American Journal of Medical Genetics 42:214 (1992)
Letter to the Editor Duchenne Muscular Dystrophy Inherited Through Paternal Lines To the Editor: In a survey of 454 families with patients affected with Duchenne muscular dystrophy (DMD)Zatz et al. [1991] found 4 kindreds with 2 or more affected patients who were related through paternal lines. The patients were third cousins in family 1,second cousins once removed in family 2, and first cousins once removed in families 3 and 4. The number of male relatives connecting the cousins in the pedigrees varied from 1(in families 2 and 3) to 5 (in family 1).As the authors calculated the probability of 2 new mutations in a family to be 1110,000 x 1/10,000, they considered the probability for these 4 families by chance among the 454 genealogies with DMD patients so low as to constitute an almost impossible event. However, this calculation does not take into account the large number of relatives in each family who are at risk for such a new mutation. If they are taken into consideration one arrives at opposite conclusions. First, as no data on the size of the 454 genealogies were known to us, we assume a uniform family structure in which each DMD patient and his ancestors have one brother and one sister. These brothers and sisters and their descendants always have (or would have if old enough) 1son and 1daughter. In such a uniform family the proband has 8 first cousins, 32 second cousins and 128 third cousins, altogether 168; of these 160 have a t least one male relative among the family members connecting them with the proband in the pedigree. Eighty of these 160 cousins will be male and are therefore a t risk for a new DMD mutation. Beside these 80 male relatives who are all in the same generation, there also are many males at risk in previous and following generations but for the sake of simplicity, they will be left out of consideration here. Next, the probability that at least one of the 80 male relatives ofa DMD patient is affected with a new mutation is 1 - (1 - 1/10,000)80or 0.008. This probability applies to each of the 454 families, assuming the uniform family structure. Therefore, the chance that at least 4 of 450 DMD families have 2 or more patients with independently arisen mutations is Received for publication February 22, 1991. Address reprint requests t o Dr. Leo ten Kate, Department of Medical Genetics, University of Groningen, Faculty of Medicine, Antonius Deusinglaan 4, 9713 AW Groningen, The Netherlands.
0 1992 Wiley-Liss, Inc.
TABLE I. Probability of Independent Occurrence of Duchenne Muscular Dystrophy in One or More Relatives of a Patient Affected With Duchenne Muscular Dystrophy Number of male relatives
0.0001
0.0002
0.0003
40 60 80 120 160
0.0040 0.0060 0.0080 0.0119 0.0159
0.0080 0.0119 0.0159 0.0237 0.0315
0.01 19 0.0178 0.0237 0.0354 0.0496
Individual risk
TABLE 11. Probability of Finding 4 or More Families With Additional Patients With an Independently Arisen Duchenne Muscular Dystrophy Mutation in 450 Families With Duchenne Muscular Dystrophy Number of male relatives
0.0001
0.0002
0.0003
40 60 80 120 160
0.1078 0.2840 0.4824 0.7847 0.9270
0.4824 0.7847 0.9270 0.9941 0.9996
0.7847 0.9597 0.9941 0.9999 1.oooo
Individual risk
-
3
1-
c
("O)
(0.008)'(1 - 0.008)450-~
r=O
or 0.4824 ( r = number of families with 2 or more DMD patients). Tables I and I1 list probabilities for other values of genealogy size and occurrence risk. It is clear from these data that the case of inheritance of DMD through paternal lines can be dismissed. The occurrence of 4 genealogies with affected patients related through paternal lines among 454 DMD families can very well be explained by chance.
REFERENCE Zatz M, Passos-Bueno R, Rapaport D, Vainzof M (1991): Familial occurrence of Duchenne dystrophy through paternal lines in four families. Am J Med Genet 38:80-84.
Leo P. ten Kate Anthonie J. van Essen Department of Medical Genetics University of Groningen Groningen, The Netherlands
Letter to the Editor Duchenne Muscular Dystrophy Inherited Through Paternal Lines To the Editor: In a survey of 454 families with patients affected with Duchenne muscular dystrophy (DMD)Zatz et al. [1991] found 4 kindreds with 2 or more affected patients who were related through paternal lines. The patients were third cousins in family 1,second cousins once removed in family 2, and first cousins once removed in families 3 and 4. The number of male relatives connecting the cousins in the pedigrees varied from 1(in families 2 and 3) to 5 (in family 1).As the authors calculated the probability of 2 new mutations in a family to be 1110,000 x 1/10,000, they considered the probability for these 4 families by chance among the 454 genealogies with DMD patients so low as to constitute an almost impossible event. However, this calculation does not take into account the large number of relatives in each family who are at risk for such a new mutation. If they are taken into consideration one arrives at opposite conclusions. First, as no data on the size of the 454 genealogies were known to us, we assume a uniform family structure in which each DMD patient and his ancestors have one brother and one sister. These brothers and sisters and their descendants always have (or would have if old enough) 1son and 1daughter. In such a uniform family the proband has 8 first cousins, 32 second cousins and 128 third cousins, altogether 168; of these 160 have a t least one male relative among the family members connecting them with the proband in the pedigree. Eighty of these 160 cousins will be male and are therefore a t risk for a new DMD mutation. Beside these 80 male relatives who are all in the same generation, there also are many males at risk in previous and following generations but for the sake of simplicity, they will be left out of consideration here. Next, the probability that at least one of the 80 male relatives ofa DMD patient is affected with a new mutation is 1 - (1 - 1/10,000)80or 0.008. This probability applies to each of the 454 families, assuming the uniform family structure. Therefore, the chance that at least 4 of 450 DMD families have 2 or more patients with independently arisen mutations is Received for publication February 22, 1991. Address reprint requests t o Dr. Leo ten Kate, Department of Medical Genetics, University of Groningen, Faculty of Medicine, Antonius Deusinglaan 4, 9713 AW Groningen, The Netherlands.
0 1992 Wiley-Liss, Inc.
TABLE I. Probability of Independent Occurrence of Duchenne Muscular Dystrophy in One or More Relatives of a Patient Affected With Duchenne Muscular Dystrophy Number of male relatives
0.0001
0.0002
0.0003
40 60 80 120 160
0.0040 0.0060 0.0080 0.0119 0.0159
0.0080 0.0119 0.0159 0.0237 0.0315
0.01 19 0.0178 0.0237 0.0354 0.0496
Individual risk
TABLE 11. Probability of Finding 4 or More Families With Additional Patients With an Independently Arisen Duchenne Muscular Dystrophy Mutation in 450 Families With Duchenne Muscular Dystrophy Number of male relatives
0.0001
0.0002
0.0003
40 60 80 120 160
0.1078 0.2840 0.4824 0.7847 0.9270
0.4824 0.7847 0.9270 0.9941 0.9996
0.7847 0.9597 0.9941 0.9999 1.oooo
Individual risk
-
3
1-
c
("O)
(0.008)'(1 - 0.008)450-~
r=O
or 0.4824 ( r = number of families with 2 or more DMD patients). Tables I and I1 list probabilities for other values of genealogy size and occurrence risk. It is clear from these data that the case of inheritance of DMD through paternal lines can be dismissed. The occurrence of 4 genealogies with affected patients related through paternal lines among 454 DMD families can very well be explained by chance.
REFERENCE Zatz M, Passos-Bueno R, Rapaport D, Vainzof M (1991): Familial occurrence of Duchenne dystrophy through paternal lines in four families. Am J Med Genet 38:80-84.
Leo P. ten Kate Anthonie J. van Essen Department of Medical Genetics University of Groningen Groningen, The Netherlands
