk beyond the variant of interest is negligible. We also assumed that the baseline cancer risk in a family is independent of and identical to the risk in a population. This allows definition of the lower bound of sample size for risk estimates with confidence intervals small enough to classify the variant without knowing clinical details about specific families. For our analysis, we assumed that equal numbers of first- and second-degree relatives would be genotyped, resulting in an overall rare variant frequency of 37.5% in the genotyped cohort. We used assumptions similar to those we used for population-based studies: one-sided α of 0.1 and 80% power. As with population-based studies, these are low estimates of sample size because correlation between family members would widen confidence intervals. More accurate power estimates would require more specific disease models, and sample sizes required for adequate power may be substantially higher.

Results

Population-based case–control sample size necessary to define risk for a low-frequency variant of uncertain significance

Population-based studies to categorize additional variants that may confer cancer risk will need to be increasingly large as both variant frequency and RR decrease ( Tables 1 and 2 ). When there is very high RR of disease, case–control studies will yield sufficient cases to prove that the variant is pathogenic, but with insufficient controls to accurately calculate ORs because of the extremely low frequency of the mutation in controls; therefore, using case-only analysis and known population disease frequencies from larger samples in the denominator might yield more accurate ORs.

Table 1 Subjects necessary to characterize a breast cancer variant as pathogenic
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Table 2 Subjects necessary to characterize a colon cancer variant as pathogenic
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Family-based sample size necessary to define risk for a low-frequency variant of uncertain significance

Family-based studies to categorize additional variants that may confer cancer risk will need to be increasingly large as RR decreases but are robust to changes in variant frequency because rare variant carrier frequency in families is a direct function of relationship to identified carriers ( Tables 3 and 4 ). Note that in the unrelated and familial study designs, the two groups being compared are orthogonal: in population-based studies, the carrier frequency is compared between cases and controls. In families, the affected frequency is compared between carriers and noncarriers.

Table 3 Family size needed to characterize a breast cancer variant as pathogenic
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Table 4 Family size needed to characterize a colon cancer variant as pathogenic
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GALNT12 example

GALNT12 has recently been identified as a colorectal cancer risk gene, but the RRs have not been established for GALNT12 variants. There are 69 exonic missense variants identified by the Exome Variant Server project in ˜6,500 individuals sequenced; 33 of these were missense variants at a frequency <0.001, of which 28 had a frequency <0.0002.35 Some of these rare variants may have been oversampled due to chance and may have actual population frequencies that are much lower.

We recently identified an individual with a GALNT12 D303N mutation. This is present at a frequency of ˜0.001 in both the 1000 Genomes and Exome Variant Server databases. There is limited literature suggesting that this variant may be pathogenic.36,37 However, the literature does not indicate what the RR or OR might be for this variant but suggests that risk may be lower than that for known pathogenic mutations in well defined hereditary nonpolyposis colon cancer genes.36,37 If the RR of colon cancer conferred by this variant is 5, we would expect that a case–control study with ˜1,089 cases and 1,089 cancer-free controls would have a reasonable likelihood of definitively categorizing the variant and generating a reasonable RR estimate ( Table 2 ). We would expect such a study to identify approximately five individuals carrying the variant among cases and one with the variant among the controls. As noted above, using a larger control data set, such as the Exome Variant Server database, may allow more accurate estimates of the OR.35 If we were to calculate risk from family-based studies, and if we can successfully sample relatives of the proband such that 37.5% of genotyped individuals carry the variant in question and are old enough to be at risk of cancer, we would need to genotype 137 relatives of the proband to classify the variant and define a reasonable independent RR estimate. In this process, we would identify ˜11 individuals who have had colon cancer, of whom, 8 would be expected to carry the variant of interest and 3 would be incidental cancer cases. Despite the substantial RR, only a portion of the ˜52 (8 + 44) related individuals carrying the risk variant would have developed cancer ( Table 4 ).

Discussion

Some patients, physicians, and genetic counselors may have the hope that many variants of uncertain significance will be classified in the near future.6 However, despite the liberal assumptions resulting in lower bounds on sample size estimates that we report, it appears unlikely that most very rare missense variants will be classifiable in the near future. Furthermore, accurate RR estimates are more challenging from an epidemiological perspective. Unfortunately, based on sample sizes necessary, independent RR estimates may not be available for most rare variants anytime in the foreseeable future. Functional studies will probably improve and may help with Bayesian classification of some variants; however, because functional assays are usually targeted at specific domains and typically generate likelihood ratios between 1.5 and 10, functional assays for many variants may not be available, and even when these functional assays exist, some epidemiological evidence would probably be required as additional support.17,38,39

Efforts to build large shared databases of cases and population-based controls are promising and may make it possible to classify and estimate risk for the highest-risk variants, i.e., those with nearly 0.1% frequency in the population, such as the GALNT12 variant described above. However, the use of population-based RR calculations may not be feasible for most rare variants. It is unlikely that the enormous research funds required could be made available to do adequate population-based surveys to classify extremely rare variants, but some data may become available from pooled results obtained from clinical testing institutions that are early adopters of genomic methodologies for cancer risk testing.

Family-based analysis requires the same sample size regardless of variant frequency; therefore, despite substantial limitations, this may be the best strategy for classifying extremely rare missense variants, particularly if RR is predicted to be high. However, it will be necessary to identify many distant relatives or multiple apparently unrelated families to classify and estimate RR for most rare variants using families. This may be challenging because average family size has been decreasing in much of the world, knowledge of family medical history is often limited, and obtaining additional family history can be difficult due to geography, family communication, and limited availability of older records. Unfortunately, the probability of finding more than one independent family carrying a rare variant is directly proportional to variant frequency. Although this type of family-based analysis might be feasible in a research setting for highly penetrant genes, in the current funding environment, it is highly unlikely that grant funding will become available for classification of private mutations in already well-characterized genes. From a clinical perspective, identifying enough family members to classify and estimate risk for most rare variants will constitute a heroic genetic counseling effort, and insurance coverage for such testing would be difficult to justify.

The GALNT12 D303N mutation example presented herein is illustrative. Although this specific variant is common enough that it may be definitively classified relatively soon, the risk conferred by this variant may remain unclear even after the variant is definitively classified. Dozens of other rare GALNT12 missense variants have already been identified in fewer than 0.5% of individuals sequenced for this gene.35 It is clear from recent population-based exome- and genome-sequencing projects that the number of rare variants with potential clinical implications identified in the future will increase with the number of individuals receiving genomic testing.4,40

We demonstrate that generating clinically actionable estimates of RR for rare missense variants will be very challenging even after extensive efforts to categorize these as Likely Pathogenic or Pathogenic. This demonstrates a significant limitation to personalized cancer risk estimates based on genetic information.

Disclosure

The authors declare no conflict of interest.