Hum Genet (1990) 84:116-118
9 Springer-Verlag 1990
Original investigations
Neurofibromatosis-l: a m a x i m u m likelihood estimation of mutation rate Maurizio Clementi 1, Guido Barbujani 2, Licia Turolla 1, and Romano Tenconi 1 1Servizio di Genetica Medica, Dipartimento di Pediatria, Universit~tdi Padova, Via Giustiniani, 3, 1-35128 Padova, Italy 2Dipartimento di Biologia, Universitg di Padova, Via Loredan, 10, 1-35100 Padova, Italy
Summary. Methods of classical segregation analysis were applied to a sample of 129 sibships with one or more individuals affected by neurofibromatosis-1 (NF-1). The sample consists only of subjects with NF-1; all the probands had been referred for genetic counselling because of cafd-au-lait spots, and a diagnostic protocol was invariably applied. No deviation from the segregation ratio expected for a fully penetrant Mendelian dominant gene was observed. A maximum likelihood estimate of the proportion of sporadic cases was obtained, and the mutation rate was estimated to be 6.5 x 10 -5 gametes per generation (95% CI 5.0-8.1).
Introduction Von Recklinghausen peripheral neurofibromatosis (NF-1), one of the most frequent (1/3000-1/5000 inhabitants) (Crowe et al. 1956; Samuelsson and Axelsson 1981; Huson et al. 1988), ubiquitous, clinically relevant, and progressive monogenic disorders in man, is inherited as an autosomal dominant condition with variable expressivity, and complete (100%) penetrance. The NF-1 gene has been mapped to the pericentromeric region of chromosome 17 (Diehl et al. 1989). At least half the index cases are sporadic events, resulting from a new mutation (Riccardi and Eichner 1986), and the mutation rate, estimated by the direct method, is 3-14 per 10 -5 (Crowe et al. 1956; Sergeyev 1975; Samuelsson and Axelsson 1981; Huson et al. 1988). Advanced paternal age has been reported as a risk factor for NF-1 mutation (Sergeyev 1975; Riccardi et al. 1984). By applying the methods of classical segregation analysis (Morton 1959; Morton 1982; Morton et al. 1983), this study tests whether there is deviation from the expected Mendelian segregation rate in a sample of 129 sibships from North East Italy. It was also possible to obtain a maximum likelihood estimate of the proportion of sporadic cases, and hence an estimation of the mutation rate. The present study is the first application of such an approach to the study of NF-1 genetics.
(CLS). These families live in two adiacent regions in North East Italy (Veneto and Friuli-Venezia Giulia), and the average age of the probands was 8.5 + 5.8 (range 0.2-40) years (Table 1). A complete family history, including the pedigree of at least three generations, was taken for each family; the proband and all available first-degree relatives of affected subjects underwent an extensive physical examination (including body measurements and blood pressure), and a slit-lamp examination. A diagnosis of NF-1 was formulated when one of the following minimal criteria were met: 6 or more cutaneous CLS with a diameter greater than 1.5 cm (0.5cm in children under 10 years), or multiple neurofibromas in different areas of the body, or multiple iris hamartomata (Lisch nodules) in a first-degree relative of an affected subject. Our study protocol, consisting of a 24-h urinary catecholamine determination, complete ophthalmologic and audiometric examinations, audiography, ECG, EEG, cranial CT scan, and X-ray survey of skull and spine, was applied in all probands; not all the tests were carried out on some affected relatives. The total number of affected individuals studied was 202.
Segregation analysis The segregation of NF-1 cases has been studied according to the classical segregation analysis methods based on the maximum likelihood principle (Morton 1959; Morton 1982; Morton et al. 1983), which allows the estimation of segregation frequency, p, and the frequency of sporadic cases, x. A third parameter, ~, the probability of ascertainment, accounts for the effects of incomplete sampling of affected individuals. These principles have also been used to test the fit of a set of p-, x- and Jr-values to the distribution of the affected individuals among the members of the relevant sibships. All families are ascertained through the affected offspring. Therefore, non-segregating families, in which one parent is
Table 1. Age of probands grouped as familial or sporadic cases and of their parents
Materials and methods
Proband
Males
Females
Average agea Probands
Fathers
Average difference of Mothers parentalagea
7.7 (5.5) 9.3 (6.1)
31.3 (5.0) 33.1 (6.8)
27.0 4.3 ( 4 . 8 ) (3.7) 28.7 4.4 ( 6 . 8 ) (4.0)
Sample One hundred and twenty-nine families with 137 probands (69 males) were referred to our genetic counselling service because at least one family member presented caf6-au-lait spots
Offprint requests to: R. Tenconi
Familial
30
26
Sporadic
25
29
a Years (standard deviation)
117 Table 2. Distribution of probands (a) among affected sibship members (r) r
a
1
2
3
1 2 3
: : :
87 7 0
6 2
0
Table 3. Distribution of affected individuals (r) among sibship members (s). Families with two or more affected individuals s
r
1
2
1 2 3 4 5
: : : : :
15 17 0 1 0
10 2 0 1
All families 3
0 1 1
s i 2 3 4 5 6
r
1
2
3
: :
24 41 13 6 1 2
10 2 0 1 0
0 1 1 0
a carrier without affected offspring, will escape sampling; hence, our segregation analysis refers to an incomplete selection (Morton 1959; Crow 1965). The estimation of (1) n, (2) zr and p simultaneously, and (3) ~r, p and x simultaneously (Morton 1959; Morton et al. 1983) is based on the distribution of probands, i.e. independently ascertained individuals among affected sibship members (a x r Table), and affected individuals among all sibship members (r x s Table). In this study, the probability of ascertainment was initially estimated on the a x r Table, referring to the whole sample (Table 2). Assuming a Mendelian dominant inheritance Qr= iv estimated; p =0.5; x = 0), we attempted to fit a simple model to a sub-sample consisting only of families with 2 or more affected members (Table 3), and where no sporadic case would be expected. In the absence of evidence of distotted segregation, the maximum likelihood estimation of p was not attempted; p = 0.5 is the expected value for a fully penetrant dominant Mendelian gene. Finally, the overall frequency of sporadic cases was estimated on the basis of the whole sample of sibships (Table 3), (~r= n estimated; p = 0.5; x = x estimated). The estimation strategy was as follows. For each parameter, say 0, two statistics are calculated, i.e. the score, UO, and the amount of information, KO0. The square root of the inverse of the information is the standard error of the estimate (Morton 1959). The UOe/KO0ratio is distributed as a chi-square with one degree of freedom, and this allows the goodness of the fit of that parameter to be tested. The estimate of each parameter was modified in successive approximation steps to the lowest ehisquare value, thus reaching the maximum likelihood.
Investigation of parental age effect The age of the parents of each proband was investigated without seeking the apparent first instance of NF-1 in each family, because family members did not adequately recall the parental phenotype, and our probands were homogeneous in ascertainment. The probands were grouped together as sporadic or familial cases, and the t-test was used to compare the average ages of fathers and mothers, and the average difference in age between the parents when the proband was born (Table 1).
We compared the average age between the parents of familial and sporadic probands, because the number of the latter is small (n = 54) and they were born over a long timespan (19441987). A comparison with the paternal age of the general population was not feasible because the regional data were only available for the period 1981-1988, whereas most of our probands (87/110) were born before this interval; moreover, the national statistics for paternal age significantly differ ( P < 10-6) from our regional data in the years in which both figures are available.
NF-1 incidence The incidence of NF-1 in North East Italy was estimated using the data in this study and that based on regional statistics in the hospitals. Since computerised recording of this diagnosis was initiated in 1980 in three contiguous provinces (including Padova) in this region, and updating is complete until 1986, we limited our study to this geographical area and to this period of time. All the regional data were checked to exclude miscoding and to identify multiple records of the same patient. The patients who were included in our study but not in the regional data, and who were living in this area during this period of time, have been added to the regional figures. As a denominator, data of the 1981 census were used, for a total of 2375304 inhabitants. The total sample (termed Incidence Sample) and the denominator have been subsequently divided into age sub-groups, each of 10 years, and the incidence has been estimated for each age interval. Results
In 102 out of 129 families, the proband's parents mad sibs were completely examined, and segregation analysis was performed (termed Segregation Sample). Of the probands, 54 were sporadic cases with normal parents and sibs, whereas 56 were familial with no significant difference in the sex of the affected parent (20 affected fathers with 24 affected probands; 28 affected mothers with 32 affected probands). As for all isolated cases, those that are sporadic are not relevant to the evaluation of ~; consequently, the maximum likelihood zc value estimated in this study (0.632+ 0.112) (Table 4, line 1) refers to both the whole sample and the sub-sample of familial cases. The simple Mendelian hypothesis (p--0.5, x =0) was tested on the latter sub-sample (Table 4, lines 2-6). All chisquares were very low, providing no evidence for segregation distortion or occurrence of additional sporadic cases. The estimated value of zc showed a good fit when checked against the r x s Table (Table 4, lines 2 and 4).When the whole sample was considered, the maximum likelihood of x was achieved in successive steps of the analysis at the value of 0.563 ___0.090 (Table 4, lines 7-9). The estimated incidence of NF-1 was 1.49 per 10000 inhabitants in the total sample, with large differences between different age-groups (0-9 years = 2.33; 10-19 years = 1.59; 20-29 years = 1.45; 30-39 years = 1.53; 40-49 years = 1.56; 50-59 years = 0.87; > 60 years = 1.10). We consider the highest incidence estimate of 1:4292 inhabitants (2.33 per 10000; 95% CI 1.79-2.87) in the age class of 0-9 years as the most reliable because of ascertainment bias in the regional data. Indeed, almost all the affected individuals are referred to a hospital for diagnosis within the first decade of life, and most of them do not need further hospital admission. Therefore, we obtain the best estimate of incidence in the first age class.
118 Table 4. Fit of the parameters n, p and x to the distribution of probands among affected individuals and of affected individuals among all sibship members. U, Scores; K, information; L, log likelihood Parameter (0)
Fitted value
Equation no.
UO
KO0
Z2
n
0.632
22
0.000
79.586
0.000
-17.557
0.632 0.500
30 a 30 a
0.267 -3.875
0.271 36.485
0.263 0.412
-3.540
p n p x
0.632 0.500 0.000
20 a 20 a 20 a
0.441 -2.299 0.192
p x
0.632 0.500 0.563
20 20 20
0.000 1.738 0.050
L
4.331 0.045 140.941 0.038 106.526 0.000
-20.798
7.968 54.028 123.016
-38.547
0.000 0.056 0.000
a Only familial cases are considered
The Incidence Sample probably includes only part of the previously diagnosed NF-1 patients in the studied period (19811986), but almost all the new cases aged 0-9 years. Furthermore, in this most reliable age-class and in the area where inhabitants are referred to us for genetic counselling (three contiguous provinces), the Segregation Sample/Incidence Sample ratio is 0.606 (43/71); this figure is very close to the theoretical value of ascertainment probability Qr= 0.632 _+0.112), which we independently estimated from the distribution of the probands among affected individuals. The spontaneous mutation rate was 6.5 x 10 -5 gametes per generation, with a 95% confidence interval ranging from 5.0 to 8.1. The estimation was obtained by the semi-direct method (Morton 1982), which assumes complete gene penetrance. Sporadic and familial cases showed no significant difference in average ages of fathers and mothers, nor in the average difference between parents' age (Table 1). Moreover, age distribution of fathers and mothers in the two groups did not significantly differ (chi-square test). Discussion No deviation from the segregation ratio expected for a fully penetrant Mendelian dominant gene was observed in this study of NF-1 in North East Italy. A l t h o u g h NF-1 is one of the most c o m m o n autosomal d o m i n a n t diseases with 100% penetrance, as this study confirms, its mutation rate is still uncertain. Indeed, using the direct method, mutation rates of 3.1 (Huson et al. 1988), 4.3 (Samuelsson and Axelsson 1981), 4.4 (Sergeyev 1975) and 14 (Crowe et al. 1956) per 10 5 gametes per generation have b e e n reported over the years. The mutation rate is calculated from the proportion of sporadic cases and the frequency of the disease. A n ascertainment bias or incorrect anamnestic data leads to over- or under-estimation of one or both of these figures. Crowe et al. (1956) probably over-estimated the NF-1 prevalence because their sample was genetically heterogeneous, as it included different forms of N F (Riccardi and Eichner 1986). Conversely, in Sergeyev's study (1975), the NF-1 prevalence is probably underestimated because of the selection of affected subjects (CLS in 16-year-old males at pre-military examination); the fraction of sporadic cases is probably over-estimated because of the low n u m b e r of cases with complete family history or physical ex-
amination of both parents. As Huson noted, her figures are probably an under-estimate because children who carried fresh mutations and had no major complications were under-ascertained (Huson et al. 1988). Finally, Samuelsson and Axelsson (1981) found a large difference in the NF-1 prevalence related to age; in the population studied, the highest rate occurred in the 40-50 years age-group, (1/3000), where the mutation rate was 6.5 per 10 -5. As a consequence, although the estimated mutation rates in the three last mentioned studies are close, the fraction of sporadic cases ( 4 0 - 4 4 % ; 5 4 - 5 8 % ; 77%) and the estimated NF-1 prevalence (1:4600; 1:4949; 1:7800) are significantly different. The estimated value in our study of 6.5 per 10 -5 gametes per generation (95% CI 5.0-8.1) is within the fringe values reported in literature. Methodological inconsistencies are unlikely to have affected the results of the present study. Our sample is homogeneous, consisting only of subjects with NF-1. All the probands had been referred because of CLS, and a diagnosis protocol was invariably applied. Families, from which a history or parental physical examination could not be obtained, were excluded from this study. NF-1 incidence may have been under-estimated because fresh mutations with minor expressivity, if any, are likely to escape ascertainment; however, our estimate is very close that of Huson et al. (1988) and Samuelsson and Axelsson (1981). Segregation analysis is thus a useful means for evaluating genetic mechanisms of this monogenic disorder; it also enables a precise estimation of n, p, and x, to be made using the maximum likelihood method. Our investigation into parental age did not disclose any significant difference; thus, we were unable to detect any effect of parental age on the NF-1 mutation rate, as reported by Sergeyev (1975) and Riccardi et al. (1984). References Crow JF (1965) Problems in ascertainment in the analysis of family data. In: Neel JV, Shaw MW, Chull WJ (eds) Genetics and epidemiology of chronic diseases. US Department of Health, Education and Welfare, Washington, DC Crowe FW, Schull WJ, Neel JV (1956) A clinical, pathological and genetic study of multiple neurofibromatosis. Thomas, Springfield, Ill Diehl SR, Boehuke M, Erickson RP, Ploughman LM, Seiler KA, Lieberman JL, Clarke HB, Bruce MA, Schorry EK, PericakVance M, O'Connel P, Collins FS (1989) A refined genetic map of the region of chromosome 17 surrounding the von Recklinghausen neurofibromatosis (NF1) gene. Am J Hum Genet 44 : 33-37 Huson SM, Harper PS, Compston DAS (1988) Von Recklinghausen neurofibromatosis: a clinical and population study in South East Wales. Brain 111 : 1355-1381 Morton NE (1959) Genetic tests under incomplete ascertainment. Am J Hum Genet 11 : 1-16 Morton NE (1982) Outline of genetic epidemiology. Karger, Basel Morton NE, Rao DC, Lalouel JM (1983) Methods in genetic epidemiology. Karger, Basel, pp 62-102 Riccardi VM, Eichner JE (1986) Neurofibromatosis. Phenotype, natural history, and pathogenesis. Johns Hopkins University Press, Baltimore Riccardi VM, Dubson I I C E , Chakraborty R, Bontke C (1984) The pathophysiology of neurofibromatosis. IX. Paternal age as a factor in the origin of new mutation. Am J Med Genet 18 : 169-176 Sanmelsson B, Axelsson R (1981) Neurofibromatosis. Acta Derm Venereol (Stockh) 95 [Suppl] : 67-71 Sergeyev AS (1975) On the mutation rate of neurofibromatosis. Humangenetik 28:129-139 Received November 28, 1988 / Revised July 10, 1989
9 Springer-Verlag 1990
Original investigations
Neurofibromatosis-l: a m a x i m u m likelihood estimation of mutation rate Maurizio Clementi 1, Guido Barbujani 2, Licia Turolla 1, and Romano Tenconi 1 1Servizio di Genetica Medica, Dipartimento di Pediatria, Universit~tdi Padova, Via Giustiniani, 3, 1-35128 Padova, Italy 2Dipartimento di Biologia, Universitg di Padova, Via Loredan, 10, 1-35100 Padova, Italy
Summary. Methods of classical segregation analysis were applied to a sample of 129 sibships with one or more individuals affected by neurofibromatosis-1 (NF-1). The sample consists only of subjects with NF-1; all the probands had been referred for genetic counselling because of cafd-au-lait spots, and a diagnostic protocol was invariably applied. No deviation from the segregation ratio expected for a fully penetrant Mendelian dominant gene was observed. A maximum likelihood estimate of the proportion of sporadic cases was obtained, and the mutation rate was estimated to be 6.5 x 10 -5 gametes per generation (95% CI 5.0-8.1).
Introduction Von Recklinghausen peripheral neurofibromatosis (NF-1), one of the most frequent (1/3000-1/5000 inhabitants) (Crowe et al. 1956; Samuelsson and Axelsson 1981; Huson et al. 1988), ubiquitous, clinically relevant, and progressive monogenic disorders in man, is inherited as an autosomal dominant condition with variable expressivity, and complete (100%) penetrance. The NF-1 gene has been mapped to the pericentromeric region of chromosome 17 (Diehl et al. 1989). At least half the index cases are sporadic events, resulting from a new mutation (Riccardi and Eichner 1986), and the mutation rate, estimated by the direct method, is 3-14 per 10 -5 (Crowe et al. 1956; Sergeyev 1975; Samuelsson and Axelsson 1981; Huson et al. 1988). Advanced paternal age has been reported as a risk factor for NF-1 mutation (Sergeyev 1975; Riccardi et al. 1984). By applying the methods of classical segregation analysis (Morton 1959; Morton 1982; Morton et al. 1983), this study tests whether there is deviation from the expected Mendelian segregation rate in a sample of 129 sibships from North East Italy. It was also possible to obtain a maximum likelihood estimate of the proportion of sporadic cases, and hence an estimation of the mutation rate. The present study is the first application of such an approach to the study of NF-1 genetics.
(CLS). These families live in two adiacent regions in North East Italy (Veneto and Friuli-Venezia Giulia), and the average age of the probands was 8.5 + 5.8 (range 0.2-40) years (Table 1). A complete family history, including the pedigree of at least three generations, was taken for each family; the proband and all available first-degree relatives of affected subjects underwent an extensive physical examination (including body measurements and blood pressure), and a slit-lamp examination. A diagnosis of NF-1 was formulated when one of the following minimal criteria were met: 6 or more cutaneous CLS with a diameter greater than 1.5 cm (0.5cm in children under 10 years), or multiple neurofibromas in different areas of the body, or multiple iris hamartomata (Lisch nodules) in a first-degree relative of an affected subject. Our study protocol, consisting of a 24-h urinary catecholamine determination, complete ophthalmologic and audiometric examinations, audiography, ECG, EEG, cranial CT scan, and X-ray survey of skull and spine, was applied in all probands; not all the tests were carried out on some affected relatives. The total number of affected individuals studied was 202.
Segregation analysis The segregation of NF-1 cases has been studied according to the classical segregation analysis methods based on the maximum likelihood principle (Morton 1959; Morton 1982; Morton et al. 1983), which allows the estimation of segregation frequency, p, and the frequency of sporadic cases, x. A third parameter, ~, the probability of ascertainment, accounts for the effects of incomplete sampling of affected individuals. These principles have also been used to test the fit of a set of p-, x- and Jr-values to the distribution of the affected individuals among the members of the relevant sibships. All families are ascertained through the affected offspring. Therefore, non-segregating families, in which one parent is
Table 1. Age of probands grouped as familial or sporadic cases and of their parents
Materials and methods
Proband
Males
Females
Average agea Probands
Fathers
Average difference of Mothers parentalagea
7.7 (5.5) 9.3 (6.1)
31.3 (5.0) 33.1 (6.8)
27.0 4.3 ( 4 . 8 ) (3.7) 28.7 4.4 ( 6 . 8 ) (4.0)
Sample One hundred and twenty-nine families with 137 probands (69 males) were referred to our genetic counselling service because at least one family member presented caf6-au-lait spots
Offprint requests to: R. Tenconi
Familial
30
26
Sporadic
25
29
a Years (standard deviation)
117 Table 2. Distribution of probands (a) among affected sibship members (r) r
a
1
2
3
1 2 3
: : :
87 7 0
6 2
0
Table 3. Distribution of affected individuals (r) among sibship members (s). Families with two or more affected individuals s
r
1
2
1 2 3 4 5
: : : : :
15 17 0 1 0
10 2 0 1
All families 3
0 1 1
s i 2 3 4 5 6
r
1
2
3
: :
24 41 13 6 1 2
10 2 0 1 0
0 1 1 0
a carrier without affected offspring, will escape sampling; hence, our segregation analysis refers to an incomplete selection (Morton 1959; Crow 1965). The estimation of (1) n, (2) zr and p simultaneously, and (3) ~r, p and x simultaneously (Morton 1959; Morton et al. 1983) is based on the distribution of probands, i.e. independently ascertained individuals among affected sibship members (a x r Table), and affected individuals among all sibship members (r x s Table). In this study, the probability of ascertainment was initially estimated on the a x r Table, referring to the whole sample (Table 2). Assuming a Mendelian dominant inheritance Qr= iv estimated; p =0.5; x = 0), we attempted to fit a simple model to a sub-sample consisting only of families with 2 or more affected members (Table 3), and where no sporadic case would be expected. In the absence of evidence of distotted segregation, the maximum likelihood estimation of p was not attempted; p = 0.5 is the expected value for a fully penetrant dominant Mendelian gene. Finally, the overall frequency of sporadic cases was estimated on the basis of the whole sample of sibships (Table 3), (~r= n estimated; p = 0.5; x = x estimated). The estimation strategy was as follows. For each parameter, say 0, two statistics are calculated, i.e. the score, UO, and the amount of information, KO0. The square root of the inverse of the information is the standard error of the estimate (Morton 1959). The UOe/KO0ratio is distributed as a chi-square with one degree of freedom, and this allows the goodness of the fit of that parameter to be tested. The estimate of each parameter was modified in successive approximation steps to the lowest ehisquare value, thus reaching the maximum likelihood.
Investigation of parental age effect The age of the parents of each proband was investigated without seeking the apparent first instance of NF-1 in each family, because family members did not adequately recall the parental phenotype, and our probands were homogeneous in ascertainment. The probands were grouped together as sporadic or familial cases, and the t-test was used to compare the average ages of fathers and mothers, and the average difference in age between the parents when the proband was born (Table 1).
We compared the average age between the parents of familial and sporadic probands, because the number of the latter is small (n = 54) and they were born over a long timespan (19441987). A comparison with the paternal age of the general population was not feasible because the regional data were only available for the period 1981-1988, whereas most of our probands (87/110) were born before this interval; moreover, the national statistics for paternal age significantly differ ( P < 10-6) from our regional data in the years in which both figures are available.
NF-1 incidence The incidence of NF-1 in North East Italy was estimated using the data in this study and that based on regional statistics in the hospitals. Since computerised recording of this diagnosis was initiated in 1980 in three contiguous provinces (including Padova) in this region, and updating is complete until 1986, we limited our study to this geographical area and to this period of time. All the regional data were checked to exclude miscoding and to identify multiple records of the same patient. The patients who were included in our study but not in the regional data, and who were living in this area during this period of time, have been added to the regional figures. As a denominator, data of the 1981 census were used, for a total of 2375304 inhabitants. The total sample (termed Incidence Sample) and the denominator have been subsequently divided into age sub-groups, each of 10 years, and the incidence has been estimated for each age interval. Results
In 102 out of 129 families, the proband's parents mad sibs were completely examined, and segregation analysis was performed (termed Segregation Sample). Of the probands, 54 were sporadic cases with normal parents and sibs, whereas 56 were familial with no significant difference in the sex of the affected parent (20 affected fathers with 24 affected probands; 28 affected mothers with 32 affected probands). As for all isolated cases, those that are sporadic are not relevant to the evaluation of ~; consequently, the maximum likelihood zc value estimated in this study (0.632+ 0.112) (Table 4, line 1) refers to both the whole sample and the sub-sample of familial cases. The simple Mendelian hypothesis (p--0.5, x =0) was tested on the latter sub-sample (Table 4, lines 2-6). All chisquares were very low, providing no evidence for segregation distortion or occurrence of additional sporadic cases. The estimated value of zc showed a good fit when checked against the r x s Table (Table 4, lines 2 and 4).When the whole sample was considered, the maximum likelihood of x was achieved in successive steps of the analysis at the value of 0.563 ___0.090 (Table 4, lines 7-9). The estimated incidence of NF-1 was 1.49 per 10000 inhabitants in the total sample, with large differences between different age-groups (0-9 years = 2.33; 10-19 years = 1.59; 20-29 years = 1.45; 30-39 years = 1.53; 40-49 years = 1.56; 50-59 years = 0.87; > 60 years = 1.10). We consider the highest incidence estimate of 1:4292 inhabitants (2.33 per 10000; 95% CI 1.79-2.87) in the age class of 0-9 years as the most reliable because of ascertainment bias in the regional data. Indeed, almost all the affected individuals are referred to a hospital for diagnosis within the first decade of life, and most of them do not need further hospital admission. Therefore, we obtain the best estimate of incidence in the first age class.
118 Table 4. Fit of the parameters n, p and x to the distribution of probands among affected individuals and of affected individuals among all sibship members. U, Scores; K, information; L, log likelihood Parameter (0)
Fitted value
Equation no.
UO
KO0
Z2
n
0.632
22
0.000
79.586
0.000
-17.557
0.632 0.500
30 a 30 a
0.267 -3.875
0.271 36.485
0.263 0.412
-3.540
p n p x
0.632 0.500 0.000
20 a 20 a 20 a
0.441 -2.299 0.192
p x
0.632 0.500 0.563
20 20 20
0.000 1.738 0.050
L
4.331 0.045 140.941 0.038 106.526 0.000
-20.798
7.968 54.028 123.016
-38.547
0.000 0.056 0.000
a Only familial cases are considered
The Incidence Sample probably includes only part of the previously diagnosed NF-1 patients in the studied period (19811986), but almost all the new cases aged 0-9 years. Furthermore, in this most reliable age-class and in the area where inhabitants are referred to us for genetic counselling (three contiguous provinces), the Segregation Sample/Incidence Sample ratio is 0.606 (43/71); this figure is very close to the theoretical value of ascertainment probability Qr= 0.632 _+0.112), which we independently estimated from the distribution of the probands among affected individuals. The spontaneous mutation rate was 6.5 x 10 -5 gametes per generation, with a 95% confidence interval ranging from 5.0 to 8.1. The estimation was obtained by the semi-direct method (Morton 1982), which assumes complete gene penetrance. Sporadic and familial cases showed no significant difference in average ages of fathers and mothers, nor in the average difference between parents' age (Table 1). Moreover, age distribution of fathers and mothers in the two groups did not significantly differ (chi-square test). Discussion No deviation from the segregation ratio expected for a fully penetrant Mendelian dominant gene was observed in this study of NF-1 in North East Italy. A l t h o u g h NF-1 is one of the most c o m m o n autosomal d o m i n a n t diseases with 100% penetrance, as this study confirms, its mutation rate is still uncertain. Indeed, using the direct method, mutation rates of 3.1 (Huson et al. 1988), 4.3 (Samuelsson and Axelsson 1981), 4.4 (Sergeyev 1975) and 14 (Crowe et al. 1956) per 10 5 gametes per generation have b e e n reported over the years. The mutation rate is calculated from the proportion of sporadic cases and the frequency of the disease. A n ascertainment bias or incorrect anamnestic data leads to over- or under-estimation of one or both of these figures. Crowe et al. (1956) probably over-estimated the NF-1 prevalence because their sample was genetically heterogeneous, as it included different forms of N F (Riccardi and Eichner 1986). Conversely, in Sergeyev's study (1975), the NF-1 prevalence is probably underestimated because of the selection of affected subjects (CLS in 16-year-old males at pre-military examination); the fraction of sporadic cases is probably over-estimated because of the low n u m b e r of cases with complete family history or physical ex-
amination of both parents. As Huson noted, her figures are probably an under-estimate because children who carried fresh mutations and had no major complications were under-ascertained (Huson et al. 1988). Finally, Samuelsson and Axelsson (1981) found a large difference in the NF-1 prevalence related to age; in the population studied, the highest rate occurred in the 40-50 years age-group, (1/3000), where the mutation rate was 6.5 per 10 -5. As a consequence, although the estimated mutation rates in the three last mentioned studies are close, the fraction of sporadic cases ( 4 0 - 4 4 % ; 5 4 - 5 8 % ; 77%) and the estimated NF-1 prevalence (1:4600; 1:4949; 1:7800) are significantly different. The estimated value in our study of 6.5 per 10 -5 gametes per generation (95% CI 5.0-8.1) is within the fringe values reported in literature. Methodological inconsistencies are unlikely to have affected the results of the present study. Our sample is homogeneous, consisting only of subjects with NF-1. All the probands had been referred because of CLS, and a diagnosis protocol was invariably applied. Families, from which a history or parental physical examination could not be obtained, were excluded from this study. NF-1 incidence may have been under-estimated because fresh mutations with minor expressivity, if any, are likely to escape ascertainment; however, our estimate is very close that of Huson et al. (1988) and Samuelsson and Axelsson (1981). Segregation analysis is thus a useful means for evaluating genetic mechanisms of this monogenic disorder; it also enables a precise estimation of n, p, and x, to be made using the maximum likelihood method. Our investigation into parental age did not disclose any significant difference; thus, we were unable to detect any effect of parental age on the NF-1 mutation rate, as reported by Sergeyev (1975) and Riccardi et al. (1984). References Crow JF (1965) Problems in ascertainment in the analysis of family data. In: Neel JV, Shaw MW, Chull WJ (eds) Genetics and epidemiology of chronic diseases. US Department of Health, Education and Welfare, Washington, DC Crowe FW, Schull WJ, Neel JV (1956) A clinical, pathological and genetic study of multiple neurofibromatosis. Thomas, Springfield, Ill Diehl SR, Boehuke M, Erickson RP, Ploughman LM, Seiler KA, Lieberman JL, Clarke HB, Bruce MA, Schorry EK, PericakVance M, O'Connel P, Collins FS (1989) A refined genetic map of the region of chromosome 17 surrounding the von Recklinghausen neurofibromatosis (NF1) gene. Am J Hum Genet 44 : 33-37 Huson SM, Harper PS, Compston DAS (1988) Von Recklinghausen neurofibromatosis: a clinical and population study in South East Wales. Brain 111 : 1355-1381 Morton NE (1959) Genetic tests under incomplete ascertainment. Am J Hum Genet 11 : 1-16 Morton NE (1982) Outline of genetic epidemiology. Karger, Basel Morton NE, Rao DC, Lalouel JM (1983) Methods in genetic epidemiology. Karger, Basel, pp 62-102 Riccardi VM, Eichner JE (1986) Neurofibromatosis. Phenotype, natural history, and pathogenesis. Johns Hopkins University Press, Baltimore Riccardi VM, Dubson I I C E , Chakraborty R, Bontke C (1984) The pathophysiology of neurofibromatosis. IX. Paternal age as a factor in the origin of new mutation. Am J Med Genet 18 : 169-176 Sanmelsson B, Axelsson R (1981) Neurofibromatosis. Acta Derm Venereol (Stockh) 95 [Suppl] : 67-71 Sergeyev AS (1975) On the mutation rate of neurofibromatosis. Humangenetik 28:129-139 Received November 28, 1988 / Revised July 10, 1989
