Multistage sampling for disease family registries

Genome-wide association scans for secondary traits using case-control samples

Genome-wide association studies (GWAS) require considerable investment, so researchers often study multiple traits collected on the same set of subjects to maximize return. However, many GWAS have adopted a case-control design; improperly accounting for case-control ascertainment can lead to biased estimates of association between markers and secondary traits. We show that under the null hypothesis of no marker-secondary trait association, naïve analyses that ignore ascertainment or stratify on case-control status have proper Type I error rates except when both the marker and secondary trait are independently associated with disease risk. Under the alternative hypothesis, these methods are unbiased when the secondary trait is not associated with disease risk. We also show that inverse-probability-of-sampling-weighted (IPW) regression provides unbiased estimates of marker-secondary trait association. We use simulation to quantify the Type I error, power and bias of naïve and IPW methods. IPW regression has appropriate Type I error in all situations we consider, but has lower power than naïve analyses. The bias for naïve analyses is small provided the marker is independent of disease risk. Considering the majority of tested markers in a GWAS are not associated with disease risk, naïve analyses provide valid tests of and nearly unbiased estimates of marker-secondary trait association. Care must be taken when there is evidence that both the secondary trait and tested marker are associated with the primary disease, a situation we illustrate using an analysis of the relationship between a marker in FGFR2 and mammographic density in a breast cancer case-control sample.

On combining family and case-control studies

Studies to detect genetic association with disease can be family-based, often using families with multiple affected members, or population based, as in population-based case-control studies. If data on both study types are available from the same population, it is useful to combine them to improve power to detect genetic associations. Two aspects of the data need to be accommodated, the sampling scheme and potential residual correlations among family members. We propose two approaches for combining data from a case-control study and a family study that collected families with multiple cases. In the first approach, we view a family as the sampling unit and specify the joint likelihood for the family members using a two-level mixed effects model to account for random familial effects and for residual genetic correlations among family members. The ascertainment of the families is accommodated by conditioning on the ascertainment event. The individuals in the case-control study are treated as families of size one, and their unconditional likelihood is combined with the conditional likelihood for the families. This approach yields subject specific maximum likelihood estimates of covariate effects. In the second approach, we view an individual as the sampling unit. The sampling scheme is accommodated using two-phase sampling techniques, marginal covariate effects are estimated, and correlations among family members are accounted for in the variance calculations. The models are compared in simulations. Data from a case-control and a family study from north-eastern Italy on melanoma and a low-risk melanoma-susceptibility gene, MC1R, are used to illustrate the approaches.

Prevalence of BRCA1 Mutation Carriers among U.S. Non-Hispanic Whites

Data from several countries indicate that 1% to 2% of Ashkenazi Jews carry a pathogenic ancestral mutation of the tumor suppressor gene BRCA1. However, the prevalence of BRCA1 mutations among non-Ashkenazi Whites is uncertain. We estimated mutation carrier prevalence in U.S. non-Hispanic Whites, specific for Ashkenazi status, using data from two population-based series of San Francisco Bay Area patients with invasive cancers of the breast or ovary, and data on breast and ovarian cancer risks in Ashkenazi and non-Ashkenazi carriers. Assuming that 90% of the BRCA1 mutations were detected, we estimate a carrier prevalence of 0.24% (95% confidence interval, 0.15-0.39%) in non-Ashkenazi Whites, and 1.2% (95% confidence interval, 0.5-2.6%) in Ashkenazim. When combined with U.S. White census counts, these prevalence estimates suggest that approximately 550,513 U.S. Whites (506,206 non-Ashkenazim and 44,307 Ashkenazim) carry germ line BRCA1 mutations. These estimates may be useful in guiding resource allocation for genetic testing and genetic counseling and in planning preventive interventions.

Two-Stage sampling designs for gene association studies

We consider two-stage case-control designs for testing associations between single nucleotide polymorphisms (SNPs) and disease, in which a subsample of subjects is used to select a panel of "tagging" SNPs that will be considered in the main study. We propose a pseudolikelihood [Pepe and Flemming, 1991: JASA 86:108-113] that combines the information from both the main study and the substudy to test the association with any polymorphism in the original set. SNP-tagging [Chapman et al., 2003: Hum Hered 56:18-31] and haplotype-tagging [Stram et al., 2003a; Hum Hered 55:27-36] approaches are compared. We show that the cost-efficiency of such a design for estimating the relative risk associated with the causal polymorphism can be considerably better than for a single-stage design, even if the causal polymorphism is not included in the tag-SNP set. We also consider the optimal selection of cases and controls in such designs and the relative efficiency for estimating the location of a causal variant in linkage disequilibrium mapping. Nevertheless, as the cost of high-volume genotyping plummets and haplotype tagging information from the International HapMap project [Gibbs et al., 2003; Nature 426:789-796] rapidly accumulates in public databases, such two-stage designs may soon become unnecessary.

Optimal designs for estimating penetrance of rare mutations of a disease-susceptibility gene

Many clinical decisions require accurate estimates of disease risks associated with mutations of known disease-susceptibility genes. Such risk estimation is difficult when the mutations are rare. We used computer simulations to compare the performance of estimates obtained from two types of designs based on family data. In the first (clinic-based designs), families are ascertained because they meet certain criteria concerning multiple disease occurrences among family members. In the second (population-based designs), families are sampled through a population-based registry of affected individuals called probands, with oversampling of probands whose families are more likely to segregate mutations. We generated family structures, genotypes, and phenotypes using models that reflect the frequencies and penetrances of mutations of the BRCA1/2 genes. We studied the effects of risk heterogeneity due to unmeasured, shared risk factors by including risk variation due to unmeasured genotypes of another gene. The simulations were chosen to mimic the ascertainment and selection processes commonly used in the two types of designs. We found that penetrance estimates from both designs are nearly unbiased in the absence of unmeasured shared risk factors, but are biased upward in the presence of such factors. The bias increases with increasing variation in risks across genotypes of the second gene. However, it is small compared to the standard error of the estimates. Standard errors from population-based designs are roughly twice those from clinic-based designs with the same number of families. Using the root-mean-square error as a measure of performance, we found that in all instances, the clinic-based designs gave more accurate estimates than did the population-based designs with the same numbers of families. Rough variance calculations suggest that clinic-based designs give more accurate estimates because they include more identified mutation carriers.

Stratified case sampling and the use of family controls

We compare the asymptotic relative efficiency (ARE) of different study designs for estimating gene and gene-environment interaction effects using matched case-control data. In the sampling schemes considered, cases are selected differentially based on their family history of disease. Controls are selected either from unrelated subjects or from among the case's unaffected siblings and cousins. Parameters are estimated using weighted conditional logistic regression, where the likelihood contributions for each subject are weighted by the fraction of cases sampled sharing the same family history. Results showed that compared to random sampling, over-sampling cases with a positive family history increased the efficiency for estimating the main effect of a gene for sib-control designs (103-254% ARE) and decreased efficiency for cousin-control and population-control designs (68-94% ARE and 67-84% ARE, respectively). Population controls and random sampling of cases were most efficient for a recessive gene or a dominant gene with an relative risk less than 9. For estimating gene-environment interactions, over-sampling positive-family-history cases again led to increased efficiency using sib controls (111-180% ARE) and decreased efficiency using population controls (68-87% ARE). Using case-cousin pairs, the results differed based on the genetic model and the size of the interaction effect; biased sampling was only slightly more efficient than random sampling for large interaction effects under a dominant gene model (relative risk ratio = 8, 106% ARE). Overall, the most efficient study design for studying gene-environment interaction was the case-sib-control design with over-sampling of positive-family-history-cases.