Parental Mating Types Research Articles

Conditioning on parental mating types can reduce necessary assumptions for Mendelian randomization.

Mendelian randomization (MR) has become a common tool used in epidemiological studies. However, when confounding variables are correlated with the instrumental variable (in this case, a genetic/variant/marker), the estimation can remain biased even with MR. We propose conditioning on parental mating types (a function of parental genotypes) in MR to eliminate the need for one set of assumptions, thereby plausibly reducing such bias. We illustrate a situation in which the instrumental variable and confounding variables are correlated using two unlinked diallelic genetic loci: one, an instrumental variable and the other, a confounding variable. Assortative mating or population admixture can create an association between the two unlinked loci, which can violate one of the necessary assumptions for MR. We simulated datasets involving assortative mating and population admixture and analyzed them using three different methods: 1) conventional MR, 2) MR conditioning on parental genotypes, and 3) MR conditioning on parental mating types. We demonstrated that conventional MR leads to type I error rate inflation and biased estimates for cases with assortative mating or population admixtures. In the presence of non-additive effects, MR with an adjustment for parental genotypes only partially reduced the type I error rate inflation and bias. In contrast, conditioning on parental mating types in MR eliminated the type I error inflation and bias under these circumstances. Conditioning on parental mating types is a useful strategy to reduce the burden of assumptions and the potential bias in MR when the correlation between the instrument variable and confounders is due to assortative mating or population stratification but not linkage.

Frequency and distribution of GJB2 (connexin 26) and GJB6 (connexin 30) mutations in a large North American repository of deaf probands

Purpose: Profound hearing loss occurs with a frequency of 1 in 1000 live births, half of which is genetic in etiology. The past decade has witnessed rapid advances in determining the pathogenesis of both syndromic and nonsyndromic deafness. The most significant clinical finding to date has been the discovery that mutations of GJB2 at the DFNB1 locus are the major cause of profound prelingual deafness in many countries.1 More recently, GJB2 mutations have been shown to cause deafness when present with a deletion of the GJB6 gene. We report on the prevalence of GJB2 and GJB6 mutations in a large North American Repository of DNA from deaf probands and document the profound effects of familial ethnicity and parental mating types on the frequency of these mutations in the population.Methods: Deaf probands were ascertained through the Annual Survey of Deaf and Hard of Hearing Children and Youth, conducted at the Research Institute of Gallaudet University. Educational, etiologic, and audiologic information was collected after obtaining informed consent. DNA studies were performed for the GJB2 and GJB6 loci by sequencing and PCR methods.Results: GJB2 mutations accounted for 22.2% of deafness in the overall sample but differed significantly among Asians, African-Americans and Hispanics and for probands from deaf by deaf and deaf by hearing matings, as well as probands from simplex and multiplex sibships of hearing parents. In our sample, the overall incidence of GJB2/GJB6 deafness was 2.57%.Conclusion: GJB2 mutations account for a large proportion of deafness in the US, with certain mutations having a high ethnic predilection. Heterozygotes at the GJB2 locus should be screened for the GJB6 deletion as a cause of deafness. Molecular testing for GJB2 and GJB6 should be offered to all patients with nonsyndromic hearing loss.

Self-fertility in Chromocrea spinulosa is a consequence of direct repeat-mediated loss of MAT1-2, subsequent imbalance of nuclei differing in mating type, and recognition between unlike nuclei in a common cytoplasm.

The filamentous fungus Chromocrea spinulosa (Trichoderma spinulosum) exhibits both self-fertile (homothallic) and self-sterile (heterothallic) sexual reproductive behavior. Self-fertile strains produce progeny cohorts that are 50% homothallic, 50% heterothallic. Heterothallic progeny can mate only with homothallic strains, and progeny also segregate 50% homothallic, 50% heterothallic. Sequencing of the mating type (MAT) region of homothallic and heterothallic strains revealed that both carry an intact MAT1-1 locus with three MAT1-1 genes (MAT1-1-1, MAT1-1-2, MAT1-1-3), as previously described for the Sordariomycete group of filamentous fungi. Homothallic strains, however, have a second version of MAT with the MAT1-2 locus genetically linked to MAT1-1. In this version, the MAT1-1-1 open reading frame is split into a large and small fragment and the truncated ends are bordered by 115bp direct repeats (DR). The MAT1-2-1 gene and additional sequences are inserted between the repeats. To understand the mechanism whereby C. spinulosa can exhibit both homothallic and heterothallic behavior, we utilized molecular manipulation to delete one of the DRs from a homothallic strain and insert MAT1-2 into a heterothallic strain. Mating assays indicated that: i) the DRs are key to homothallic behavior, ii) looping out of MAT1-2-1 via intra-molecular homologous recombination between the DRs in self-fertile strains results in two nuclear types in an individual (one carrying both MAT1-1 and MAT1-2 and one carrying MAT1-1 only), iii) self-fertility is achieved by inter-nuclear recognition between these two nuclear types before meiosis, iv) the two types of nuclei are in unequal proportion, v) having both an intact MAT1-1-1 and MAT1-2-1 gene in a single nucleus is not sufficient for self-fertility, and vi) the large truncated MAT1-1-1 fragment is expressed. Comparisons with MAT regions of Trichoderma reesei and Trichoderma virens suggest that several crossovers between misaligned parental MAT chromosomes may have led to the MAT architecture of homothallic C. spinulosa.

Family-based association test using both common and rare variants and accounting for directions of effects for sequencing data.

Current family-based association tests for sequencing data were mainly developed for identifying rare variants associated with a complex disease. As the disease can be influenced by the joint effects of common and rare variants, common variants with modest effects may not be identified by the methods focusing on rare variants. Moreover, variants can have risk, neutral, or protective effects. Association tests that can effectively select groups of common and rare variants that are likely to be causal and consider the directions of effects have become important. We developed the Ordered Subset - Variable Threshold - Pedigree Disequilibrium Test (OVPDT), a combination of three algorithms, for association analysis in family sequencing data. The ordered subset algorithm is used to select a subset of common variants based on their relative risks, calculated using only parental mating types. The variable threshold algorithm is used to search for an optimal allele frequency threshold such that rare variants below the threshold are more likely to be causal. The PDT statistics from both rare and common variants selected by the two algorithms are combined as the OVPDT statistic. A permutation procedure is used in OVPDT to calculate the p-value. We used simulations to demonstrate that OVPDT has the correct type I error rates under different scenarios and compared the power of OVPDT with two other family-based association tests. The results suggested that OVPDT can have more power than the other tests if both common and rare variants have effects on the disease in a region.

Epigenetics: Keeping one's sex.

Progeny of the protist Paramecium tetraurelia always retain the parental mating type. This inheritance is revealed to result from an RNA-guided DNA-deletion pathway that protects the genome from foreign DNA sequences. See Article p.447 The protozoan Paramecium, widely studied as a typical ciliate, multiplies asexually by binary fission much of the time, but under certain conditions will reproduce sexually. Two mating types, E and O, were discovered in 1937 but only now has the molecular basis for maternal inheritance of mating type been elucidated. Eric Meyer and colleagues show in Paramecium tetraurelia that mating type E depends on expression of the transmembrane protein mtA, and the default type O is determined during development by excision of the mtA promoter by scnRNAs, a class of small 'scan' RNA that reprograms the Paramecium genome during sexual reproduction by recognizing and excising transposable elements. A similar switch mechanism, involving a different gene, mtB, has evolved independently in a sibling species P. septaurelia, implying that exaptation of the scnRNA pathway may be a general mechanism for transgenerational epigenetic inheritance of differentiated states in Paramecium.

Genotyping Without Phenotyping

Genotyping Without Phenotyping

First Evidence of a Polygenic Susceptibility to Pain in a Pediatric Cohort

There is currently no evidence about the genetic bases of postoperative pain variability in children. We prospectively followed a cohort of 168 children after orthopedic or abdominal surgery, who were under morphine patient-controlled analgesia. The children and their parents were genotyped for 6 candidate-gene polymorphisms (single-nucleotide polymorphisms [SNPs]) implicated in nociception and opiate metabolism: ABCB1C3435T, COMTVal158Met, NTRK1His40Tyr, OPRMA118G, POMCArg236Gln, and a haplotype of CYP2D6. Postoperative pain was assessed using the Faces Pain Scale (FPS), at rest and during mobilization, 11 times during the first 24 postoperative hours. At rest, and to a lesser extent, at mobilization, having at least 4 pain peaks of FPS score >6 in 24 hours was more frequent in children with ABCB1_CC than in children with ABCB1_CT and ABCB1_TT (adjusted risk ratio = 4.5; 95% confidence interval [CI],1.5-13.4; corrected CI for multiple comparisons, 0.98-20.55) and was more frequent in children with OPRM_GA than those with OPRM_AA (adjusted risk ratio = 3.5; 95% CI, 1.1-11.2; corrected CI, 0.70-17.30). After adjusting for parental mating type and correcting for multiple comparisons, mean FPS scores across the 24 postoperative hours were higher for OPRM_GA than for OPRM_AA at rest (P < 0.0002), higher for NTRK1_ CT or NTRK1_ TT than NTRK1_ CC during mobilization (P = 0.002), and lower for COMT_GG than COMT_AA and COMT_GA, during mobilization (P = 0.005). ABCB1 and OPRM genotypes are associated with clinically meaningful pain variability, whereas NTRK1 and COMT are linked to subclinical effects. This first but small cohort study provides clues to further explore the genetic foundations of pediatric pain.

On the Use of Allelic Transmission Rates for Assessing Gene‐by‐Environment Interaction in Case‐Parent Trios

Allelic transmission rates from parents to cases are frequently stratified by an environmental risk factor E and compared, with heterogeneity interpreted as gene-environment interaction or GxE. Though generally invalid, such analyses continue to appear. We revisit why heterogeneity is not equivalent to GxE in a range of settings not considered previously. The objective is a fuller understanding of the bias in transmission rates and what is driving it. Extending previously published findings, we derive parental mating-type probabilities in cases and use them to obtain transmission rates, which we then compare to GxE. Through simulation, we investigate the practical implications of the bias for a transmission-based test of GxE. We find that general population characteristics distort the picture of GxE obtained from transmission rates: the stratum-specific mating-type probabilities under G - E dependence and the allele frequency under independence. Furthermore, the transmission-based test has inflated error rates relative to a likelihood-based test. Our investigation provides further insight into how and why transmission-based tests and descriptive summaries can mislead about GxE. For exploring GxE, we suggest graphical displays of the transmission rates within parental mating types, as they are robust to population stratification and the penetrance model.

A doubly robust test for gene-environment interaction in family-based studies of affected offspring

We develop a locally efficient test for (multiplicative) gene-environment interaction in family studies that collect genotypic information and environmental exposures for affected offspring along with genotypic information for their parents or relatives. The proposed test does not require modeling the effects of environmental exposures and is doubly robust in the sense of being valid if either a model for the main genetic effect holds or a model for the expected environmental exposure (given the offspring affection status and parental mating types) but not necessarily both. It extends the FBAT-I to allow for missing parental mating types and families of arbitrary size. Simulation studies and the analysis of an Alzheimer's disease study confirm the adequate performance of the proposed test.

Mapping quantitative trait loci from a single-tail sample of the phenotype distribution including survival data.

A new effective Bayesian quantitative trait locus (QTL) mapping approach for the analysis of single-tail selected samples of the phenotype distribution is presented. The approach extends the affected-only tests to single-tail sampling with quantitative traits such as the log-normal survival time or censored/selected traits. A great benefit of the approach is that it enables the utilization of multiple-QTL models, is easy to incorporate into different data designs (experimental and outbred populations), and can potentially be extended to epistatic models. In inbred lines, the method exploits the fact that the parental mating type and the linkage phases (haplotypes) are known by definition. In outbred populations, two-generation data are needed, for example, selected offspring and one of the parents (the sires) in breeding material. The idea is to statistically (computationally) generate a fully complementary, maximally dissimilar, observation for each offspring in the sample. Bayesian data augmentation is then used to sample the space of possible trait values for the pseudoobservations. The benefits of the approach are illustrated using simulated data sets and a real data set on the survival of F(2) mice following infection with Listeria monocytogenes.

No evidence for a preferential transmission of the methylenetetrahydrofolate reductase 677T allele in families with schizophrenia offspring

The methylenetetrahydrofolate reductase (MTHFR) 677C > T polymorphism has been associated with an increased risk of schizophrenia in various case-control studies. However, case-control studies are sensitive to population stratification, which is not an issue in family-based studies. We conducted a family-based study comprising 120 families with a schizophrenic family member to explore the association between the parental MTHFR 677C > T polymorphism and schizophrenia risk in offspring. In addition, a meta-analysis was performed using the available studies with data on this subject. Transmission Disequilibrium Test (TDT) analysis showed no preferential transmission of the 677T allele from parents heterozygous for the MTHFR 677C > T polymorphism to schizophrenia offspring (P = 0.27). The genotype relative risks were 1.43 (95% CI: 0.83-2.47) for the 677TT and 1.42 (95% CI: 0.54-3.78) for the 677CT genotype, relative to the 677CC genotype. A meta-analysis using data from family-based studies comprising a total of 416 parent-child triads yielded no evidence implicating the 677T allele in schizophrenia risk (P = 0.58). By applying a log-linear model, we found no asymmetry within parental mating type. Our data provided no evidence that transmission of the MTHFR 677T allele is associated with schizophrenia risk. In addition, we found no evidence that the maternal genotype influences the risk of having schizophrenia offspring substantially.

Estimating the odds ratios of Crohn disease for the main CARD15/NOD2 mutations using a conditional maximum likelihood method in pedigrees collected via affected family members

Estimation of genotype-specific risks at a disease susceptibility locus is an important question that is best carried out in a prospective study. Nevertheless it is usually desirable to make use of data from the families that have already been collected to identify the susceptibility locus. Assuming that the families have been collected without regard to genotype at the locus in question, most of the information can be extracted by writing the likelihood in terms of the risk for a genotype relative to the standard genotype and conditional on the parental mating type. Parameters may then be estimated by explicit solution of likelihood equations. This method permits estimation of risks for heterozygotes and homozygotes for different alleles, testing of different modes of inheritance and heterogeneity of risk between alleles. It is applicable to risk alleles for any disease locus or incompletely penetrant phenotype. We have used the method to estimate risks of Crohn disease for different CARD/NOD2 15 mutations, using the families originally collected to identify this susceptibility locus. The odds ratio of Crohn disease were, respectively, 1.97+/-0.85, 3.05+/-* and 4.55+/-1.34 for the R702W, G9068R and 1007fs heterozygotes and 3.29+/-0.64, 12.13+/-* and 34.66+/-12.87 for the corresponding homozygotes. (* Signifies insufficient data to estimate these values.) These results confirm the dosage effect for CARD15/NOD2 mutations and demonstrate that the disease risks are very different in homozygotes. This last observation illustrates the power of this approach, especially for alleles with low or moderate frequency in the general population.

X-APL: An Improved Family-Based Test of Association in the Presence of Linkage for the X Chromosome

Family-based association methods have been developed primarily for autosomal markers. The X-linked sibling transmission/disequilibrium test (XS-TDT) and the reconstruction-combined TDT for X-chromosome markers (XRC-TDT) are the first association-based methods for testing markers on the X chromosome in family data sets. These are valid tests of association in family triads or discordant sib pairs but are not theoretically valid in multiplex families when linkage is present. Recently, XPDT and XMCPDT, modified versions of the pedigree disequilibrium test (PDT), were proposed. Like the PDT, XPDT compares genotype transmissions from parents to affected offspring or genotypes of discordant siblings; however, the XPDT can have low power if there are many missing parental genotypes. XMCPDT uses a Monte Carlo sampling approach to infer missing parental genotypes on the basis of true or estimated population allele frequencies. Although the XMCPDT was shown to be more powerful than the XPDT, variability in the statistic due to the use of an estimate of allele frequency is not properly accounted for. Here, we present a novel family-based test of association, X-APL, a modification of the test for association in the presence of linkage (APL) test. Like the APL, X-APL can use singleton or multiplex families and properly infers missing parental genotypes in linkage regions by considering identity-by-descent parameters for affected siblings. Sampling variability of parameter estimates is accounted for through a bootstrap procedure. X-APL can test individual marker loci or X-chromosome haplotypes. To allow for different penetrances in males and females, separate sex-specific tests are provided. Using simulated data, we demonstrated validity and showed that the X-APL is more powerful than alternative tests. To show its utility and to discuss interpretation in real-data analysis, we also applied the X-APL to candidate-gene data in a sample of families with Parkinson disease.

Mapping Quantitative Trait Loci in Noninbred Mosquito Crosses

The identification of genes that affect quantitative traits has been of great interest to geneticists for many decades, and many statistical methods have been developed to map quantitative trait loci (QTL). Most QTL mapping studies in experimental organisms use purely inbred lines, where the two homologous chromosomes in each individual are identical. As a result, many existing QTL mapping methods developed for experimental organisms are applicable only to genetic crosses between inbred lines. However, it may be difficult to obtain inbred lines for certain organisms, e.g., mosquitoes. Although statistical methods for QTL mapping in outbred populations, e.g., humans, can be applied for such crosses, these methods may not fully take advantage of the uniqueness of these crosses. For example, we can generally assume that the two grandparental lines are homozygous at the QTL of interest, but such information is not be utilized through methods developed for outbred populations. In addition, mating types and phases can be relatively easy to establish through the analysis of adjacent markers due to the large number of offspring that can be collected, substantially simplifying the computational need. In this article, motivated by a mosquito intercross experiment involving two selected lines that are not genetically homozygous across the genome, we develop statistical methods for QTL mapping for genetic crosses involving noninbred lines. In our procedure, we first infer parental mating types and use likelihood-based methods to infer phases in each parent on the basis of genotypes of offspring and one parent. A hidden Markov model is then employed to estimate the number of high-risk alleles at marker positions and putative QTL positions between markers in each offspring, and QTL mapping is finally conducted through the inferred QTL configuration across all offspring in all crosses. The performance of the proposed methods is assessed through simulation studies, and the usefulness of this method is demonstrated through its application to a mosquito data set.

Linkage and association analysis in pedigrees from different populations

Using the Genetic Analysis Workshop 14 simulated datasets we carried out nonparametric linkage analyses and applied a log-linear method for analysis of case-parent-triad data with stratification on parental mating type. We proposed and applied a random effect modelling approach to explore the impact of population heterogeneity on tests of association between genetic markers and disease status. The estimated genetic effect may appear to be strongly significant in one population but nonsignificant in another population, leading to confusion about interpretation. However, when results are interpreted in the light of a random effects model, both studies may be making similar statements about a genetic effect that varies depending on environment and background.

Power and Related Statistical Properties of Conditional Likelihood Score Tests for Association Studies in Nuclear Families with Parental Genotypes

SummaryBoth population based and family based case control studies are used to test whether particular genotypes are associated with disease. While population based studies have more power, cryptic population stratification can produce false‐positive results. Family‐based methods have been introduced to control for this problem. This paper presents the full likelihood function for family‐based association studies for nuclear families ascertained on the basis of their number of affected and unaffected children. The likelihood of a family factors into the probability of parental mating type, conditional on offspring phenotypes, times the probability of offspring genotypes given their phenotypes and the parental mating type. The first factor can be influenced by population stratification, whereas the latter factor, called the conditional likelihood, is not. The conditional likelihood is used to obtain score tests with proper size in the presence of population stratification (see also Clayton (1999) and Whittemore &amp; Tu (2000)). Under either the additive or multiplicative model, the TDT is known to be the optimal score test when the family has only one affected child. Thus, the class of score tests explored can be considered as a general family of TDT‐like procedures. The relative informativeness of the various mating types is assessed using the Fisher information, which depends on the number of affected and unaffected offspring and the penetrances. When the additive model is true, families with parental mating type Aa×Aa are most informative. Under the dominant (recessive) model, however, a family with mating type Aa×aa(AA×Aa) is more informative than a family with doubly heterozygous (Aa×Aa) parents. Because we derive explicit formulae for all components of the likelihood, we are able to present tables giving required sample sizes for dominant, additive and recessive inheritance models.

Power and Related Statistical Properties of Conditional Likelihood Score Tests for Association Studies in Nuclear Families with Parental Genotypes

Both population based and family based case control studies are used to test whether particular genotypes are associated with disease. While population based studies have more power, cryptic population stratification can produce false-positive results. Family-based methods have been introduced to control for this problem. This paper presents the full likelihood function for family-based association studies for nuclear families ascertained on the basis of their number of affected and unaffected children. The likelihood of a family factors into the probability of parental mating type, conditional on offspring phenotypes, times the probability of offspring genotypes given their phenotypes and the parental mating type. The first factor can be influenced by population stratification, whereas the latter factor, called the conditional likelihood, is not. The conditional likelihood is used to obtain score tests with proper size in the presence of population stratification (see also Clayton (1999) and Whittemore & Tu (2000)). Under either the additive or multiplicative model, the TDT is known to be the optimal score test when the family has only one affected child. Thus, the class of score tests explored can be considered as a general family of TDT-like procedures. The relative informativeness of the various mating types is assessed using the Fisher information, which depends on the number of affected and unaffected offspring and the penetrances. When the additive model is true, families with parental mating type Aa x Aa are most informative. Under the dominant (recessive) model, however, a family with mating type Aa x aa(AA x Aa) is more informative than a family with doubly heterozygous (Aa x Aa) parents. Because we derive explicit formulae for all components of the likelihood, we are able to present tables giving required sample sizes for dominant, additive and recessive inheritance models.

Characterization of protoplasts prepared from the edible fungus, Stropharia rugoso-annulata

Protoplast preparation and regeneration conditions of the edible fungus, Stropharia rugoso-annulata Farlow apud Murrill were studied, and the regenerated progenies were characterized in this study. The optimal condition for protoplast preparation was incubation of young mycelia with gentle shaking in 1.5%(w/v) Lywallzyme at 30 °C for 3 h. PGPM (potato/glucose/peptone/mannitol) was the most suitable regeneration medium. Served as osmotic stabilizer, sugars (mannitol and sucrose) were better than inorganic salts (MgSO4) for clone development and growth. Pre-incubation of protoplasts in liquid regeneration medium resulted in a significantly decreased regeneration rate. Both dikaryotic isolates and monokaryotic isolates could be identified from protoplast-regenerated progenies, with a much higher frequency of monokaryotic isolates identified from the early-developed and fast-growing regenerated clones. Two parental mating types were also identified from protoplasted monokaryotic isolates, but not segregated by 1:1. The mycelial growth rate of protoplasted monokaryotic isolates showed a mating type-dependent model when cultured at different incubation temperatures and pH values, with A2B2 mating type monokaryotic isolates growing faster than those of A1B1 mating type monokaryotic isolates.

Case/pseudocontrol analysis in genetic association studies: A unified framework for detection of genotype and haplotype associations, gene-gene and gene-environment interactions, and parent-of-origin effects.

Estimation and testing of genetic effects (genotype relative risks) are often performed conditionally on parental genotypes, using data from case-parent trios. This strategy avoids having to estimate nuisance parameters such as parental mating type frequencies, and also avoids generating spurious results due to confounding causes of association such as population stratification. For effects at a single locus, the resulting analysis is equivalent to matched case/control analysis via conditional logistic regression, using the case and three "pseudocontrols" derived from the untransmitted parental alleles. We previously showed that a similar approach can be used for analyzing genotype and haplotype effects at a set of closely linked loci, but with a required adjustment to the conditioning argument that results in varying numbers of pseudocontrols, depending on the disease model that is to be fitted. Here we extend this method to include the analysis of epistatic effects (gene-gene interactions) at unlinked loci, to include parent-of-origin effects at one or more loci, and to allow additional incorporation of gene-environment interactions. The conditional logistic approach provides a natural and flexible framework for incorporating these additional effects. By relaxing the conditioning on parental genotypes to allow exchangeability of parental genotypes, we show how the power of this approach can be increased when studying parent-of-origin effects. Simulations suggest that there is limited power to distinguish between parent-of-origin effects and effects due to interaction between genotypes of mother and child.

Candidate gene association analysis for a quantitative trait, using parent-offspring trios.

With the increasing availability of genetic data, many studies of quantitative traits focus on hypotheses related to candidate genes, and also gene-environment (G x E) and gene-gene (G x G) interactions. In a population-based sample, estimates and tests of candidate gene effects can be biased by ethnic confounding, also known as population stratification bias. This paper demonstrates that even a modest degree of ethnic confounding can lead to unacceptably high type I error rates for tests of genetic effects. The parent-offspring trio design is reviewed, and several forms of the quantitative transmission disequilibrium test (QTDT) are summarized. A variation of the QTDT (QTDTM) is described that is based on a linear regression model with multiple intercepts, one per parental mating type. This and other models are expanded to allow testing of G x E and G x G interactions. A method for computing required sample sizes using direct computations is described. Sample size requirements for tests of genetic main effects and G x E and G x G interactions are compared across various QTDT approaches to infer their efficiencies relative to one another. The QTDTM is found to meet or exceed the efficiency of other QTDT approaches. For example, the QTDTM is approximately 3% more efficient than the QTDT of Rabinowitz ([1997] Hum. Hered. 47:342-350) for testing a genetic main effect, but can be as much as twice as efficient for testing G x E interaction, and three times more efficient for testing G x G interaction.