European Journal of Human Genetics (2011) 19, 173–179 & 2011 Macmillan Publishers Limited All rights reserved 1018-4813/11 www.nature.com/ejhg ARTICLE Estimating penetrance from multiple case families with predisposing mutations: extension of the ‘genotype-restricted likelihood’ (GRL) method Bernard Bonaı¨ti1,2, Vale´rie Bonadona3,4, Herve´ Perdry2,5, Nadine Andrieu6,7,8 and Catherine Bonaı¨ti-Pellie´*,2,5 Some diseases are due to germline mutations in predisposing genes, such as cancer family syndromes. Precise estimation of the age-specific cumulative risk (penetrance) for mutation carriers is essential for defining prevention strategies. The genotype- restricted likelihood (GRL) method is aimed at estimating penetrance from multiple case families with such a mutation. In this paper, we proposed an extension of the GRL to account for multiple trait disease and to allow for a parent-of-origin effect. Using simulations of pedigrees, we studied the properties of this method and the effect of departures from underlying hypotheses, misspecification of disease incidence in the general population or misspecification of the index case, and penetrance heterogeneity. In contrast with the previous version of the GRL, accounting for multiple trait disease allowed unbiased estimation of penetrance. We also showed that accounting for a parent-of-origin effect allowed a powerful test for detecting this effect. We found that the GRL method was robust to misspecification of disease incidence in the population, but that misspecification of the index case induced a bias in some situations for which we proposed efficient corrections. When ignoring heterogeneity, the penetrance estimate was biased toward that of the highest risk individuals. A homogeneity test performed by stratifying the families according to the number of affected members was shown to have low power and seems useless for detecting such heterogeneity. These extensions are essential to better estimate the risk of diseases and to provide valid recommendations for the management of patients. European Journal of Human Genetics (2011) 19, 173–179; doi:10.1038/ejhg.2010.158; published online 6 October 2010 Keywords: penetrance; bias; pleiotropy; parent-of-origin; families INTRODUCTION called the ‘genotype-restricted likelihood’ (GRL) method, provides Some diseases with variable age of onset are due to the presence of unbiased penetrance estimates whatever criteria are used for ascertain- predisposing gene mutations, such as mismatch repair (MMR)genes ment of families and without having to model the ascertainment in hereditary non-polyposis colorectal cancer or BRCA1 and BRCA2 process. The GRL method corrects for the bias due to the selection on in breast–ovarian cancer syndrome. These genes may be responsible carrier genotype of the index case, as only families with an identified for hereditary forms of these diseases. Precise estimation of the age- carrier individual are informative for penetrance estimation. This specific cumulative risk (penetrance function) for mutation carriers is method is especially appropriate for hereditary predispositions to essential for defining prevention strategies. common diseases when numerous and complex familial criteria Families in which such mutations have been identified can con- involving several affected relatives are used to recommend genetic tribute to estimate these risks, as long as adjustment is made for these testing. It has been shown to be independent of selection criteria, in families generally ascertained because of several affected members.1 particular on the number of affected individuals and on the age at Such families are usually referred by physicians to genetic counsellors diagnosis of affected family members.4 who propose genetic testing when specific criteria are fulfilled. For Beside the numerous advantages mentioned above, the GRL method hereditary cancers, for example, most criteria used for recommending relies on assumptions, which may not be fulfilled in some situations. In genetic testing are based on familial aggregation of specific cancers.2,3 order to evaluate its robustness to a departure from these hypotheses, When a mutation is identified in an affected member (defined as we studied the sensitivity of the GRL in various situations such as index case), genetic testing is proposed to close relatives who, if disease frequency of the general population overestimated or under- carriers, will be offered intensive surveillance, which will improve estimated or a genetic heterogeneity not taken into account. Addition- the prognosis, or prophylactic surgery when possible. ally, the previous GRL version allows estimating the penetrance of only An ascertainment-adjusted method, based on maximum likelihood, one trait once at a time and this might bias penetrance estimates in has been proposed for estimating the age-specific cumulative risk family syndromes where several different traits may occur (pleiotropy), (penetrance) of a given disease associated with a deleterious mutation like different tumour localizations. Therefore, we proposed in this paper from families in which such a mutation has been identified.4 This method, to extend the method to account for pleiotropy. We also extended the 1INRA-GABI, Jouy-en-Josas, France; 2INSERM, U669, Villejuif, France; 3Universite´ Lyon 1, UMR CNRS 5558, Lyon, France; 4Centre Le´on Be´rard, Lyon, France; 5Universite´ Paris-Sud, Villejuif, France; 6INSERM, U900, Paris, France; 7Institut Curie, Paris, France; 8Ecole des Mines de Paris, ParisTech, Fontainebleau, France *Correspondence: Dr C Bonaı¨ti-Pellie´, INSERM U669, Baˆtiment 15/16, Hoˆpital Paul Brousse, 94807 Villejuif Cedex, France. Tel: +33 14 559 5349; Fax: +33 14 559 5331; E-mail: [email protected] Received 13 April 2010; revised 30 June 2010; accepted 19 August 2010; published online 6 October 2010 Extension of the GRL method B Bonaı¨ti et al 174 method to allow for a parent-of-origin effect, that is, penetrance Extensions of the GRL functions differing according to the gender of the parent who trans- Multiple trait phenotype. The contribution to the likelihood of each indivi- mitted the deleterious mutation. This effect has been described in some dual was modified to simultaneously take into account the phenotype of a diseases5–8 buthasnotbeenyetaccountedfor in penetrance estimation. variable number of possible traits, under the hypothesis that, given the genotype, These extensions are essential to better estimate the risk of diseases and the occurrence of a disease does not modify the risk of developing subsequently to provide valid recommendations for the management of patients. other diseases. If tijk is the age at onset or the age at censoring of the kth disease and dijk istheindicatoroftheoccurrenceofthekth disease before censoring time on the jth member of the ith family, yij¼(tij1 tijky, dij1, dijky, gij)with METHODS probability: The GRL method 4,9 Y ÀÁÀÁ The GRL uses a retrospective likelihood conditioned on the phenotypes of all qijk Prðyij=uij ¼ lÞ¼ 1 À Fðtijk; yklÞ Â hðtijk; yklÞ Âjðgij; lÞ family members and on the genotype of the index case. It estimates penetrance k parameters for mutation carriers by maximizing the probability of observed genotypes (G) of family members who have been tested for the mutation found in the index case, conditional on observed phenotypes (P) and on index case Parent-of-origin effect. To take into account a parent-of-origin effect, we being a carrier (I). Owing to the fact that the index case is always tested, the modified the likelihood by splitting the heterozygote genotype in to two conditional probability may be written as: different genotypes according to the paternal or maternal origin of the mutated PrðG=P;IÞ¼PrðG;PÞ=PrðP;IÞ allele. Four genotypes were considered: AA, Aa, aA and aa,whereAa and aA are the ordered heterozygous genotypes in which the first allele is transmitted Following the cure model of De Angelis,10 we considered that a proportion k by the father and the second one by the mother. The matrix of genotype of individuals will never be affected and a Weibull model for penetrance for the probabilities from one generation to another was modified accordingly, and others. The cumulative risk by age t is: three penetrance functions instead of two were considered for gene carriers. al PrðTotÞ¼Fðt; kl; al; llÞ¼ð1 À klÞð1 À expðÀðÞllt ÞÞ Simulations of pedigrees To study the statistical properties of the method, and in particular its where l is the genotype for the mutation (l¼1, 2, 3 for AA, Aa and aa robustness to departures from underlying hypotheses, as well as the interest genotypes, respectively, A being the mutated allele), a and l are the Weibull l l of the extensions implemented in the method, we simulated four generation shape and scale parameters, k is the probability of never being affected given l families with a fixed number of relatives: starting from the index case, we l and T is the age at disease occurrence. simulated a couple of his (her) parents and two couples of grandparents. The Let y ¼(t , d , g ) be the set of observations on the jth member of the ith ij ij ij ij grandparents and parents of the index case (generations 1 and 2) had, family, t is the age at onset of the disease or the age at censoring (earliest date ij respectively, two and three children. Each of them had two children as well among dates of prophylactic surgery, death or last news), d is the indicator of ij as all their offspring until the fourth generation (Figure 1). Genotypes of family occurrence of the disease before the age at censoring and g is the observed ij members were randomly generated according to the mutated allele frequency genotype, which is coded as 0 when unknown. Let F(t; y ) be the cumulative l in ancestors and spouses and to Mendel’s laws for offspring except the index risk by age t for the lth genotype and h(t; y ) be the corresponding hazard l case who had at least one mutated allele.