Ability of known susceptibility SNPs to predict colorectal cancer risk for persons with and without a family history

Abstract

Before SNP-based risk can be incorporated in colorectal cancer (CRC) screening, the ability of these SNPs to estimate CRC risk for persons with and without a family history of CRC, and the screening implications need to be determined. We estimated the association with CRC of a 45 SNP-based risk using 1181 cases and 999 controls, and its correlation with CRC risk predicted from detailed family history. We estimated the predicted change in the distribution across predefined risk categories, and implications for recommended screening commencement age, from adding SNP-based risk to family history. The inter-quintile risk ratio for colorectal cancer risk of the SNP-based risk was 3.28 (95% CI 2.54–4.22). SNP-based and family history-based risks were not correlated (r = 0.02). For persons with no first-degree relatives with CRC, screening could commence 4 years earlier for women (5 years for men) in the highest quintile of SNP-based risk. For persons with two first-degree relatives with CRC, screening could commence 16 years earlier for men and women in the highest quintile, and 7 years earlier for the lowest quintile. This 45 SNP panel in conjunction with family history, can identify people who could benefit from earlier screening. Risk reclassification by 45 SNPs could inform targeted screening for CRC prevention, particularly in clinical genetics settings when mutations in high-risk genes cannot be identified. Yet to be determined is cost-effectiveness, resources requirements, community, patient and clinician acceptance, and feasibility with potentially ethical, legal and insurance implications.

Appendix

Risk distributions

The distribution of the risk under a genetic mixed model, which incorporates major gene and an unmeasured polygene components [23, 24], was calculated as follows.

The polygene component modelled the combined effect on colorectal cancer (CRC) susceptibility of a large number of independent genetic loci that individually have small, multiplicative effects on the incidence of CRC. Therefore the polygene was modelled as a normally distributed random variable $X \sim N\left( {\mu ,\sigma^{2} } \right)$ with mean μ and standard deviation σ, and the incidence of CRC at age t years for a person with polygene X = x was modelled as $e^{x} HR_{major} \lambda_{0} \left( t \right)$, where HR_major is the hazard ratio corresponding to the person’s genotype at the major gene (which is assumed to be independent of X) and $\lambda_{0} \left( t \right)$ is the population incidence at age t years. Note that we therefore must take $\mu = - \sigma^{2} /2$ to ensure that the population incidence $\lambda_{0} \left( t \right)$ is the average incidence for persons with HR_major = 1.

The age-specific CRC incidence is the hazard function of the random variable T giving the age at CRC diagnosis of a person who is randomly selected from the population. Therefore the cumulative risk to age 80 years for someone with polygene X = x and a major gene hazard ratio of HR_major is

$$Pen\left( x \right) = P\left( {T \le 80 |X = x} \right) = 1 - \exp \left( { - \mathop \smallint \limits_{0}^{80} e^{x} HR_{major} \lambda_{0} \left( t \right)dt} \right) = 1 - s^{{e^{x} HR_{major} }} ,$$

where ${\text{s}} = \exp \left( { - \mathop \smallint \limits_{0}^{80} \lambda_{0} \left( t \right)dt} \right)$ is the survival probability to age 80 years for someone at population risk. Inverting this equation therefore gives the cumulative distribution function of Pen(X)(since, for any c between 0 and 1, we have

$$P\left( {Pen\left( X \right) \le c} \right) = P\left( {1 - s^{{e^{X} HR_{major} }} \le c} \right) = P\left( {{ \log }\left( {\frac{{\log \left( {1 - c} \right)}}{{HR_{major} \log \left( s \right)}}} \right) \ge X} \right) = 1 - \varPhi \left( {{ \log }\left( {\frac{{\log \left( {1 - c} \right)}}{{HR_{major} \log \left( s \right)}}} \right)} \right),$$

where $\varPhi$ is the cumulative distribution function for $X \sim N\left( { - \sigma^{2} /2 ,\sigma^{2} } \right)$.

In this paper, we took the population incidence $\lambda_{0} \left( t \right)$ to be the age-specific CRC incidence for the USA 1998–2002, averaged over sex [25]. For the main analyses we also took a polygenic standard deviation of σ = 1.124, since this corresponds under Pharoah’s formula [26] to a familial relative risk of 1.88, which is the residual familial relative risk for CRC after accounting for the effects of 45 known CRC-associated SNPs [5].

Adjustment for oversampling of controls for not having a family history from the Colon Cancer Family Registry Phase I GWAS dataset that used for SNP-based risk estimation

Controls were preferentially selected for GWAS Phase-I testing if they had no family history of CRC, so we would expect them to have a slightly different distribution of the 45 SNP score K compared with controls if they had been recruited regardless of family history. Simulations were used to assess the differences between the distributions of K in these two groups of controls, and the effect of these differences on our final odds ratio estimates.

We considered a nuclear family consisting of two parents (individuals i = 1 and i = 2) and two children (individuals i = 3 and i = 4). As above, we decomposed the polygene $X_{i} = K_{i} + U_{i}$ for person i in the nuclear family into a component K_i due to the 45 known SNPs and an independent component U_i due to all other unknown genetic variants that are associated with CRC. We assumed $K_{i} \sim N\left( { - \sigma_{K}^{2} /2 ,\sigma_{K}^{2} } \right)$ and $U_{i} \sim N\left( { - \sigma_{U}^{2} /2 ,\sigma_{U}^{2} } \right)$ with σ_U = 0.6011 and σ_K = 1.124, as above. We also assumed that the joint distribution of K₁,K₂,K₃,K₄ followed a multivariate normal distribution with the correlation between parents being 0 and the correlation between all other pairs of (first-degree) family members being 0.5, and similarly for U₁,U₂,U₃,U₄. As above (but with HR_major = 1), we assumed that if individual i has K_i= k and U_i= u then he or she has a lifetime CRC risk $1 - s^{{e^{k + u} }}$. We then used these assumptions to simulate the known SNP scores K₁,K₂,K₃,K₄, the unknown variant scores U₁,U₂,U₃,U₄ and the (lifetime) affected statuses of all four family members, and we did this for 10,000,000 nuclear families. The distribution of the known variant score K₄ for individual i = 4 (one of the children) was calculated firstly for all families with no affected family members and secondly for all families where individual i = 4 was unaffected. The means of K₄ in these two types of families were − 0.385 and − 0.361, respectively, and the standard deviations of K₄ in these two types of families were both 0.60. Therefore the known variant score K₄ for controls with a null family history was shifted by − 0.021 compared to controls ascertained regardless of family history, which is − 0.021/0.60 = − 0.035 standard deviations. For a risk factor which, in cases and controls, is normally distributed with the same standard deviation and a difference in means of Δ standard deviations, it can be shown that the odds ratio is exp(Δ) [27]. Our simulations show that our ascertainment criterion is causing us to overestimate Δ by 0.035, so we are therefore overestimating the odds ratio by a factor of exp(0.035) = 1.04, i.e. by 4%.