Letters to the Editor References Committee for the Study of Inborn Errors of Metabolism (1975) Genetic screening: programs, principles, and research. National Academy of Sciences, Washington, DC Milunsky A, Alpert E (1978) Maternal serum AFP screening. N Engl J Med 298:738-739 i 1992 by The American Society of Human Genetics. All rights reserved. 0002-9297/92/5003-0026$02.00
Am. J. Hum. Genet. 50:645-646, 1992
Segregation Analysis in Alzheimer Disease: No Evidence for a Major Gene To the Editor: There is a general agreement to say that, in some multiple-case families, Alzheimer disease (AD) is very likely to be of genetic origin. In those families the disease onset is usually early, and the transmission pattern suggests an autosomal dominant mode of inheritance. Furthermore, there is some evidence that a disease-causing gene is on chromosome 21, although one recent linkage study has failed to locate it precisely (St George Hyslop et al. 1990). However, the origin of the great majority of AD cases -in particular those with a late onset -remains very controversial, and, although the single-gene hypothesis with no sporadic cases is attractive because of its simplicity, it is by no means certain. Under this hypothesis, the absence of familial clustering in most AD cases would be explained by the censoring bias due to the late onset of the disease: most of the unaffected gene carriers in a family would have died of a competing risk prior to the age at onset. Other hypotheses have been proposed -e.g., a second locus, on chromosome 21, for susceptibility to AD; a locus on chromosome 19; nongenetic factors; or the interaction of multiple genetic and environmental factors but none is yet conclusive. In this context, segregation analysis is of major interest, as it can help to gauge the likelihood of these hypotheses (Morton and MacLean 1974). It is surprising that very few segregation analyses of AD had been published, until the paper by Farrer et al. (1991) in a recent issue of the Journal. The authors performed a segregation analysis, with a correction of censoring bias due to age, on 232 nuclear families ascertained
645
through a memory disorder unit. Their conclusion is that in AD there is some evidence for a major gene associated with a multifactorial component. However, although the authors referred to the original paper of Morton and MacLean (1974), they incorrectly used the mixed model in their model comparisons. Indeed, to assess the likelihood of the transmission of a major gene, the authors compared the multifactorial model (Farrer et al. 1991, model 2 in table 3) with the mixed model with unrestricted d and r's (Farrer et al. 1991, model 13 in table 3), which is in fact the unified model proposed by Lalouel et al. (1983). The likelihood-ratio (x2) test between these models was highly significant (X6 = 13.27, P< .001), and the hypothesis of the absence of a major-locuscomponent transmission of AD was rejected by the authors. As a matter of fact, the mixed model, as defined by Morton and MacLean, is model 12 (Farrer et al. 1991, table 3) with transmission probabilities constrained to their Mendelian values. The likelihood-ratio (X2) test between this model and the multifactorial model is not significant (X3 = 5.56, P = .135). This means that the hypothesis of the absence of a major-locus-component transmission of AD is not rejected. Conversely, the multifactorial component is highly significant (model 7 vs. model 12; X2 = 15.68, P< .001). In the absence of any evidence for a major gene in AD, there is no indication to test other hypotheses -in particular the Mendelian T's - and the model that best explains these data is the multifactorial model. This conclusion was already reached by MacGuffin et al. (1991) in a previous segregation analysis, but it does not prove that a major gene could not be involved in AD etiology: the impossibility of detecting its presence could be due to a lack of power in the analyses. However, the impossibility of finding a major-gene effect in a large-scale, censoring-corrected, segregation-analysis study suggests that this effect would be responsible only for a very few cases and that most AD cases are of a multifactorial origin. C. TzoURIO,* C. BONAITI4 F. CLERGET-DARPOUX,t AND A. ALPEROVITCH*
*National Institute of Health and Medical Research (INSERM) U169 Villejuif and tINSERM U155 Longchamp, France References Farrer LA, Myers RH, Connor L, Cupples LA, Growdon JH (1991) Segregation analysis reveals evidence of a major
646 gene for Alzheimer disease. Am J Hum Genet 48:10261033 Lalouel JM, Rao DC, Morton NE, Elston RC (1983) A unified model for complex segregation analysis. Am J Hum Genet 35:816-826 McGuffin P, Sargeant M, Weppner G (1991) The genetics of Alzheimer's disease and the ethical implications for prevention. In: Sram RJ, Bulyzhenkov V, Prilipko L, Christen Y (eds) Ethical issues of molecular genetics in psychiatry. Springer, Berlin and Heidelberg, pp 42-56 Morton NE, MacLean CJ (1974) Analysis of family resemblance. III. Complex segregation of quantitative traits. Am J Hum Genet 26:489-503 St George-Hyslop PH, Haines JL, Farrer LA, Polinsky R, Van Broeckhoven C, Goate A, Crapper McLachlan DR, et al (1990) Genetic linkage studies suggest that Alzheimer's disease is not a single homogeneous disorder. Nature 347:194-197 © 1992 by The American Society of Human Genetics. All rights reserved. 0002-9297/92/5003-0027$02.00
Am. J. Hum. Genet. 50:646-648, 1992
Reply to Tzourio et al. To the Editor: In some respects, Alzheimer disease (AD) is a genetic epidemiologist's nightmare. The disorder has a very late age at onset, cannot be diagnosed with certainty among living people, and is heterogeneous (Farrer et al. 1990; St George-Hyslop et al. 1990) even among rare families in which the trait is dominantly transmitted and linked to chromosome 21 (Chartier-Harlin et al. 1991; Tanzi et al. 1991). In our recent paper published in the Journal (Farrer et al. 1991), we applied the method of segregation analysis to compare the likelihoods of a variety of genetic, nongenetic, and complex transmission models for AD in patients consecutively ascertained through a diagnostic referral center for memory disorders. Tzourio et al. suggest that our conclusion of having found evidence for a major gene (in association with a multifactorial component) is fallacious because our rejection of the multifactorial model was based on an ostensibly incorrect comparison between the multifactorial model and the unified model (which is the mixed model with unrestricted transmission probabilities) proposed by Lalouel et al. (1983). Tzourio et al. assert that, when the multifactorial model is appropriately compared with
Letters to the Editor
the mixed model with Mendelian transmission probabilities, the multifactorial model is not rejected, and, consequently, there is no evidence in our study for a major gene for AD. We agree with Tzourio et al. that one would not reject multifactorial inheritance for AD on the basis of comparison of this model with the mixed model of Morton and MacLean (1974). However, we strongly disagree with their implication that no other model comparisons (which would lead to rejection of the multifactorial model) are permissible and with their conclusion that there is no evidence for a major gene for AD. We support our position with the following arguments: 1. The theory of maximum-likelihood-ratio testing is founded upon the notion of hierarchical testing of nested hypotheses (Cox and Hinkley 1974, pp. 311337). In this context one hypothesis is nested within another if the parameters of the former consist of a subset of the latter, with the remaining parameters specified by the null hypothesis. A test of the null hypothesis is obtained by comparing the log likelihoods of the two models with the df determined by the difference in df for the two models (or, equivalently, the number of parameters being tested by the null hypothesis). In this approach there is no restriction on appropriate models as long as the two models are nested. In our particular example, model 2 (multifactorial model with no cohort effect) qualifies as a nested model of model 13 (mixed model with unrestricted d and T's), the null hypothesis testing that the parameters d, t, q, and xi, T2, T3 are all equal to zero. Since this test rejects the null hypothesis, we conclude that not all these parameters are equal to zero. Hence, model 2 is rejected. The problem now is the interpretation of the preferred model which indicates non-Mendelian inheritance of a major effect. We offered several explanations for the apparent excess transmission from the heterozygote, including multiple major loci, reduced ascertainment of AD gene carriers among parents, and phenocopies (Farrer et al. 1991). 2. Even if we ignore the arguments in point 1 and assume that model comparisons must be sequential starting with the most specific models, the multifactorial model would still be legitimately rejected by comparing model 3 (multifactorial model allowing for cohort effect in heritability) with model 14 (mixed model with transmission probabilities constrained to Mendelian values and allowing for a cohort effect) in the paper by Farrer et al. (1991, table 3) (X% = 7.88, P = .049).
Am. J. Hum. Genet. 50:645-646, 1992
Segregation Analysis in Alzheimer Disease: No Evidence for a Major Gene To the Editor: There is a general agreement to say that, in some multiple-case families, Alzheimer disease (AD) is very likely to be of genetic origin. In those families the disease onset is usually early, and the transmission pattern suggests an autosomal dominant mode of inheritance. Furthermore, there is some evidence that a disease-causing gene is on chromosome 21, although one recent linkage study has failed to locate it precisely (St George Hyslop et al. 1990). However, the origin of the great majority of AD cases -in particular those with a late onset -remains very controversial, and, although the single-gene hypothesis with no sporadic cases is attractive because of its simplicity, it is by no means certain. Under this hypothesis, the absence of familial clustering in most AD cases would be explained by the censoring bias due to the late onset of the disease: most of the unaffected gene carriers in a family would have died of a competing risk prior to the age at onset. Other hypotheses have been proposed -e.g., a second locus, on chromosome 21, for susceptibility to AD; a locus on chromosome 19; nongenetic factors; or the interaction of multiple genetic and environmental factors but none is yet conclusive. In this context, segregation analysis is of major interest, as it can help to gauge the likelihood of these hypotheses (Morton and MacLean 1974). It is surprising that very few segregation analyses of AD had been published, until the paper by Farrer et al. (1991) in a recent issue of the Journal. The authors performed a segregation analysis, with a correction of censoring bias due to age, on 232 nuclear families ascertained
645
through a memory disorder unit. Their conclusion is that in AD there is some evidence for a major gene associated with a multifactorial component. However, although the authors referred to the original paper of Morton and MacLean (1974), they incorrectly used the mixed model in their model comparisons. Indeed, to assess the likelihood of the transmission of a major gene, the authors compared the multifactorial model (Farrer et al. 1991, model 2 in table 3) with the mixed model with unrestricted d and r's (Farrer et al. 1991, model 13 in table 3), which is in fact the unified model proposed by Lalouel et al. (1983). The likelihood-ratio (x2) test between these models was highly significant (X6 = 13.27, P< .001), and the hypothesis of the absence of a major-locuscomponent transmission of AD was rejected by the authors. As a matter of fact, the mixed model, as defined by Morton and MacLean, is model 12 (Farrer et al. 1991, table 3) with transmission probabilities constrained to their Mendelian values. The likelihood-ratio (X2) test between this model and the multifactorial model is not significant (X3 = 5.56, P = .135). This means that the hypothesis of the absence of a major-locus-component transmission of AD is not rejected. Conversely, the multifactorial component is highly significant (model 7 vs. model 12; X2 = 15.68, P< .001). In the absence of any evidence for a major gene in AD, there is no indication to test other hypotheses -in particular the Mendelian T's - and the model that best explains these data is the multifactorial model. This conclusion was already reached by MacGuffin et al. (1991) in a previous segregation analysis, but it does not prove that a major gene could not be involved in AD etiology: the impossibility of detecting its presence could be due to a lack of power in the analyses. However, the impossibility of finding a major-gene effect in a large-scale, censoring-corrected, segregation-analysis study suggests that this effect would be responsible only for a very few cases and that most AD cases are of a multifactorial origin. C. TzoURIO,* C. BONAITI4 F. CLERGET-DARPOUX,t AND A. ALPEROVITCH*
*National Institute of Health and Medical Research (INSERM) U169 Villejuif and tINSERM U155 Longchamp, France References Farrer LA, Myers RH, Connor L, Cupples LA, Growdon JH (1991) Segregation analysis reveals evidence of a major
646 gene for Alzheimer disease. Am J Hum Genet 48:10261033 Lalouel JM, Rao DC, Morton NE, Elston RC (1983) A unified model for complex segregation analysis. Am J Hum Genet 35:816-826 McGuffin P, Sargeant M, Weppner G (1991) The genetics of Alzheimer's disease and the ethical implications for prevention. In: Sram RJ, Bulyzhenkov V, Prilipko L, Christen Y (eds) Ethical issues of molecular genetics in psychiatry. Springer, Berlin and Heidelberg, pp 42-56 Morton NE, MacLean CJ (1974) Analysis of family resemblance. III. Complex segregation of quantitative traits. Am J Hum Genet 26:489-503 St George-Hyslop PH, Haines JL, Farrer LA, Polinsky R, Van Broeckhoven C, Goate A, Crapper McLachlan DR, et al (1990) Genetic linkage studies suggest that Alzheimer's disease is not a single homogeneous disorder. Nature 347:194-197 © 1992 by The American Society of Human Genetics. All rights reserved. 0002-9297/92/5003-0027$02.00
Am. J. Hum. Genet. 50:646-648, 1992
Reply to Tzourio et al. To the Editor: In some respects, Alzheimer disease (AD) is a genetic epidemiologist's nightmare. The disorder has a very late age at onset, cannot be diagnosed with certainty among living people, and is heterogeneous (Farrer et al. 1990; St George-Hyslop et al. 1990) even among rare families in which the trait is dominantly transmitted and linked to chromosome 21 (Chartier-Harlin et al. 1991; Tanzi et al. 1991). In our recent paper published in the Journal (Farrer et al. 1991), we applied the method of segregation analysis to compare the likelihoods of a variety of genetic, nongenetic, and complex transmission models for AD in patients consecutively ascertained through a diagnostic referral center for memory disorders. Tzourio et al. suggest that our conclusion of having found evidence for a major gene (in association with a multifactorial component) is fallacious because our rejection of the multifactorial model was based on an ostensibly incorrect comparison between the multifactorial model and the unified model (which is the mixed model with unrestricted transmission probabilities) proposed by Lalouel et al. (1983). Tzourio et al. assert that, when the multifactorial model is appropriately compared with
Letters to the Editor
the mixed model with Mendelian transmission probabilities, the multifactorial model is not rejected, and, consequently, there is no evidence in our study for a major gene for AD. We agree with Tzourio et al. that one would not reject multifactorial inheritance for AD on the basis of comparison of this model with the mixed model of Morton and MacLean (1974). However, we strongly disagree with their implication that no other model comparisons (which would lead to rejection of the multifactorial model) are permissible and with their conclusion that there is no evidence for a major gene for AD. We support our position with the following arguments: 1. The theory of maximum-likelihood-ratio testing is founded upon the notion of hierarchical testing of nested hypotheses (Cox and Hinkley 1974, pp. 311337). In this context one hypothesis is nested within another if the parameters of the former consist of a subset of the latter, with the remaining parameters specified by the null hypothesis. A test of the null hypothesis is obtained by comparing the log likelihoods of the two models with the df determined by the difference in df for the two models (or, equivalently, the number of parameters being tested by the null hypothesis). In this approach there is no restriction on appropriate models as long as the two models are nested. In our particular example, model 2 (multifactorial model with no cohort effect) qualifies as a nested model of model 13 (mixed model with unrestricted d and T's), the null hypothesis testing that the parameters d, t, q, and xi, T2, T3 are all equal to zero. Since this test rejects the null hypothesis, we conclude that not all these parameters are equal to zero. Hence, model 2 is rejected. The problem now is the interpretation of the preferred model which indicates non-Mendelian inheritance of a major effect. We offered several explanations for the apparent excess transmission from the heterozygote, including multiple major loci, reduced ascertainment of AD gene carriers among parents, and phenocopies (Farrer et al. 1991). 2. Even if we ignore the arguments in point 1 and assume that model comparisons must be sequential starting with the most specific models, the multifactorial model would still be legitimately rejected by comparing model 3 (multifactorial model allowing for cohort effect in heritability) with model 14 (mixed model with transmission probabilities constrained to Mendelian values and allowing for a cohort effect) in the paper by Farrer et al. (1991, table 3) (X% = 7.88, P = .049).
