Power calculations for the transmission/disequilibrium and affected sib pair tests using elementary probability methods

The transmission/disequilibrium test (TDT) and the affected sib pair test (ASP) both test for the association of a marker allele with some conditions. Here, we present methods for calculating the probability of detecting the association (power) for a study examining a fixed number of families for suitability for the study and for calculating the number of such families to be examined. Both calculations use a genetic model for the association. The model considered posits a bi-allelic marker locus that is linked to a bi-allelic disease locus with a possibly nonzero recombination fraction between the loci. The penetrance of the disease is an increasing function of the number of disease alleles. The TDT tests whether the transmission by a heterozygous parent of a particular allele at a marker locus to an affected offspring occurs with probability greater than 0.5. The ASP tests whether transmission of the same allele to two affected sibs occurs with probability greater than 0.5. In either case, evidence that the probability is greater than 0.5 is evidence for association between the marker and the disease. Study inclusion criteria (IC) can greatly affect the necessary sample size of a TDT or ASP study. IC considered by us include a randomly selected parent at least one parent or both parents required to be heterozygous. It also allows a specified minimum number of affected offspring to be required (TDT only). We use elementary probability calculations rather than complex mathematical manipulations or asymptotic methods (large sample size approximations) to compute power and requisite sample size for a proposed study. The advantages of these methods are simplicity and generality.     

Experimental verification of microsatellite null alleles in Norway spruce (Picea abies [L.] Karst.): Implications for population genetic studies

Three stands ofPicea abies [L.] Karst. with different density in the Harz Mountains (Lower Saxony, Germany) were characterized at 4 microsatellite loci. An excess of homozygotes was observed in all 3 stands at 1 simple sequence repeat (SSR) locus, suggesting the presence of null alleles. To test for the segregation of a null allele, 24 openpollinated seeds (haploid megagametophytes and embryos) from apparently homozygous mother trees were analyzed. For 1 of 3 trees that could be identified as heterozygous for a null allele, no significant deviation from the expected 1∶1 segregation into marker absence (null allele) and marker presence of the second maternal allele could be observed in the haploid megagametophyte. Concordantly, the numbers of embryos heterozygous for the null allele and for the other maternal allele were not significantly different from each other. Inheritance analyses in seedlings and corresponding megagametophytes of gymnosperms were used as a direct experimental verification of microsatellite null alleles in single-tree progeny. Microsatellites with an abundance of null alleles should be discarded from further analysis because inclusion of these loci results in incorrect estimation of allele frequencies.     

Transferrin subtypes and variants in Germany; Further evidence for a Tf null allele

Summary Isoelectric focusing (IEF) with carrier ampholytes was used for the determination of transferrin C subtypes and transferrin B and D variants in a sample of 1125 unrelated individuals from Southern Germany. The observed TfC allele frequencies were Tf*C1=0.7872, Tf*C2=0.1365, and Tf*C3=0.0675. The rare C subtype C6 was observed twice. A new C subtype, called C10, was observed and identified by IEF with immobilized pH gradients. The rare C subtypes C4 and C8 were also studied by this method. TfB and TfD variants were found with a heterozygous frequency of 1.53%. One new TfD was found which is located between D1 and D2 and therefore named D1-2. Evidence for a Tf null allele was obtained in a child and the putative father; they were considered to be heterozygous for an allele Tf0. The theoretical exclusion rate for paternity examinations was calculated for the Tf system and found to be 17.95%.     

Differential allelic expression of the type II collagen gene (COL2A1) in osteoarthritic cartilage.

Osteoarthritis (OA) is a common debilitating disease resulting from the degeneration of articular cartilage. The major protein of cartilage is type II collagen, which is encoded by the COL2A1 gene. Mutations at this locus have been discovered in several individuals with inherited disorders of cartilage. We have identified 27 primary OA patients who are heterozygous for sequence dimorphisms located in the coding region of COL2A1. These dimorphisms were used to distinguish the mRNA output from each of the two COL2A1 alleles in articular cartilage obtained from each patient. Three patients demonstrated differential allelic expression and produced < 12% of the normal level of mRNA from one of their COL2A1 alleles. The same allele shows reduced expression in all three patients, and this allele is more frequent in a well-defined OA population than in a control group, suggesting the possible existence of a rare COL2A1 allele that predisposes to OA.     

A pseudodeficiency allele common in non-Jewish Tay-Sachs carriers: Implications for carrier screening

Deficiency of beta-hexosaminidase A (Hex A) activity typically results in Tay-Sachs disease. However, healthy subjects found to be deficient in Hex A activity (i.e., pseudodeficient) by means of in vitro biochemical tests have been described. We analyzed the HEXA gene of one pseudodeficient subject and identified both a C739-to-T substitution that changes Arg247----Trp on one allele and a previously identified Tay-Sachs disease mutation on the second allele. Six additional pseudodeficient subjects were found to have the C739-to-T mutation. This allele accounted for 32% (20/62) of non-Jewish enzyme-defined Tay-Sachs disease carriers but for none of 36 Jewish enzyme-defined carriers who did not have one of three known mutations common to this group. The C739-to-T allele, together with a "true" Tay-Sachs disease allele, causes Hex A pseudodeficiency. Given both the large proportion of non-Jewish carriers with this allele and that standard biochemical screening cannot differentiate between heterozygotes for the C739-to-T mutations and Tay-Sachs disease carriers, DNA testing for this mutation in at-risk couples is essential. This could prevent unnecessary or incorrect prenatal diagnoses.     

A robust method using propensity score stratification for correcting verification bias for binary tests

Sensitivity and specificity are common measures of the accuracy of a diagnostic test. The usual estimators of these quantities are unbiased if data on the diagnostic test result and the true disease status are obtained from all subjects in an appropriately selected sample. In some studies, verification of the true disease status is performed only for a subset of subjects, possibly depending on the result of the diagnostic test and other characteristics of the subjects. Estimators of sensitivity and specificity based on this subset of subjects are typically biased; this is known as verification bias. Methods have been proposed to correct verification bias under the assumption that the missing data on disease status are missing at random (MAR), that is, the probability of missingness depends on the true (missing) disease status only through the test result and observed covariate information. When some of the covariates are continuous, or the number of covariates is relatively large, the existing methods require parametric models for the probability of disease or the probability of verification (given the test result and covariates), and hence are subject to model misspecification. We propose a new method for correcting verification bias based on the propensity score, defined as the predicted probability of verification given the test result and observed covariates. This is estimated separately for those with positive and negative test results. The new method classifies the verified sample into several subsamples that have homogeneous propensity scores and allows correction for verification bias. Simulation studies demonstrate that the new estimators are more robust to model misspecification than existing methods, but still perform well when the models for the probability of disease and probability of verification are correctly specified.     

Rapid and direct detection of the most frequent Mediterranean beta-thalassemic mutations by multiplex allele-specific enzymatic amplification.

A rapid nonradioactive method for the diagnosis of the most frequent Mediterranean beta-thalassemic mutations is described based on a multiplex allele-specific polymerase chain reaction (PCR). This method allows direct detection of normal or mutated alleles on genomic DNA. We have used this approach to detect the most frequent Mediterranean mutations: IVS-1 nt 110 (G----A) and 39 nonsense (C----T). For each mutation three allele-specific oligonucleotides were used: one common upstream primer and two downstream primers differing in their terminal 3' nucleotide (one specific for the normal allele and one for the mutant allele). For each sample two PCR reactions were performed in parallel using in one case IVS-1 nt 110 and codon 39 normal primers and in the second case using the corresponding mutated primers. In both cases the different PCR fragments were visualized. After optimization these primers directed only amplification of their complementary allele. A single blind study was performed on the DNA of 18 individuals who were homozygous or heterozygous for these mutations. In comparison with a parallel investigation, using oligonucleotide probes, all the results were unambiguous. This diagnosis method, which is rapid, easy, direct, and inexpensive, allows the screening of a population group, including heterozygotes, which is required from an epidemiological and anthropological point of view. It could be extended to the large series screening of haplotypes before targeted diagnosis of various genetic diseases.     

Two-stage designs in case-control association analysis

DNA pooling is a cost-effective approach for collecting information on marker allele frequency in genetic studies. It is often suggested as a screening tool to identify a subset of candidate markers from a very large number of markers to be followed up by more accurate and informative individual genotyping. In this article, we investigate several statistical properties and design issues related to this two-stage design, including the selection of the candidate markers for second-stage analysis, statistical power of this design, and the probability that truly disease-associated markers are ranked among the top after second-stage analysis. We have derived analytical results on the proportion of markers to be selected for second-stage analysis. For example, to detect disease-associated markers with an allele frequency difference of 0.05 between the cases and controls through an initial sample of 1000 cases and 1000 controls, our results suggest that when the measurement errors are small (0.005), approximately 3% of the markers should be selected. For the statistical power to identify disease-associated markers, we find that the measurement errors associated with DNA pooling have little effect on its power. This is in contrast to the one-stage pooling scheme where measurement errors may have large effect on statistical power. As for the probability that the disease-associated markers are ranked among the top in the second stage, we show that there is a high probability that at least one disease-associated marker is ranked among the top when the allele frequency differences between the cases and controls are not <0.05 for reasonably large sample sizes, even though the errors associated with DNA pooling in the first stage are not small. Therefore, the two-stage design with DNA pooling as a screening tool offers an efficient strategy in genomewide association studies, even when the measurement errors associated with DNA pooling are nonnegligible. For any disease model, we find that all the statistical results essentially depend on the population allele frequency and the allele frequency differences between the cases and controls at the disease-associated markers. The general conclusions hold whether the second stage uses an entirely independent sample or includes both the samples used in the first stage and an independent set of samples.     

Prediction of individual genetic risk of complex disease

Most common diseases are caused by multiple genetic and environmental factors. In the last 2 years, genome-wide association studies (GWAS) have identified polymorphisms that are associated with risk to common disease, but the effect of any one risk allele is typically small. By combining information from many risk variants, will it be possible to predict accurately each individual person's genetic risk for a disease? In this review we consider the lessons from GWAS and the implications for genetic risk prediction to common disease. We conclude that with larger GWAS sample sizes or by combining studies, accurate prediction of genetic risk will be possible, even if the causal mutations or the mechanisms by which they affect susceptibility are unknown.     

Digenic junctional epidermolysis bullosa: mutations in COL17A1 and LAMB3 genes

Junctional epidermolysis bullosa (JEB), a genetically heterogeneous group of blistering skin diseases, can be caused by mutations in the genes encoding laminin 5 or collagen XVII, which are components of the hemidesmosome-anchoring filament complex in the skin. Here, a family with severe nonlethal JEB and with mutations in genes for both proteins was identified. The index patient was compound heterozygous for the COL17A1 mutations L855X and R1226X and was heterozygous for the LAMB3 mutation R635X. As a consequence, two functionally related proteins were affected. Absence of collagen XVII and attenuated laminin 5 expression resulted in rudimentary hemidesmosome structure and separation of the epidermis from the basement membrane, with severe skin blistering as the clinical manifestation. In contrast, single heterozygotes carrying either (1) one or the other of the COL17A1 null alleles or (2) a double heterozygote for a COL17A1 and a LAMB3 null allele did not have a pathological skin phenotype. These observations indicate that the known allelic heterogeneity in JEB is further complicated by interactions between unlinked mutations. They also demonstrate that identification of one mutation in one gene is not sufficient for determination of the genetic basis of JEB in a given family.     

A missense mutation in the endothelin-B receptor gene is associated with Lethal White Foal Syndrome: an equine version of Hirschsprung Disease

Lethal White Foal Syndrome is a disease associated with horse breeds that register white coat spotting patterns. Breedings between particular spotted horses, generally described as frame overo, produce some foals that, in contrast to their parents, are all white or nearly all white and die shortly after birth of severe intestinal blockage. These foals have aganglionosis characterized by a lack of submucosal and myenteric ganglia from the distal small intestine to the large intestine, similar to human Hirschsprung Disease. Some sporadic and familial cases of Hirschsprung Disease are due to mutations in the endothelin B receptor gene (EDNRB). In this study, we investigate the role of EDNRB in Lethal White Foal Syndrome. A cDNA for the wild-type horse endothelin-B receptor gene was cloned and sequenced. In three unrelated lethal white foals, the EDNRB gene contained a 2-bp nucleotide change leading to a missense mutation (I118K) in the first transmembrane domain of the receptor, a highly conserved region of this protein among different species. Seven additional unrelated lethal white foal samples were found to be homozygous for this mutation. No other homozygotes were identified in 138 samples analyzed, suggesting that homozygosity was restricted to lethal white foals. All (40/40) horses with the frame overo pattern (a distinct coat color pattern that is a subset of overo horses) that were tested were heterozygous for this allele, defining a heterozygous coat color phenotype for this mutation. Horses with tobiano markings included some carriers, indicating that tobiano is epistatic to frame overo. In addition, horses were identified that were carriers but had no recognized overo coat pattern phenotype, demonstrating the variable penetrance of the mutation. The test for this mutant allele can be utilized in all breeds where heterozygous animals may be unknowingly bred to each other including the Paint Horse, Pinto horse, Quarter Horse, Miniature Horse, and Thoroughbred. Received: 25 November 1997 / Accepted: 3 February 1998     

Genetic dissection of nodal function in patterning the mouse embryo

Loss-of-function analysis has shown that the transforming growth factor-like signaling molecule nodal is essential for mouse mesoderm development. However, definitive proof of nodal function in other developmental processes in the mouse embryo has been lacking because the null mutation blocks gastrulation. We describe the generation and analysis of a hypomorphic nodal allele. Mouse embryos heterozygous for the hypomorphic allele and a null allele undergo gastrulation but then display abnormalities that fall into three distinct mutant phenotypic classes, which may result from expression levels falling below critical thresholds in one or more domains of nodal expression. Our analysis of each of these classes provides conclusive evidence for nodal-mediated regulation of several developmental processes in the mouse embryo, beyond its role in mesoderm formation. We find that nodal signaling is required for correct positioning of the anteroposterior axis, normal anterior and midline patterning, and the left-right asymmetric development of the heart, vasculature, lungs and stomach.     

Estimating null allele frequencies at a microsatellite locus in the oystercatcher (Haematopus ostralegus)

A significant heterozygote deficiency was found for microsatellite locus 20H7 among adult breeding birds in four populations of the oystercatcher ( Haematopus ostralegus ). Genotype frequencies at seven other loci were according to Hardy–Weinberg equilibria. Deviations between observed and expected genotype numbers decreased substantially when the data were corrected based on the estimated frequency of a putative null allele at locus 20H7 . However, no null homozygotes were observed in the total sample of 378 individuals. The probability that, because of chance effects, null homozygotes were not represented in the sample ( n =230) from the most intensively studied population (Schiermonnikoog) was estimated to be less than 1%. Parent–offspring comparisons from Schiermonnikoog showed that observed genotype numbers in the offspring were in accordance with expected values based on the estimated frequency of the putative null allele in the population. Moreover, a null homozygote was observed among the nestlings. The combined results indicated that a null allele is present at locus 20H7 in oystercatchers and that the inheritance is according to normal Mendelian segregation. If the absence of null homozygotes among adult animals cannot be ascribed to statistical effects, null homozygotes may suffer a selective disadvantage during the juvenile stage.     

Statistical genetic considerations for maintaining germ plasm collections

One objective of the regeneration of genetic populations is to maintain at least one copy of each allele present in the original population. Genetic diversity within populations depends on the number and frequency of alleles across all loci. The objectives of this study on outbreeding crops are: (1) to use probability models to determine optimal sample sizes for the regeneration for a number of alleles at independent loci; and (2) to examine theoretical considerations in choosing core subsets of a collection. If we assume that k-1 alleles occur at an identical low frequency of p₀ and that the k^th allele occurs at a frequency of 1-[(k-1)p₀], for loci with two, three, or four alleles, each with a p₀ of 0.05, 89–110 additional individuals are required if at least one allele at each of 10 loci is to be retained with a 90% probability; if 100 loci are involved, 134–155 individuals are required. For two, three, or four alleles, when p₀ is 0.03 at each of 10 loci, the sample size required to include at least one of the alleles from each class in each locus is 150–186 individuals; if 100 loci are involved, 75 additional individuals are required. Sample sizes of 160–210 plants are required to capture alleles at frequencies of 0.05 or higher in each of 150 loci, with a 90–95% probability. For rare alleles widespread throughout the collection, most alleles with frequencies of 0.03 and 0.05 per locus will be included in a core subset of 25–100 accessions.     

Generation of a Twist1 conditional null allele in the mouse

Twist1 is the mouse ortholog of TWIST1, the human gene mutated in Saethre-Chotzen syndrome. Previously, a Twist1 null allele was generated by gene targeting in mouse embryonic stem cells. Twist1 heterozygous mice develop polydactyly and a craniofacial phenotype similar to Saethre-Chotzen patients. Mice homozygous for the Twist1 null allele die around embryonic day 11.5 (E11.5) with cranial neural tube closure and vascular defects, hindering in vivo studies of Twist1 function at later stages of development. Here, we report the generation of a Twist1 conditional null allele in mice that functions like a wild-type allele but can be converted to a null allele upon Cre-mediated recombination.     

Analysis of meiotic segregation, using single-sperm typing: meiotic drive at the myotonic dystrophy locus.

Meiotic drive at the myotonic dystrophy (DM) locus has recently been suggested as being responsible for maintaining the frequency, in the human population, of DM chromosomes capable of expansion to the disease state. In order to test this hypothesis, we have studied samples of single sperm from three individuals heterozygous at the DM locus, each with one allele larger and one allele smaller than 19 CTG repeats. To guard against the possible problem of differential PCR amplification rates based on the lengths of the alleles, the sperm were also typed at another closely linked marker whose allele size was unrelated to the allele size at the DM locus. Using statistical models specifically designed to study single-sperm segregation data, we find no evidence of meiotic segregation distortion. The upper limit of the two-sided 95% confidence interval for the estimate of the common segregation probability for the three donors is at or below .515 for all models considered, and no statistically significant difference from .5 is detected in any of the models. This suggests that any greater amount of segregation distortion at the myotonic dystrophy locus must result from events following sperm ejaculation. The mathematical models developed make it possible to study segregation distortion with high resolution by using sperm-typing data from any locus.     

Alpha 1-antitrypsin Null(isola di procida): an alpha 1-antitrypsin deficiency allele caused by deletion of all alpha 1-antitrypsin coding exons.

alpha 1-Antitrypsin (alpha 1AT) deficiency, a common hereditary disorder responsible for emphysema in Caucasians of northern European descent, is caused by single base substitutions, deletions, or additions in the seven exons (IA-IC and II-V), of the 12.2-kb alpha 1AT gene located on chromosome 14 at q31-32.3. Of the five known representatives of the "null" group of alpha 1AT-deficiency alleles (alpha 1AT genes incapable of producing alpha 1AT protein detectable in serum) evaluated at the gene level, all result from mutations causing the formation of stop codons in coding exons of the alpha 1AT gene. The present study identifies an alpha 1AT allele (referred to as "Null(isola di procida")) caused by complete deletion of the alpha 1AT coding exons. The Null(isola di procida) allele was identified in an individual with heterozygous inheritance of M(procida) (an allele associated with alpha 1AT deficiency) and a null allele. Although results of karyotypic analysis were normal, quantification of the copies of alpha 1AT genes in this individual revealed that the index case had only half the normal copies of alpha 1AT genes. Cloning and mapping of the Null(isola di procida) gene demonstrated a deletion of a 17-kb fragment that included exons II-V of the alpha 1AT structural gene. As a consequence of the deletion, the normal noncoding exons (IA-IC) were followed by exons II-V of the downstream alpha 1AT-like gene. Sequence analysis of the deletion demonstrated a 7-bp repeat sequence (GAGGACA) both 5' to the deletion and at the 3' end of the deletion, a 4-bp palindromic sequence (ACAG vs. CTGT) bracketing the deletion, and a novel inserted 4-bp sequence (CCTG) at the breakpoint, suggesting that the mechanism of the deletion may have been "slipped mispairing."     

Genetic heterogeneity in adenosine deaminase (ADA) deficiency: five different mutations in five new patients with partial ADA deficiency.

Complete genetic deficiency of adenosine deaminase (ADA) results in a fatal syndrome of severe combined immunodeficiency (SCID). Genetic partial deficiency of ADA, with no detectable enzyme activity in erythrocytes but with variable amounts of enzyme activity detectable in other cells, is usually associated with normal immunologic function but can give rise to a late-onset, cellular immunodeficiency syndrome. We have previously described four different mutant alleles in four such partially ADA-deficient children. We have now examined ADA in lymphoid cells from five additional newly ascertained children with partial ADA deficiency with respect to electrophoretic mobility in starch gel, isoelectric point, heat-stability, and apparent Km and Vmax. These techniques identify at least five different abnormal alleles in these five additional unrelated subjects. Three of these abnormal alleles result in expression of abnormal allelic isozymes (allozymes) different from those previously described. These are: (1) an acidic allozyme that is less acidic than the acidic allozyme we have previously reported; (2) an allozyme that is even less acidic than (1); and (3) an allozyme with apparently normal charge but which is so heat sensitive that the lability to heat can easily be detected at physiologic to febrile temperatures. Two abnormal alleles detected in these five children could correspond with previously reported mutants. These are (4) a basic allozyme that could (but probably doesn't) correspond to the basic allozyme we have previously reported and (5) a "null" allele that cannot be differentiated by these methods from any other "null" allele seen in complete ADA- -SCIDs. Three of the five new patients are genetic compounds, identified either by the presence of two electrophoretically distinguishable allozymes or by family studies that demonstrate presence of a "null" allele in addition to an electrophoretically abnormal allozyme. In three patients, one or both allozymes are phenotypically indistinguishable from an abnormal allozyme also seen in a different individual. Determination of the nucleotide sequence will be required to determine whether or not the phenotypically indistinguishable mutations are indeed genotypically identical. The newly ascertained individuals appear to share a common ethnic West Indian background, out of proportion to the frequency of this ethnic background in the newborn population from which they were ascertained, suggesting that partial ADA deficiency may confer a selective advantage to the homozygous or heterozygous phenotype.     

Alpha-1-antitrypsin and transferrin null alleles in the Portuguese population

In a Portuguese family, a null allele was found in the Pi system. An apparent 'exclusion' of the mother was found to be due to the presence of null alleles in mother and child. A transferrin (Tf) null allele was found in a case of disputed paternity. The mother and putative father were heterozygous for Tf null alleles and the child was homozygous (TfQ0) and presented hypotransferrinemia.     

Linkage disequilibrium between an allele at the dopamine D4 receptor locus and Tourette syndrome, by the transmission-disequilibrium test.

Dopaminergic abnormalities are implicated in the pathogenesis of Tourette syndrome (TS) and chronic multiple tics. We used the transmission-disequilibrium test (TDT) method to test for linkage disequilibrium between a specific allele (the seven-repeat allele (DRD4*7R) of the exon 3 VNTR polymorphic site) at the D4 dopamine receptor locus (DRD4) and expression of chronic multiple tics and TS. This particular allele had been shown in functional studies to have different binding properties compared with the other common alleles in this DRD4 polymorphic system. We studied 64 family trios (consisting of an affected person and two parents, at least one heterozygous for DRD4*7R), including 12 nuclear family trios and 52 trios from four large TS kindreds. The DRD4*7R allele was transmitted significantly more frequently than expected (chi 2 TDT ranging from 8.47 [P < .004] to 10.80 [P = .001], depending on breadth of disease definition and inclusion or exclusion of inferred genotypes). Confirmation of this finding will depend on either replication in other samples or the identification of a transmitted functional mutation within this sample.