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Modelling allele dynamicsTABLE 12 Risk of expansion from PM to FM in affected families: results from four studiesStudy Mothers with PM Offspring with her mutation Excluding probandsNo. Repeat size No. No. with FM (%) No. No. with FM (%)USA,Texas 32 50–113 63 44 (70) – –Fu et al, 1991France 102 55–205 175 145 (83) 131 101 (77)Heitz et al, 1992Finland 66 60–130+ 122 92 (75) 79 49 (62)Väisänen et al, 1994USA, NY 110 50–130+ – – 184 119 (65)Fisch et al, 1995All 310 50–205 360 281 (78) 447 269 (60)40Risk of expansion accordingto PM sizeThe risk of expansion to the FM is correlated withthe size of the PM allele of the carrier mother. Thelarger the repeat size of PM, the greater the riskof expansion to an FM. There also appears to bea threshold PM size at which expansion to FMalways occurs. This is shown in Table 13, basedTABLE 13 Risk of expansion to FM according to PM size inaffected families: results from four studiesPM sizein motherStudyUSA, France Finland USA,Texas Heitz Väisänen NewFu et al, et al, et al, York1991 1992 1994 Fischet al,1995}50–550%20%55–6010%60–70 } 17% } } 46% } 17%70–80} 48% } 39%77% 56%80–90}} 92% } 76%90–100}}} 89%100–10590% } 91%100%}105–110100%110–115115–120 100% 100%120–130> 130}}}}on the four studies of expansion risks in affectedfamilies shown in Table 12.The studies report risks for groups of mothersand, since the groupings do not coincide betweenthe studies, it is difficult to combine the data.However, we have performed a meta-analysis andlogistic regression analysis of risk on size usingthe combined results, assuming that the risk forthe group applies at its mid-point. In addition, wewere able to compare the effect of ascertainmentbias by analysing data according to whether theproband was included or excluded. The valuespredicted from the regression equations are shownin Table 14 and appear to be close to the observedrisks. The equations are given in a footnote to thetable. The effect of excluding the proband fromthe analysis can be seen in Figure 7.Risk of expansion in thegeneral populationThe risk of expansion from PM to FM is likely tobe lower in the general population compared withthat observed in families with fragile X syndrome.There are two reasons for expecting this. First, inaffected families the distribution of PMs must, ofnecessity, be shifted towards greater repeat sizes:which is why the proband presented. Second, fora given size it is possible that in affected familiesthe risk of expansion from PM to FM is greaterthan in others due to some unknown factor. It isbelieved that, in the general population, silent PMsmay take several generations to expand to the FM(Richards et al, 1992; Chakravarti, 1992; Morton &Macpherson, 1992; Oudet et al, 1993a), and a PMthat took three generations to expand has actuallybeen observed (Brown et al, 1993). There are nopublished studies reporting the expansion risk in
Health Technology Assessment 1997; Vol. 1: No. 4TABLE 14 Logistic regression analysis * to predict the expansionrisk from the PM sizePM size Risk (%)in motherNumber Observed Predicted(confidenceinterval)With proband60 22 18 23 (6–57)65 32 41 34 (11–70)75 41 56 62 (27–88)80 22 68 74 (40–93)85 42 88 84 (54–96)95 21 100 95 (79–99)100 69 93 97 (87–100)105 23 100 99 (92–100)Excluding proband55 5 20 9 (5–16)60 20 10 15 (9–25)65 45 27 23 (14–36)75 60 38 46 (31–61)80 16 56 59 (43–73)85 51 78 71 (56–82)95 40 90 87 (79–93)100 50 90 92 (86–96)105 20 95 95 (91–97)* Based on studies in Table 13, the regression formulae wererisk = 100%/(1 + 2963 x 0.8933 size ) for studies with theproband, and risk = 100% / (1 + 3080 x 0.9004 size ) forthose where the proband was excluded.the general population but indirect estimates canbe made.From PM size distributionOne indirect approach is to estimate the expectedexpansion risk for the known PM size distributionin the general population. Applying the regressioncurves from Figure 7 to the PM size frequencydistribution in Figure 6 yields an average expansionrisk of between 27% and 37%, less than half the60–78% risk seen in affected families (see Table12). However, even this lower rate is too great tobe consistent with the PM and FM populationfrequency. Thus, if one in 273 women has a PMallele (see Table 11) which is passed on to halfher children, and in 27–37% of cases it expands,the FM frequency would be between 1 in 2000and 1 in 1500 (27% and 37% multiplied by halfof 1 in 273), even discounting the FM childrenborn to women who have an FM allele. This is atvariance with the observed frequency of 1 in 4000.Thus, either one of the frequency estimates iswrong, or the curve in Figure 7 only applies toaffected families, or there is a tendency for thenormal X chromosome to be transmitted to theconceptus rather than the mutated one. Thereis some evidence to support the latter from asegregation ratio of 30:51 observed in a prospectivestudy, although this could be a chance findingin a relatively small series (Sherman et al, 1994).Working backwardsAnother indirect way of estimating the generalpopulation risk is to work backwards from the FM100Expansion risk (%)90With proband807060Excludingproband5040302010050 55 60 65 70 75 80 85 90 95 100 105 110PM sizeFIGURE 7 Risk of expansion from PM to FM in one female generation41
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