Since 1994, several genes have been identified the mutations of which are responsible for hereditary forms of cancer, in particular breast/ovarian cancer and colorectal cancer; guidelines for genetic testing and clinical management have been published and the detection of mutations is now routinely organized.19, 20
In France, >2500 mutations in BRCA1
were found in index cases and >7000 relatives had genetic testing between 2003 and 2007. For MMR
genes, a mutation was found in >1000 index cases and nearly 3000 relatives were tested (http://www.e-cancer.fr/v1/fichiers/public/synthese_evolutio
). Such familial data provide unique information on carrier risk, as long as adjustment for selection criteria of these families is adequately performed. These criteria are complex and have evolved with time. Moreover, these criteria are proposed as guidelines for genetic counsellors and, therefore, are not purely applied. Therefore, a formal correction for these criteria is completely unfeasible and the GRL method appears particularly appropriate for estimating disease risks in carriers.
In this paper, we investigated the statistical properties of the GRL method and proposed some extensions. As any maximum likelihood estimator, the GRL estimator is unbiased only asymptotically. Indeed, we observed a small bias in penetrance estimate for samples of moderate size, particularly at old ages. This bias should be kept in mind when analysing small samples of families. Regarding precision of the estimates, we showed that the standard errors in current situations were rather small, although retrospective likelihood methods are known to be poorly efficient.21, 22
We studied the robustness of the GRL to departures from underlying hypotheses. We found that the method was very robust to a misspecification of disease incidence in the general population, even for important errors. Such an error could be due to a cohort effect as observed in some cancers.23
Our results indicated that the method is expected to perform well when using an average disease incidence at an intermediate period between the periods of oldest and youngest generation of the families.
Regarding the specification of the index case, there is no ambiguity if the index is an incident case who asked for genetic counselling and the GRL should be used as it. If there is any doubt on the index identification in some families, when all affected family members are prevalent cases, our recommendation is to use, for these families only, either the random procedure or the conditioning on the genotype of all individuals affected by a disease under study,16
provided that they had genetic testing proving their carrier status. In general, the random procedure provides the least biased estimates but Quehenberger's method16
is a good alternative.
Regarding penetrance heterogeneity, we found that the estimated penetrance was close to that of highest risk individuals because of selection on multiple case families. A homogeneity test performed by stratifying the families according to the number of affected members was shown to have low power and appears useless for detecting such heterogeneity. However, one must keep in mind that nearly all families referred to genetic counselling so far are multiple case families and that the average penetrance estimated from a sample of such families may be the most appropriate one to predict disease occurrence and to recommend or not genetic testing in such context.
Another source of bias could be that we did not take into account a possible family-specific random effect due to low penetrance genes with multiplicative effects, such as those found by Antoniou et al24
in breast cancer, nor modifier genes such as those found to influence cancer risk in BRCA2
Such an effect could affect major gene penetrance estimate.22, 27, 28
The GRL will have to be extended to take into account such effects when better identified.
The GRL method assumes that the frequency of deleterious mutations is low in the general population. A departure from this hypothesis would invalidate our approximation for risks in non-carriers that are set to be equal to the risks in the general population. The sample size needed to estimate the risk in non-carriers by the GRL is prohibitive and this approximation is necessary. Therefore, we do not recommend using the GRL for mutations with frequency that would exceed 0.01 for a dominant predisposition, or 0.10 for a recessive one, in the general population.
Finally, we could evaluate the efficiency of the extensions of the GRL that we proposed, that is, possible multiple trait phenotype and parent-of-origin effect. Regarding the former, we found that analysing separately each trait induced a bias, which was corrected when using the multiple trait option. The bias is due to the fact that a single trait analysis uses an inaccurate ascertainment correction when conditioning on only one trait whereas several traits led to the ascertainment of families. Indeed, our results showed that the risks of CRC in men were unbiased when performing a single trait analysis, which is most probably due to the fact that CRC is almost the only tumour observed in carrier men. Therefore, this extension, in addition to sparing time by performing only one analysis, avoids bias, particularly for low-risk traits. This is most probably the reason why we found a lower risk of endometrial cancer than other studies when we analysed a sample of 36 French families using our first version of the GRL.9
Among studies that used a retrospective likelihood for estimating cancer risk in Lynch syndrome,9, 16, 17, 29
note that only Quehenberger et al16
used a multiple trait approach. This may partly explain the variability of estimates among studies.
The test for a parent-of-origin effect was shown to be very efficient with samples of moderate size when the difference in penetrance was large. It would be interesting to apply the method for testing such an effect in hereditary forms of diseases, such as breast and ovarian cancers associated with mutations of BRCA1 or BRCA2 or Lynch syndrome associated with mutations of the MMR genes, as this hypothesis has not been tested yet.
The two extensions of the GRL have also been implemented in the proband's phenotype exclusion likelihood that estimates penetrance in case of single ascertainment.30
Both methods are two different options of the GENERISK software, which can be obtained from the authors (bernard.bonaiti/at/inserm.fr