Mary L. Marazita
Segregation analysis refers to statistical methods that are used to determine the mode of inheritance of a trait. Segregation in this context therefore is derived from Mendel's laws regarding the segregation of alleles in the formation of gametes (Mendel, 1866; translated by Bateson, 1902, 1909). According to the Oxford English Dictionary (Burchfield, 1986), the first usage of the word was by Weldon (1902) in his description of Mendel's laws. Therefore, segregation analysis originated from the assessment of Mendelian patterns of inheritance, i.e., testing whether family data were consistent with a single genetic locus. Today, the term is used more broadly, to encompass tests of many types of transmission of traits not limited to Mendelian patterns. Complex segregation analysis is sometimes used to describe statistical methods that incorporate two or more distinct, functionally independent parameters (Ellandt-Johnson, 1971).
The importance of inheritance in the etiology of cleft lip (CL) and cleft palate (CP) has been noted by scientists for more than 200 years. The first published description of a family with several affected members was in 1757 (Trew, 1757). Charles Darwin (1875) pointed out a publication of “the transmission during a century of hare-lip with a cleft-palate” by Sproule (1863) describing the author's family. Rischbieth (1910) summarized pre-1900 publications of familial cases of CL (“hare-lip”) and CP (abridged facsimile of Rischbieth, 1910, and commentary putting Rischbieth's conclusions into historical perspective are provided by Melnick, 1997). Rischbieth (1910) epitomized the antiMendelian view of Pearson and the other members of the Galton Laboratory by concluding that inheritance of CL and CP was an expression of general physical and racial degeneracy which could be traced to poor protoplasm (Melnick, 1997). Bateson, however, was a leading proponent of Mendelism and included “hare-lip” as one of a group of “dominant hereditary diseases and malformations” (Bateson, 1909; Melnick, 1997).
The fundamental tenet of Mendelism, i.e., unit inheritance, has since been demonstrated to be correct and has led to today's burgeoning field of genetics. Rischbieth (1910), although fundamentally incorrect in his assessment of the meaning of familial cases of oral-facial clefts, did provide a pertinent charge to modern scientists studying the inheritance of CL and CP:
The cause of these defects lies in the family tendency, but it is only when the family is considered as a whole, in all its branches and when normal as well as deformed individuals are included in the records, that we shall begin to understand the mode of working of the hereditary influence. This fact has long been known to students of insanity, but in the case of hare-lip and cleft palate inquiry has usually gone no further than to ask how many relatives (usually in the direct line) showed this defect.
This succinctly describes the key components of study designs of human disorders. When appropriate data are collected, statistical models can be applied to derive an unbaised conclusion regarding the inheritance pattern of a human trait.
Segregation analysis methods were developed to address the inherent biases of most studies of human family data. In studies of experimental animals, it is possible to design controlled matings that allow direct inference of the inheritance pattern of the trait of interest. The ideal human family study design would involve obtaining a large, random, population-based sample of families; taking a subset of the random families in which there are individuals with clefts; and then determining the genotypic mating type and offspring for each family. However, for a number of reasons, this ideal study design is not feasible for most human traits, including oral-facial clefts. The necessary fully infor-mative matings are generally not available, and the genotypes of the family members are usually unknown. A further difficulty in studying inheritance patterns in humans is that the traits most often under study are relatively rare. Oral-facial clefts, for example, are common birth defects but still occur in only 1/500 to 1/1000 births. Therefore, it is generally not possible to take a random sample of a population and obtain the necessary numbers of families with cleft individuals. Families for study of human traits are most often ascertained through affected individuals, therefore requiring appropriate statistical correction to eliminate potential biases introduced by the mode of ascertainment.
Classical Segregation Ratio Analysis
To illustrate some important concepts in segregation analysis, I will focus on the first and simplest segregation analysis parameter, the segregation ratio. A segregation ratio is the proportion of affected children among the progeny of a particular mating type. Consider a two-allele autosomal genetic locus. There are six possible genotypic mating types, representing six phenotypically distinguishable mating types under codominance or three phenotypic mating types if dominance exists for the trait. Table 18.1 shows the possible matings and the expected proportions of affected children for each mating type. As can be seen, only some of the mating types are expected to produce affected children. Therefore, in the usual human study situation of ascertaining families through affected individuals, only some of the possible mating types will be represented in the resulting data set. This is one of the limitations that the statistical methods of segregation analysis are designed to address. The other major limitation and source of potential bias that segregation analysis addresses is the mode of ascertainment.
There are two major classes of ascertainment, complete and incomplete ascertainment. The ascertainment probability is, conceptually, the proportion of probands among affected individuals. Complete ascertainment is the situation in which all possible offspring sets for a particular mating type will enter a study, i.e., independent of the phenotype of the offspring. An example of complete ascertainment is defining a sample of affected people and then estimating the segregation ratio in their children. Incomplete ascertainment refers to situations in which not all possible offspring sets are found. An example of incomplete ascertainment is defining a sample of affected people, their siblings, and parents and then estimating the segregation ratio in the children sets. This is incomplete because the only offspring sets entering the study will be those with at least one affected offspring. As can be seen in Table 18.1, many of the mating types that can produce affected offspring can also produce unaffected offspring. By chance, there will be an appreciable proportion of families with only unaffected offspring. Consider an autosomal recessive trait. If the affected allele is rare, the only genotypic mating type capable of producing affected children that is likely to be present in the data set will be AB × AB (Table 18.1). This mating type has an expected segregation ratio of 25%; therefore, the expected proportion of unaffected children is 75%. For three-child families, applying the multiplication rule of combining probabilities yields the probability of all three children being unaffected as 0.753 = 0.4219. Therefore, ascertaining three-child families through affected children will miss 42.19% of the families that would be necessary for an unbiased estimate of the segregation ratio.
One of the first methods of correcting for ascertainment bias in segregation analysis was the Weinberg proband method, originally proposed by Weinberg (1912, 1927) with standard error formulas derived by Fisher (1934). For Weinberg's method and for all subsequent methods of segregation analysis, it is crucial to define the term proband carefully. A proband (Weinberg, 1927; Morton, 1959; Wright, 1968) is an affected person who is necessary and sufficient to ascertain a family for study. Depending on the comprehensiveness of the sampling frame, there may be more than one proband per family. The first proband in a family is sometimes termed the propositus or index case. Additional nonproband affected individuals in a family are termed secondary cases (Morton, 1982). Careful delineation of probands and nonprobands in families is extremely important in correcting for ascertainment biases in the statistical genetic analysis of patterns of inheritance, although even then problems may arise (Greenberg, 1986; Vieland and Hodge, 1995). A dichotomy has developed in the use of the term proband by clinicians as opposed to researchers (Marazita, 1995). Clinicians tend to use proband and index case interchangeably (Thompson et al., 1991; Bennett et al., 1995a), implying that there would be only one proband indicated per family in clinical genetic records. This dichotomy would seriously bias analysis of such records (Marazita, 1995). Therefore, Bennett et al. (1995b) recommended that the research definition be followed in clinical genetic situations.
|
TABLE 18.1. Expected Segregation Ratios for Mating Types at a Single Genetic Locus with Two Alleles, A and B, with A Representing the Affected Allele |
||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||
The essence of the Weinberg method is that the proband individuals provide the information that a particular mating type is segregating, i.e., capable of producing affected offspring. Therefore, Weinberg (1912, 1927) proposed calculating the segregation ratio in the nonproband children to obtain an unbiased estimate. Refinements were later introduced to incorporate a correction factor for large sibship sizes.
The next major advance in segregation analysis was by Morton (1959), in which the segregation ratio was assumed to follow the binomial probability distribution and likelihood methods were used to estimate the parameters and to test hypotheses. Morton also considered the ascertainment probability to be binomially distributed and estimable. Morton divided incomplete ascertainment into three categories: truncate, single, and multiple. Under single incomplete ascertainment, each family has only one proband (even if the family has multiple affected members) and the ascertainment probability is close to 0. Under truncate incomplete ascertainment, every affected individual in a family is a proband and the ascertainment probability is 1.0. Multiple incomplete ascertainment is intermediate between these two extremes, with some families having more than one proband but not all affected offspring being probands (ascertainment probability between 0 and 1.0). Table 18.2 summarizes the key points of incomplete ascertainment and the bias in the segregation ratio due to incomplete ascertainment. Table 18.3 summarizes the parameters that were estimated in classical segregation ratio analysis.
Segregation ratio analysis methods were limited to analysis of single-locus, Mendelian patterns in nuclear family data. Such analyses were amenable to analytic solution. The next wave of advances in segregation analysis included methods that were developed to address more complex models in larger family structures. The theoretical underpinnings of such methods were developed in the 1970s, before there were computers that were able to apply such methods fully. With improved computers, application of such models became a reality and laid the foundation for other important statistical methods in human genetics today, such as linkage analysis in extended kindreds (Ott, 1991). Related statistical methods for investigating the inheritance of oral-facial clefts are reviewed in other chapters (Chapters 17,19,21). In the discussion of complex segregation analysis methods, I will focus on those that have been applied to oral-facial cleft data, in particular, the major locus transmission model (Elston and Stewart, 1971; Elston, 1980), the mixed/unified model (Morton and MacLean, 1974; Lalouel Morton, 1981; Lalouel et al., 1983), and regressive models (Bonney, 1984, 1986). Because the oral-facial cleft phenotypes analyzed to date have been qualitative in nature (i.e., “affected” vs. “unaffected”), I will focus on the qualitative application of these methods, though each method also has applications for quantitative traits.
|
TABLE 18.2. General Incomplete Ascertainment Model of Morton (1959) for Selection through Affected Children |
|||||||||||||||||||||||||||||||
|
|||||||||||||||||||||||||||||||
|
TABLE 18.3. Parameters Estimated for Classical Single-Locus Segregation Analysis, Utilizing Segregation Ratios in Nuclear Families |
|||||||||||||||||||||||||||||||
|
|||||||||||||||||||||||||||||||
Each of the approaches defines an underlying general model with assumptions as to the probability distributions and parameters of interest. The hypotheses to be tested are each nested within the underlying general model; i.e., each hypothesis corresponds to restrictions on the parameters of the underlying model. Likelihoods are calculated for each hypothesis; parameters are estimated by maximum likelihood (Edwards, 1992). The likelihood ratio criterion is used to compare the likelihood of each restricted hypothesis to that of the most general, unrestricted model. Twice difference in In-likelihoods between the unrestricted hypothesis and each of the restricted hypotheses is asymptotically distributed as a X 2 with degrees of freedom corresponding to the difference in the numbers of parameters estimated between the restricted and unrestricted hypotheses. If there are multiple equally likely hypotheses, the Akaike information criterion (AIC; Akaike, 1974) is often applied. The AIC for any hypothesis equals -2(ln-likelihood) + 2(number of parameters estimated). The model with the smallest AIC is the most parsimonious.
Major Locus Transmission Models
Under the major locus transmission model of Elston and Stewart (1971), segregation at a major locus is parameterized by use of transmission probabilities for each of three possible types in the data (AA, AB, or BB). Two individuals have the same type if and only if the expected phenotypic distribution of their offspring by a mate of a given type is identical (Cannings et al., 1978). Genotypes are the special case of types (or “ousiotypes,” following Cannings et al., 1978) that transmit to offspring in a Mendelian fashion. When there is no transmission from one generation to the next, the model allows for only a single type. Table 18.4 summarizes the parameters of the model.
Elston and Stewart (1971) also provided a major advance for genetic analysis of extended kindreds by developing an efficient computational algorithm for calculating the likelihoods of any general family structure (Lange, 1997). Their algorithm is the basis for the most widely used linkage analysis computer program, LINKAGE (Terwilliger and Ott, 1994).
|
TABLE 18.4. Parameters for Major Locus Segregation Analysis of Qualitative Traits Utilizing Transmission Probabilities in General Pedigrees |
|||||||||||||||||||||||
|
|||||||||||||||||||||||
|
TABLE 18.5. Parameters Estimated for Complex Segregation Analysis of Qualitative Traits under the Mixed Model (i.e., Major Locus with Multifactorial and Sporadic Components) in General Pedigrees Broken Down into Their Component Nuclear Families |
|||||||||||||||||||||||
|
Mixed/Unified Model
Under the mixed/unified model, an individual's pheno- type is assumed to be due to a major locus component and a multifactorial component (Morton and MacLean, 1974; Lalouel and Morton, 1981; Lalouel et al., 1983). This model has had particular appeal for segregation analyses of oral-facial clefting because of the desire to contrast multifactorial hypotheses with major locus hypotheses. The parameters of the model are summarized in Table 18.5. The original mixed model of Morton and MacLean (1974) was extended to incorporate the transmission probabilities of the Elston and Stewart (1971) major locus model to create the so-called unified model (Lalouel et al., 1983). Ascertainment corrections are done by breaking the extended kindreds into their component nuclear families and specifying the mode of ascertainment of each nuclear family. This method of ascertainment correction has the advantage of allowing multiple ascertainment schemes, each with its own ascertainment probability; however, some of the transmisison information from extended kindreds is lost.
Regressive Models
Regression analysis methods were first applied to complex segregation analysis by Bonney (1984, 1986), who combined aspects of the transmission approach of Elston and Stewart (1971) with the flexibility of regression analysis. In regression models for complex segregation analysis as proposed by Bonney (1984), the dependence among family members is modeled as a Markovian process, where each individual's trait value (phenotype) is influenced by his or her own covariates, as well as the observed phenotypes of preceding family members. Class A, B, C, and D models were defined (Bonney, 1984, 1986), which differ in the assumptions regarding the dependence between siblings. In class A, B, and C models, the correlations between siblings differ depending on how close in age the siblings are. In the class D model, correlations between siblings are assumed not to differ by age relationships but, at the same time, are necessarily due to common parentage alone. The concept of types introduced by Elston and Stewart (1971) and summarized by Cannings et al. (1978) plus the structure of transmission probabilities was incorporated into the regressive models. Table 18.6 summarizes the primary parameters of the regression model. Ascertainment corrections were incorporated by conditioning on the subsets of proband individuals in each family.
Family Studies of Oral-Facial Clefts
Oral-facial clefts are a major public health problem, affecting 1/500 to 1/1000 births worldwide (Murray, 1995). Therefore, many research groups have attempted to elucidate the etiology of oral-facial clefts, with limited success. Oral-facial clefts can occur as part of Mendelian syndromes, certain chromosomal anomalies include oral-facial clefts in the phenotype, and certain teratogens can increase the risk of having an off-spring with a cleft. However, phenotypes of known etiology comprise only a small portion of all individuals with an oral-facial cleft; therefore, a major research focus has been on the genetics of nonsyndromic forms of clefting (the focus of this chapter).
There have been many essentially descriptive publications of oral-facial cleft families, summarized in Table 18.7. Each of the descriptive studies presented an hypothesis as to the inheritance of oral-facial clefts and described how their data fit the hypothesis, without attempting any statistical tests. In Rischbieth's (1910) summary of pre-1900 oral-facial cleft families, the hypothesis was that such families were the result of general physical degeneracy. Bateson (1909), however, attributed the clefts in such families to dominantly inherited genes. Fogh-Andersen (1942) was the first to collect a systematic data set of cleft families and to evaluate the observed inheritance patterns. He concluded that the CL with or without CP (CL/P) families were consistent with segregation of alleles at a single genetic locus with variable penetrance and that CP families were consistent with autosomal dominant inheritance with greatly reduced penetrance.
|
TABLE 18.6. Parameters Estimated for Complex Segregation Analysis of a Qualitative Trait under Regressive Models in General Pedigrees |
||||||||||||||||||||||||||
|
In the 1960s and 1970s, there was a paradigm shift. A specific statistical model, termed the multifactorial threshold model (MFT), was described and invoked to explain the familial patterns of oral-facial clefts (Carter, 1976; Fraser, 1976). Under the MFT model, the occurrence of a cleft depends on a very large number of genes, each of equal, minor, and additive effect, plus environmental factors. An accumulation of these genes and environmental factors is tolerated by the developing fetus to a point, termed the threshold, beyond which there is the risk of malformation. This model has testable predictions and, in theory, could explain many of the features observed for oral-facial clefts in families. The early proponents of the MFT model published several large series of cleft families from a variety of populations, each concluding that the data were consistent with the MFT model (Table 18.7) (Woolf et al., 1963, 1964; Carter et al., 1982a,b; Hu et al., 1982). However, none of these early studies attempted any statistical tests of the MFT model.
The early descriptive studies were followed by studies that did test the predictions of the MFT model (Table 18.7) (Bear, 1976; Melnick et al., 1980; Marazita et al., 1984). In each of these studies, some or all of the predictions of the MFT model could be rejected. However, statistical tests of the predictions of a model do not constitute statistical tests of that model. Other investigators then formulated and parameterized models to test the goodness-of-fit of the MFT model; a number of investigators applied such models to oralfacial cleft family data (Table 18.7) (Melnick et al., 1980; Mendell et al., 1980; Marazita et al., 1986b). The results of the goodness-of-fit studies were mostly inconclusive, with the MFT model being rejected for some portions of the parameter space in most studies.
In the late 1970s and early 1980s, investigators began to apply segregation analysis methods, such as mixed models, to test the MFT model and to evaluate the major locus alternative. Table 18.8summarizes published segregation analyses of oral-facial clefting. Some of the first mixed-model studies of oral-facial clefts were inconclusive (Chung et al., 1974; Demenais et al., 1984) because the sample sizes were inadequate to distinguish between models. There were then a number of mixed or unified model studies of sufficient sample sizes (Table 18.8). In virtually every such study of CL/P, the MFT model could be rejected in favor of either a mixed model (major locus plus multifactorial background) (Marazita et al., 1984; Chung et al., 1986) or a major locus alone (Hecht et al., 1991; Marazita et al., 1992; Nemana et al., 1992). Most such studies were conducted in Caucasian populations, although there were a few in Asian populations (Table 18.8) (Marazita et al., 1992). Given these segregation analysis results, gene mapping studies of CL/P were then considered feasible and are a current focus of intensive research (see Chapters 20,21, and 23).
There are many fewer segregation analyses of nonsyndromic CP than there are of CL/P. There are only three published studies, one in Hawaii (Chung et al., (1974)) and two in Caucasian populations (Demenais et al., 1984; Clementi et al., 1997). Chung al. (1974) and Demenais et al. (1984) could not distinguish between the MFT and major locus models; Clementi et al. (1997) concluded that a single recessive major locus with reduced penetrance was sufficient to explain their data. There is also a significant subset of non-syndromic CP families in which CP is X-linked, as evidenced by the descriptive studies of Rushton (1979) and Rollnick and Kaye (1986, 1987). The X-linked form of CP includes ankyloglossia and has been confirmed by linkage analysis (Moore et al., 1987, 1991; Bjornsson et al., 1989; Gorski et al., 1992, 1994) and physical mapping (Forbes et al., 1995, 1996).
|
TABLE 18.7. Summary of Published Family Studies of Cleft Lip with or without Cleft Palate (CL/P) and Cleft Palate Alone (CP) Using Methods Other Than Segregation Analysis |
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
In summary, segregation analyses of oral-facial clefts, both CL/P and CP, have consistently resulted in evidence for genes of major effect. Although such studies imply a single major locus, hypotheses of multiple interacting loci or genetic heterogeneity cannot be ruled out and, indeed, have not been explicitly tested in any of the published segregation analyses to date (see Jarvik, 1998, for a summary review of this issue with respect to complex segregation analysis). Analyses of recurrence risk patterns (Table 18.7) (Farrall and Holder, 1992; Mitchell and Risch, 1992; Fitzpatrick and Farrall, 1993; Christensen and Mitchell, 1996;
Mitchell and Christensen, 1996) (see also Chapter 17) have been consistent with oligenic models, with approximately four to seven interacting loci. Other potential limitations of complex segregation analysis include difficulty in determining the power of specific sample sizes and difficulty in appropriately adjusting for the method of ascertainment (Jarvik, 1998).
|
TABLE 18.8. Summary of Published Segregation Analyses of Cleft Lip with or without Cleft Palate (CL/P) and Cleft Palate Alone (CP) |
|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Role of Segregation Analysis in Future Studies of Oral-Facial Clefts
Segregation analyses to date have primarily been concerned with testing the MFT hypothesis regarding the etiology of nonsyndromic oral-facial clefts. Although in some sense oral-facial clefts are due to multiple factors, the specific MFT statistical model that was invoked for several years (Carter, 1976; Fraser, 1976) was not well supported. As summarized in Table 18.8, in most studies, the MFT model either could be rejected or was equally as likely as major locus models.
In the current age of gene mapping, ultimate confirmation of the existence major genetic loci for clefting may be at hand (see Chapters 20,21, and 23 for progress to date). Until that time, there are still several important roles for segregation analysis to play. Parametric linkage analysis methods require estimates of parameters such as gene frequency, which are obtained from segregation analyses. Most segregation analyses to date have been Caucasian populations; thus, there is a need for studies in other ethnic/racial groups to determine if the family patterns are the same across groups. Furthermore, the lack of major gene mapping successes in oral-facial clefting highlights the fact that clefts are unlikely to be due to the proximate phenotypic expression of the genes involved. Segregation analyses can be used to refine the phenotype, with a focus on either subclinical expressions in unaffected relatives [e.g., anatomic differences in the obicularis oris muscle (Martin et al., 2000)] or associated phenotypic features that may be markers for developmental instability [e.g., handedness (Wentzlaff et al., 1997) or cephalometric features (Ward et al., 1994)]. Once genes have been identified, segregation analysis methods can also be used to help identify other factors that modify expression at those genes.
Despite over 200 years of interest in the familial aggregation of oral-facial clefts, we still do not have a definitive understanding genetic component of the familiality. Segregation analyses have provided significant insights, and the powerful statistical and molecular approaches available to geneticists today should continue to build on that foundation.
References
Akaike, H (1974). A new look at the statistical model identification. IEEE Trans Automatic Control AC 19: 616–623.
Bateson, W (1902). Mendel's principles of heredity: a defence. Cambridge University Press, Cambridge, England.
Bateson, W (1909). Mendel's principles of hereditary. Cambridge University Press, Cambridge, England.
Bear, JC (1976). A genetic study of facial clefting in Northern England. Clinical Genetics 9: 277–284.
Bennett, RL, Steinhaus, KA, Uhrich, SB, O'Sullivan, CK, Resta, RG, Lochner-Doyle, D, Markel, DS, et al. (1995b). Reply to Marazita and Curtis. Am J Hum Genet 57: 983–984.
Bennett, RL, Steinhaus, KA, Uhrih, SB, O'Sullivan, CK, Resta, RG, Lochner-Doyle, D, Markel, DS et al. (1995a). Recommendations for standardized human pedigree nomenclature. Am J Hum Genet 56: 745–752.
Bjornsson, A, Arnason, A, Tippet, P (1989). X-linked cleft palate and ankyloglossia in an Icelandic family. Cleft Palate J 26 (1): 3–8.
Bonney, GE (1984). On the statistical determination of major gene mechanisms in continuous human traits: regressive models. Am J Hum Genet 18: 731–749.
Bonney, GE (1986). Regressive logistic models for familial disease and other binary traits. Biometrics 42: 348–353.
Burchfield, RW (1986). A supplement to the Oxford English dictionary: Volume IV, Se-Z. Clarendon Press, Oxford, England.
Cannings, C, Thompson, EA, Skolnick, MH (1978). Probability functions on complex pedigrees. Am Hum Genet 10: 26–61.
Carter, CO (1976). Genetics of common single malformations. Br Med Bull 32: 21–26.
Carter, CO, Evans, K, Coffey, R, Roberts, JA, Buck, A, Roberts, ME (1982a). A family study of isolated cleft palate. J of Medical genetics 19: 329–331.
Carter, CO, Evans, K, Coffey, R, Roberts, JA, Buck, A, Roberts, ME (1982b). A three generation family study of cleft lip with or without cleft palate. J of Medical Genetics 19: 246–261.
Case Western Reserve University, Department of Epidemiology and Biostatistics (1997). SAGE (Statistical analysis for genetic epidemiology), Cleveland, OH.
Ching, GH, Chung, CS (1974). A genetic study of cleft lip and cleft palate in Hawaii. I. Interracial crosses. Am J Hum Genet 26: 162–176.
Christensen, K, Mitchell, LE (1996). Familial recurrence-pattern analysis of nonsyndromic isolated cleft palate-a Danish registry study. Am J Hum Genet 58: 182–190.
Chung, CS, Beechert, AM, Lew, RE (1989). Test of genetic heterogeneity of cleft lip with or without palate as related to race and severity. Genetic Epidemiology 6: 625–631.
Chung, CS, Bixler, D, Watanabe, T, et al. (1986). Segregation analysis of cleft lip with or without palate: a comparison of Danish and Japanese data. Am J Hum Genet 39: 603–611.
Chung, CS, Ching, GH, Morton, NE (1974). A genetic study of cleft lip and palate in Hawaii. II. Complex segregation analysis genetic risks. Am J Hum Genet 26: 177–188.
Clementi, M, Tenconi, R, Collins, A, et al. (1995). Complex segregation analysis in a sample of consecutive newborns with cleft lip with or without cleft palate in Italy. Hum Hered 45: 157–164.
Clementi, M, Tenconi, R, Forabosco, P, et al. (1997). Inheritance of cleft palate in Italy. Evidence for a major autosomal recessive locus. Hum Genet 100: 204–209.
Czeizel, A, Tusnady, G (1972). A family study on cleft lip with or without cleft palate and posterior cleft palate in Hungary. Hum Hered 22: 405–416.
Darwin, C (1875). The variation of animals and plants under domestication, Vol. 1, second edition. New York: Appleton.
Demenais, F, Bonaiti-Pellie, C, Briard, ML, Feingold, J (1984). An epidemiological and genetic study of facial clefting in France. II. Segregation analysis. J Med Genet 21: 436–440.
Edwards, AWF (1992). Likelihood, Expanded Edition. Baltimore: Johns Hopkins University Press.
Ellandt-Johnson, RC (1971). Probability Models and Statistical Methods in Genetics. New York: John Wiley & Sons.
Elston, RC (1980). Segregation analysis. In: Current Developments in Anthropological Genetics, Vol. 1, edited by JH Mielke and MH Crawford. New York: Plenum Press, pp. 327–354.
Elston, RC, Stewart, J (1971). A general model for the genetic analysis of pedigree data. Hum Hered 21: 523–542.
Farrall, M, Holder, S (1992). Familial recurrence-pattern analysis of cleft lip with or without cleft palate. Am J Hum Genet 50: 270–277.
Fisher, RA (1934). The effect of methods of ascertainment upon the estimation of frequencies. Ann Eugen (Lond) 6: 13–25.
Fitzpatrick, D, Farrall, M (1993). An estimation of the number of susceptibility loci for isolated cleft palate. J Craniofac Dev Biol 13: 230–235.
Fogh-Andersen, P (1942). Inheritance of Harelip and Cleft Palate. Copenhagen: Arnold Busck.
Forbes, SA, Brennan, L, Richardson, M, et al. (1996). Refined mapping and YAC contig construction of the X-linked cleft palate and ankyloglossia locus (CPX) including the proximal X-Y homology breakpoint within Xq21.3. Genomics 31: 36–43.
Forbes, SA, Richardson, M, Brennan, L, et al. (1995). Refinement of the X-linked cleft palate and ankyloglossia (CPX) localisation by genetic mapping in an Icelandic kindred. Hum Genet 95: 342–346.
Fraser, FC (1970). Genetics of cleft lip and cleft palate. Am J Hum Genet 22: 336–352.
Fraser, FC (1976). The multifactorial threshold concept—uses and misuses. Teratology 14: 267–280.
Gladstien, K, Lange, K, Spence, MA (1978). A goodness-of-fit test for the polygenic threshold model: application to pyloric stenosis. Am J Med Genet 2: 7–13.
Gorski, SM, Adams, KJ, Birch, PH, et al. (1994). Linkage analysis of X-linked cleft palate and ankyloglossia in Manitoba Mennonite and British Columbia native kindreds. Hum Genet 94: 141–148.
Gorski, SM, Adams, KJ, Birch, PH, et al. (1992). The gene responsible for X-linked cleft palate (CPX) in a British Columbia native kindred is localized between PGKI and DXYSI. Am J Hum Genet 50: 1129–1136.
Greenberg, DA (1986). The effect of proband designation on segregation analysis. Am J Hum Genet 39: 329–339.
Hasstedt, SJ (1994). PAP, Pedigree Analysis Program. Salt Lake City: University of Utah Technical Report.
Hecht, JT, Yang, P, Michels, W, Buetow, KH (1991). Complex segregation analysis of nonsyndromic cleft lip and palate. Am J Hum Genet 49: 674–681.
Hu, DN, Li, JH, Chen, HY, et al. (1982). Genetics of cleft lip and cleft palate in China. Am J Hum Genet 34: 999–1002.
Jarvik, GP (1998). Complex segregation analyses: uses and limitations. Am J Hum Genet 63: 942–946.
Koguchi, H (1975). Recurrence rate in offspring and siblings of patients with cleft lip and/or cleft palate. Jpn J Hum Genet 20: 207–221.
Lalouel, JM, Morton, NE (1981). Complex segregation analysis with pointers. Hum Hered 31: 312–321.
Lalouel, JM, Rao, DC, Morton, NE, Elston, RC (1983). A unified model for complex segregation analysis. Am J Hum Genet 35: 816–826.
Lange, K (1997). Mathematical and Statistical Methods for Genetic Analysis. New York: Springer-Verlag.
Marazita, M (1995). Defining proband. Am J Hum Genet 57: 981–982.
Marazita, ML, Goldstein, AM, Smalley, SL, Spence, MA (1986a). Cleft lip with or without cleft palate: reanalysis of a three-generation family study from England. Genet Epidemiol 3: 335–342.
Marazita, ML, Hu, DN, Spence, MA, et al. (1992). Cleft lip with or without cleft palate in Shanghai, China: evidence for autosomal major locus. Am J Hum Genet 51: 648–653.
Marazita, ML, Spence, MA, Melnick, M (1984). Genetic analysis of cleft lip with or without cleft palate in Danish kindreds. Am J Hum Genet 19: 9–18.
Marazita, ML, Spence, MA, Melnick, M (1986b). Major gene determination of liability to cleft lip with or without cleft palate: a multiracial view. J Craniofac Genet Dev Biol 2: 89–97.
Martin, RA, Hunter, V, Neufeld-Kaiser, W, et al. (2000). Ultrasonographic detection of orbicularis oris defects in first degree relatives of isolated cleft lip patients. Am J Med Genet 90: 155–161.
Melnick, M (1997). Cleft lip and palate etiology and its meaning in early 20th century England: Galton/Pearson vs. Bateson; polygenically poor protoplasm vs. Mendelism. J Craniofac Genet Dev Biol 17: 65–79.
Melnick, M, Bixler, D, Fogh-Andersen, P, Conneally, PM (1980). Cleft lip ± cleft lip ± cleft palate: an overview of the literature and an analysis of Danish cases born between 1941 and 1968. Am J Med Genet 6: 83–97.
Melnick, M, Marazita, ML, Hu, DN (1986). Genetic analysis of cleft lip with or without cleft palate in Chinese kindreds. Am J Med Genet 21: 183–190.
Mendel, G (1866). Versuche uber pflanzenhybriden. Verhandenlungen des Naturforshenden Vereines Brunn 4: 3–17.
Mendell, NR, Spence, MA, Gladstien, K, et al. (1980). Multifactorial/threshold models and their application to cleft lip and cleft palate. In: Etiology of Cleft Lip and Cleft Palate, edited by M Melnick, D Bixler, and ED Shields. New York: Alan R. Liss, pp. 387–406.
Mitchell, LE, Christensen, K (1996). Analysis of the recurrence patterns for nonsyndromic cleft lip with or without cleft palate in the families of 3,073 Danish probands. Am J Med Genet 61: 371–376.
Mitchell, LE, Risch, N (1992). Mode of inheritance nonsyndromic cleft lip with or without cleft palate: a reanalysis. Am J Hum Genet 51: 323–332.
Moore, GE, Ivens, A, Chambers, J, et al. (1987). Linkage of an X-chromosome cleft palate gene. Nature 326: 91–92.
Moore, GE, Williamson, R, Jensson, O, et al. (1991). Localization of a mutant gene for cleft palate and ankyloglossia in an X-linked Icelandic family. J Craniofac Genet Dev Biol 11: 372–376.
Morton, NE (1959). Genetic tests under incomplete ascertainment. Am J Hum Genet 11: 1–16.
Morton, NE (1982). Outline of Genetic Epidemiology. New York: Karger.
Morton, NE, MacLean, CJ (1974). Analysis of family resemblance. III. Complex segregation of quantitative traits. Am J Hum Genet 26: 489–503.
Morton, NE, Rao, DC, Lalouel, JM (1983). Methods in Genetic Epidemiology. Basel: Karger.
Murray, JC (1995). Face facts: genes, environment, and clefts. Am J Med Genet 57: 227–232.
Nemana, LJ, Marazita, ML, Melnick, M (1992). Genetic analysis of cleft lip with or without cleft palate in Madras, India. Am J Med Genet 42: 5–9.
Ott, J (1991). Analysis of Human Genetic Linkage, rev. ed. Baltimore: Johns Hopkins University Press.
Palomino, H, Cerda-Flores, R, Blanco, R, et al. (1997). Complex segregation analysis of facial clefting in Chile. J Craniofac Genet Dev Biol 17: 57–64.
Palomino, H, Li, SC, Palomino, HM, et al. (1991). Complex segregation analysis of facial clefting in Chile. Am J Med Genet Suppl 49: 154.
Ray, AK, Field, LL, Marazita, ML (1993). Nonsyndromic cleft lip with or without cleft palate in West Bengal, India: evidence for an autosomal major locus. Am J Hum Genet 52: 1006–1011.
Rischbieth, H (1910). Hare-lip and cleft palate. In: Treasury of Human Inheritance. Part IV, edited by K Pearson. London: Dulau, pp 79–123.
Rollnick, BR, Kaye, CI (1986). Mendelian inheritance of isolated nonsyndromic cleft palate. Am J Med Genet 24: 465–473.
Rollnick, BR, Kaye, CI (1987). A response: a further X-linked isolated nonsyndromic cleft palate family with a nonexpressing obligate affected male. Am J Med Genet 26: 241.
Rushton, AR (1979). Sex-linked inheritance of cleft palate. Hum Genet 48: 179–181.
Scapoli, C, Collins, A, Martinelli, M, et al. (1999). Combined segregation and linkage analysis of nonsyndromic orofacial cleft in two candidate regions. Am J Hum Genet 63: 17–25.
Spence, MA, Westlake, J, Lange, K, Gold, DP (1976). Estimation of polygenic recurrence risk for cleft lip and palate. Hum Hered 26: 327–336.
Sproule, J (1863). Hereditary nature of hare-lip. BMJ 1: 412.
Tanaka, K, Fujino, H, Fujita, Y, et al. (1969). Cleft lip and palate: some evidence for multifactorial trait and estimation of heritability based upon Japanese data. Jinrui Idengaku Zasshi 14: 1–9.
Temple, K, Calvert, M, Flint, D, et al. (1989). Dominantly inherited cleft lip and palate in two families. J Med Genet 26: 386–389.
Terwilliger, JD, Ott, J (1994). Handbook of Human Genetic Linkage. Baltimore: Johns Hopkins University Press.
Thompson, MW, Mclnnes, RR, Willard, HF (1991). Thompson and Thompson: Genetics in Medicine, 5th ed. Philadelphia: W.B. Saunders.
Trew, CJ (1757). Sistens plura exempla palati deficientis. Nova Acta Physico-Medica Academiae caesarae Leopoldion-Carolinae 1: 445–447.
Vieland, VJ, Hodge, SE (1995). Inherent intractability of the ascertainment problem for pedigree data: a general likelihood frame-work. Am J Hum Genet 56: 33–43.
Ward, RE, Bixler, D, Jamison, PL (1994). Cephalometric evidence for a dominantly inherited predisposition to cleft lip-cleft palate in a single large kindred. Am J Hum Genet 50: 57–63.
Weinberg, W (1912). Methode und fellerquellen der untersuhung auf Mendelsche Zahlen beim Menschen. Arch Rass Ges Biol 6: 165–174.
Weinberg, W (1927). Mathematische grundlagen der probanden-methode. Z Induktive Abstammungs Vererbungslehre 48: 179–228.
Weldon, WFR (1902). Mendel's laws of alternative inheritance in peas. Biometrika 1: 228–254.
Wentzlaff, KA, Cooper, ME, Yang, P, et al. (1997). Association between non-right-handedness and cleft lip with or without cleft palate in a Chinese population. J Craniofac Genet Dev Biol 17: 141–147.
Woolf, CM, Woolf, RM, Broadbent, TR (1963). A genetic study of cleft lip and palate in Utah. Am J Hum Genet 25: 209–215.
Woolf, CM, Woolf, RM, Broadbent, TR (1964). Cleft lip and heredity. Plast Reconstr Surg 34: 11–14.
Wright, S (1968). Evolution and the genetics of populations. Genetic and biometric foundations, Vol. 1. Chicago: University of Chicago Press.