Chromosome Abnormalities and Genetic Counseling , 3rd Edition

3. Deriving and Using a Risk Figure

Risk is a central concept in genetic counseling. By risk we mean the probability that a particular event will happen. Probability is conventionally measured with a number ranging from zero to 1. A probability (P) of zero means never, and a probability of 1 means always. For two or more mutually exclusive possible outcomes, the individual probabilities sum to 1.0 (or 100%). Thus, someone who is a heterozygote for a particular rearrangement might, in any given pregnancy, have a probability of 0.1 (10%) of having an abnormal child and a probability of 0.9 (90%) of having a normal child. We may speak in terms of risks of recurrence or of occurrence: the probability that an event will happen again, or that it will happen for the first time. Risk can also be presented as odds: the ratio of two mutually exclusive probabilities. The odds for the preceding hypothetical heterozygote would be 9:1 in favor of a normal child.

The word risk has two important meanings in the English language. First, there is the scientific sense of probability that we already discussed. Second, as most people use the word, it conveys a sense of exposure to danger. Our hypothetical heterozygote runs the risk that an unfortunate outcome may occur (an abnormal child, or an abnormal result at prenatal diagnosis). In the genetic counseling clinic these meanings of risk coalesce in some ways, to which the counselor needs to be sensitive. We might instead use such everyday words as chance or likelihood, which have no negative connotation, to refer to the fortunate outcome of normality. The words fortunate and unfortunate are also chosen deliberately: the wanted or the unwanted event will occur entirely by chance, analogous to tossing a coin, throwing a dice, or being dealt a card.

Different Types of Risk Figure

Geneticists arrive at risk figures in a number of ways (Harper, 1998), two of which have particular application to cytogenetics.

1. Mendelian risks. If a clear model of inheritance is known, risk figures derived by reference to that theory may be used. In practice, only Mendel's law of segregation is applied in this context. When a pair of homologous chromosomes segregate at meiosis, it is a random matter which chromosome enters the gamete that will produce the conceptus. Each has an equal chance—a probability of 0.5. As an example, the X chromosomes in the fragile X heterozygote, the normal X and the fragile X, display 1:1 segregation. This is assumed to be a true risk, not an estimate: it is 0.5 exactly.

2. Empiric risks. In the great majority of chromosomal situations, no clear theory exists from which the risk can be derived, and one must observe what has happened previously in (as far as one can judge) the same situation in other families, and make an extrapolation to the family in question. Empiric risks thus appeal to experience, and they only estimate the intrinsic, true, probability. The data may be available in the literature record, or in specific databases; or, the counselor may need to derive a “private estimate” from an analysis of the client's family. The risk estimate has a greater or lesser degree of precision, depending on how much data have been accumulated upon which the estimate is based.

Consider, for example, the common situation of a young couple having had a child with Down syndrome. Nothing is known about nondisjunction that could provide a theoretical model on which to base a recurrence risk figure. We therefore use information obtained from surveying large numbers of other such families. It may be observed, for example, that in these families about 1 pregnancy in 100, subsequent to the index case of Down syndrome, produced another child with Down syndrome. Formally expressed, this is a segregation analysis. From this rate of 1/100 we can derive a risk figure of 1%, which we then have as the basis for advising patients. (Actually, it is not quite as straightforward as this in Down syndrome; see Chapter 16). Likewise for the circumstance of the parent heterozygous for a chromosomal rearrangement, the counselor can consult data that have been accumulated by workers in the field, foremost among whom, with respect to reciprocal translocations, are Stengel-Rutkowski et al. (1988) and Cohen et al. (1992, 1994). Since almost all reciprocal translocations are unique to one family, it is not necessarily simple to estimate a figure for a family with a “new” translocation, but an attempt can be made (see Chapter 4). For the Robertsonian translocations, by contrast, each type of which can generally be regarded as the same between families, extrapolation of risk figures from historical data to a current family is usually valid.

Hook and Cross (1982) note the importance of distinguishing between the rate (which may be thought of as past tense) and the risk (which is future tense). They emphasize that, while geneticists routinely extrapolate from rates in one population at one point in time and may use these figures as risk estimates in another population and certainly at a later point in time, they should be on their guard for any evidence that a condition varies with time, geography, or ethnicity. So far, in fact, there is little indication that any such variation exists for at least the latter two factors (p. 366).

Doing a Segregation Analysis

Segregation analysis is essentially a simple exercise. A farmer who surveys a flock of newborn lambs and notes that 3 are black and 97 are white has done a segregation analysis. In human cytogenetic segregation analysis, the exercise involves looking at a (preferably large) number of offspring of a particular category of parent: parents who carry some particular chromosome rearrangement, or those who have had a child with a chromosomal abnormality, they themselves being karyotypically normal. The proportion of these parents' children who are abnormal is noted, and this datum serves as the point estimate of the recurrence risk.

Although segregation analysis is simple in principle, there are potential pitfalls in its application, the most important of which is ascertainment bias. We will deal with this problem here only briefly. It is important that the counselor know of ascertainment bias and recognize whether or not it has been accounted for in the published works they consult. But it is not necessary to understand the complex and sophisticated mechanics of segregation analysis in detail. The reader wishing fuller instruction is referred to Murphy and Chase (1975), Emery (1986), and Stene and Stengel-Rutkowski (1988). The classic example of ascertainment bias is that of the analysis of the sex ratio in sibships of military recruits in the First World War. Adding up the numbers of brothers and sisters, there was a marked excess of males. But of course (in 1914–18) the recruit himself had to be male. Once he was excluded from the total in each sibship, the overall sex ratio was normal. Likewise, in a cytogenetic segregation analysis, the individual whose abnormality brought the family to attention—the proband—is excluded from the calculation. That person had to be abnormal. Furthermore, that individual's carrier parent, grandparent, and so on in a direct vertical line had to be (almost always) phenotypically normal to have been a parent. They must also be excluded from an analysis of their own sibship, if that generation is available for study. Other sibships may be included in full.

These manipulations of dropping the proband and the heterozygous direct-line antecedents are the major steps to be taken to avoid the distorting effects of ascertainment bias. Another potential methodological confounder for the aficionado is ascertainment probability. For example, families with more affected members may be more likely to come to medical attention, which would unduly weight the data. There are means to overcome this problem.

Essential to a good analysis is good data, or at least as good as possible. Some retrospective information may be uncertain. Did a phenotypically abnormal great uncle who died as a child in 1950 have the “family aneuploidy”? (Old photos may be very helpful in this respect.) Some family skeletons may remain in cupboards unopened to the interviewer. The investigative zeal, clinical judgment, and personal qualities of the researcher are crucial in getting the right information, and getting it all.

Derivation of a Private Recurrence Risk Figure

We will demonstrate some of the previously noted principles in estimating a private recurrence risk figure for the hypothetical family depicted in Figure 3-1. Six sibships are available for analysis: one in generation II, two in generation III, and three in generation IV. We determine the segregation ratio in each. It is conventional to form a table with a row for each sibship, noting the numbers of phenotypically normal (carrier, noncarrier, unkaryotyped) and phenotypically abnormal offspring. The proband (IV:4) and his heterozygous antecedents (II:1 and III:1) are excluded from their sibships. Thus, we have the following:

Parent of Sibship

Phenotypically Normal

Affected

Carrier

Noncarrier

Unkaryotyped

I:1

0

1

2

0

II:1

1

1

0

2

II:2

0

1

0

1

III:1

2

0

1

0

III:2

0

1

0

0

III:7

0

0

1

0

Total

3

4

4

3

Figure 3-1. Hypothetical pedigree in which a chromosomal rearrangement is segregating. Filled symbol, abnormal individual with unbalanced karyotype; half-filled symbol, balanced carrier; N in symbol, 46,N. The proband is indicated by an arrow, as is conventional.

(Note that I:1's heterozygosity must be inferred from his wife's and children's karyotypes. It is a subtle question whether his offspring should properly be included in the analysis, which we will not pursue here). We see that the offspring of heterozygous parents total 14, the proband and the heterozygous antecedents having been excluded. The proportion of abnormal children is 3/14 (0.21). This, then, is a point estimate of the risk for recurrence in a future pregnancy of a heterozygote. The reader should know intuitively that an estimate based on just 14 children is not going to be very precise. And what of children who died in infancy, before the family cytogenetic study has been done? Let us suppose this was the case with III:4 and 5. If there was good evidence for their having been chromosomally abnormal, a better estimate would be 5/14 (0.36).

Genetic Heterogeneity and the Use of Empiric Risk Data

It is not necessarily valid to extrapolate from one family's experience to a prediction for another. Different factors may cause an abnormality in different families. As an obvious example, it would be misleading to lump all Down syndrome families together to determine a recurrence risk figure. Splitting this category into the different karyotypic classes of standard trisomy, familial translocations, and de novo translocations is a start. The standard trisomic category requires further splitting in terms of maternal age. In a unique case, a woman had three trisomy 21 conceptions and displayed a tendency to produce multiple cells with differing (“variegated”) aneuploidies in at least skin, blood, and gonad (Fitzgerald et al., 1986; see Chapter 19). She required unique advice. And in reciprocal translocation families, uniqueness is the rule! It is generally reasonable (and often all that is feasible or possible) to apply a risk figure derived from the study of families with a similar, albeit not exactly identical, chromosomal arrangement. But occasionally a family is large enough for a private estimate of the recurrence risk to be made from the family itself. This estimate, if it is precise enough (see the discussion below of confidence limits and standard error), is the most valid to offer that family.

Pregnancy Outcomes to Which Risk Figures Refer

With particular reference to the situation of a parent heterozygous for a chromosomal rearrangement, risk figures are generally presented in terms of “the risk that a liveborn child would have a chromosome imbalance related to the parental translocation.” The numerator is the number of aneuploid babies, and the denominator the number of pregnancies. Thus, for the example of the common t(11;22)(q23;q11) translocation (p. 75), Stengel-Rutkowski et al. (1988)accumulated data on a total of 318 pregnancies (the denominator) to carrier parents, of whom, after ascertainment correction, 9 (the numerator) had the 47,der(22) aneuploidy; 9/318 gives the risk expressed as a percentage, 2.8%. Separating out mothers and fathers, the respective risk figures are 3.7% (9/241) and <0.7% (0/77). For those choosing prenatal diagnosis, the risk figure of interest relates to the timing of the procedure, generally chorionic villus sampling (usually done at 10–12 weeks) and amniocentesis (15–17 weeks). In other words, they want to know how likely it is they will have to face the actuality of termination. The risk here is likely to be higher (7% in the case of the t(11;22) discussed above), given that some of the abnormal pregnancies would have spontaneously aborted some time after that period of gestation. Table 3-1 sets out these and other possible ways of considering risk.

Association: Coincidental or Causal?

The counselor not infrequently encounters the problem of a chromosomal “abnormality” discovered in a phenotypically abnormal individual, but in whose family others, who are quite normal, are then shown to have apparently exactly the same rearrangement. Does a genetic risk apply, then, to children of the carrier, to whom the same rearranged chromosome may be transmitted? The familial paracentric inversion is a good example. In a review of 69 probands, Price et al. (1987) list the phenotypic abnormalities that led to these individuals coming to a chromosome study. There was a collection of various clinical indications, with no consistent pattern (other than that mental retardation was frequent), and several ascertained quite by chance at prenatal diagnosis. By definition, one parent carries the same inversion; and, if the net is widened, often other relatives as well (Groupe de Cytogénéticiens Français, 1986a). In this context, provided, of course, that the carrier relatives are phenotypically normal, one would reach the conclusion that the chromosome rearrangement was balanced, with no functional compromise of the genome; and that it was coincidence that led to its discovery (Romain et al., 1983).

Table 3.1. Different Ways of Looking at the Quantum of Reproductive Risk Due to a Parent Being a Carrier of a Chromosomal Rearrangement

Numerator

Denominator

Abnormal liveborn baby

All liveborns

Abnormal liveborn baby

All recognized pregnancies

Abnormal amniocentesis result (early second trimester)

All pregnancies at ~16 weeks

8- to 14-week miscarriage

All recognized pregnancies

Abnormal embryo on biopsy

All embryos from one IVF procedure

Normal embryo on biopsy

All embryos from one IVF procedure

IVF, in vitro fertilization.

But when some very unusual clinical picture is associated with a paracentric inversion that is rare or previously undescribed (as most inversions are), some writers are skeptical of coincidence and propose a causal link (Fryns et al., 1994; Urioste et al., 1994a). Similarly, Wenger et al. (1995), noting the coincidence of children with an apparently balanced familial translocation, and being phenotypically abnormal, write that “the chance that two rare events in the same individual are unrelated seems unlikely to us.” Here, there is a risk of deception due to “Kouska's fallacy”—Kouska was a fictional nineteenth century philosopher who concluded that the combination of unlikely events that led to his parents meeting was too implausible to believe, and that therefore he himself could not exist (Lubinsky, 1986). As does Lubinsky, we must insist on the point that the proband had to be phenotypically abnormal, and the coexistence of a subsequently discovered different abnormal event (the karyotype) need not be seen as necessarily remarkable.

This is not to exclude the possibility of a causal link. Biological plausibility is an important criterion. It is not straightforward to explain the normality of a parent and other relatives if they carry the same abnormal chromosome. For the apparently balanced translocation, Wenger et al. (1995) offer the speculative explanation of instability of fragile sites at or near the translocation breakpoint; while Wagstaff and Hemann (1995) provide an actual demonstration of a biological mechanism (a cryptic insertion). When a balanced rearrangement has a breakpoint in the region of a suspected disease locus a causal link is a reasonable proposition, the perplexing fact of a normal heterozygous parent notwithstanding, as Rizzu et al. (1995) propose in a child with Cornelia de Lange syndrome and a paracentric inv(3). Thus, it may truly be that, perhaps in no more than a very few of these apparently balanced rearrangements, a real biological mechanism exists to explain the observed kary-otypic–phenotypic association.

A similar question arises when two rare karyotypes are seen in the same family, or when one individual has more than one aneuploidy. A double aneuploidy such as Klinefelter plus Down syndrome, 48,XXY,21, could be interpreted as two separately arising nondisjunctions, but each occurring on the basis of the same underlying predisposing factor (such as maternal age). The two conditions occur together more often than the product of the frequency of each singly, which would be consistent with that interpretation. Alternatively, if the XXY component could be shown to reflect a paternal meiotic error, while the trisomy 21 was of maternal origin, then the association could be seen as fortuitous. Two different types of abnormality, such as Klinefelter plus Prader-Willi syndrome, 47,XXY,del(15)(q11q13), as reported in Rego et al. (1997), might also be judged to reflect two unrelated abnormal events, given that the mechanisms leading to nondisjunction and to deletion are quite different, even if both might have arisen in the same parent. The prior probability of two abnormal karyotypes coinciding might be a very small figure (1/2000 × 1/15,000 = 1/30,000,000 in the foregoing example); but recalling that the range of abnormal karyotypes is very wide, it should not necessarily be seen as reflecting some extraordinary predisposition when two abnormalities are diagnosed in the one individual or family. Coincidences do happen.

Presentation of a Risk Figure

A risk figure is a probability statement, and should be presented as such to the counselee in everyday language—for example: “there is a 50/50 chance for such and such an event”; “the risk for such and such to happen is around 1 chance in 10.” The raw probability figure may not of itself be sufficient, and it is a test of the counselor's skill to interpret figures so as to provide empathic guidance rather than presumptuous direction. Loaded interpretative comments such as “the risk is quite high that …” or “there is only a small chance that …” should be used with great care. The perception of a risk figure as high or low may vary greatly according to an indi-vidual's personality and past life experiences and the way they use the language of numbers; the very act of discussing the risk may help the client see it in a less threatening light (Kessler and Levine, 1987). A helpful perspective may be provided by noting that about 3% of all babies have a major congenital malformation or a substantial degree of mental retardation. People can see the same risk from different positions. For example, older women having an increased age-related risk (say, 1 in 100) for a child with Down syndrome may decide against an amniocentesis if a maternal serum screening test gives a risk (say, 1 in 200) which is above the cutoff for access to amniocentesis (1 in 250) but lower than their “starting figure,” whereas a younger woman with an age-related risk of, say, 1 in 500 is likely to opt for amniocentesis if she were to have the same 1 in 200 result from the screening test (Beekhuis et al., 1994).

As noted earlier, theoretical risk figures are true and empiric risk figures are estimates; the former are exact, and the latter are not. For an empiric figure we have a point estimate (e.g., 10%) and a likely range (e.g., 5%–15%) of where the risk actually is. The more data that have been gathered, the more accurate the estimate and the narrower the likely range—and the more confidently, therefore, can the counselor present the figure. The likely range can be measured in different ways. The standard error, which formally measures the precision of the estimate, can be used to give a sense of the region within which the true risk can realistically be considered to lie. The 95% confidence limits define the broad range that very probably (P = 0.95) encompasses the true risk. Formulas to determine these parameters are set out in Appendix C.