A simulation study of the effects of assignment of prior identity-by-descent probabilities to unselected sib pairs, in covariance-structure modeling of a quantitative-trait locus

Sib pair-selection strategies, designed to identify the most informative sib pairs in order to detect a quantitative-trait locus (QTL), give rise to a missing-data problem in genetic covariance-structure modeling of QTL effects. After selection, phenotypic data are available for all sibs, but marker data-and, consequently, the identity-by-descent (IBD) probabilities-are available only in selected sib pairs. One possible solution to this missing-data problem is to assign prior IBD probabilities (i.e., expected values) to the unselected sib pairs. The effect of this assignment in genetic covariance-structure modeling is investigated in the present paper. Two maximum-likelihood approaches to estimation are considered, the pi-hat approach and the IBD-mixture approach. In the simulations, sample size, selection criteria, QTL-increaser allele frequency, and gene action are manipulated. The results indicate that the assignment of prior IBD probabilities results in serious estimation bias in the pi-hat approach. Bias is also present in the IBD-mixture approach, although here the bias is generally much smaller. The null distribution of the log-likelihood ratio (i.e., in absence of any QTL effect) does not follow the expected null distribution in the pi-hat approach after selection. In the IBD-mixture approach, the null distribution does agree with expectation.     

Advances in statistical methods to map quantitative trait loci in outbred populations

Statistical methods to map quantitative trait loci (QTL) in outbred populations are reviewed, extensions and applications to human and plant genetic data are indicated, and areas for further research are identified. Simple and computationally inexpensive methods include (multiple) linear regression of phenotype on marker genotypes and regression of squared phenotypic differences among relative pairs on estimated proportions of identity-by-descent at a locus. These methods are less suited for genetic parameter estimation in outbred populations but allow the determination of test statistic distributions via simulation or data permutation; however, further inferences including confidence intervals of QTL location require the use of Monte Carlo or bootstrap sampling techniques. A method which is intermediate in computational requirements is residual maximum likelihood (REML) with a covariance matrix of random QTL effects conditional on information from multiple linked markers. Testing for the number of QTLs on a chromosome is difficult in a classical framework. The computationally most demanding methods are maximum likelihood and Bayesian analysis, which take account of the distribution of multilocus marker-QTL genotypes on a pedigree and permit investigators to fit different models of variation at the QTL. The Bayesian analysis includes the number of QTLs on a chromosome as an unknown.     

Modeling hazard functions in families

A genetic frailty model is presented for censored age of onset data in nuclear families where individuals carrying a genetic susceptibility gene have an increased risk of becoming affected. We use maximum likelihood via the EM algorithm to estimate the genetic relative risk and the allele frequency under a dominant susceptibility type and a proportional hazards model. When sampling is from a disease registry, likelihood corrections are necessary for reducing bias in the parameter estimates. In these biased samples, the full conditional likelihood is approximated by a likelihood conditional on the proband's age of onset. For unbiased samples, simulations show the distributions of the estimates are similar under both a semiparametric and the correctly specified parametric likelihoods. For biased samples, simulations under the approximate conditional likelihood show the median estimates of the allele frequency and genetic relative risk tend to under- and overestimate, respectively, the true values; however, the approximation is better for rarer allele frequencies (0.0033 vs. 0.01). In practice, large samples or more complex ascertainment corrections are recommended. Using the approximate conditional likelihood on familial breast cancer onset data collected as part of a case-control study at the Fred Hutchinson Cancer Research Center in Seattle, Washington, we estimate an allele frequency of 0.0009 (approximate 95% CI 0.0006-0.002) and a genetic relative risk of 104 (approximate 95% CI 55-181).     

Comparison of four sib-pair linkage methods for analyzing sibships with more than two affecteds: interest of the binomial maximum likelihood approach

Family samples collected for sib-pair linkage studies usually include some sibships with more than two affecteds (multiplex sibships). Several methods have been proposed to take into account these multiplex sibships, and four of them are discussed in this work. Two methods, which are the most widely used, are based on the number of alleles shared by the sib-pairs constitutive of the multiplex sibship, with the first using the total number of these shared alleles ("all possible pairs" method) and the second considering a weighted number of these alleles (weighted method). The two other approaches considered the sibship as a whole, with in particular a likelihood method based on a binomial distribution of parental alleles among affected offspring. We theoretically show that, in the analysis of sibships with two affecteds, this likelihood method is expected to be more powerful than the classical mean test when a common asymptotic type I error is used. The variation of the sibship informativeness (assessed by the proportion of heterozygous parents) according to the number of affected sibs is investigated under various genetic models. Simulations under the null hypothesis of no linkage indicate that the "all possible pairs" is anticonservative, especially for type I errors < or = 0.001, whereas the weighted method generally provides satisfactory results. The likelihood method shows very consistent results in terms of type I errors, whatever the sample size, and provides power levels similar to those of the other methods. This binomial likelihood approach, which accounts in a natural way for multiplex sibships and provides a simple likelihood-ratio test for linkage involving a single parameter, appears to be a quite interesting alternative to analyze sib-pair studies.     

Nonparametric simulation-based statistics for detecting linkage in general pedigrees

We present here four nonparametric statistics for linkage analysis that test whether pairs of affected relatives share marker alleles more often than expected. These statistics are based on simulating the null distribution of a given statistic conditional on the unaffecteds' marker genotypes. Each statistic uses a different measure of marker sharing: the SimAPM statistic uses the simulation-based affected-pedigree-member measure based on identity-by-state (IBS) sharing. The SimKIN (kinship) measure is 1.0 for identity-by-descent (IBD) sharing, 0.0 for no IBD status sharing, and the kinship coefficient when the IBD status is ambiguous. The simulation-based IBD (SimIBD) statistic uses a recursive algorithm to determine the probability of two affecteds sharing a specific allele IBD. The SimISO statistic is identical to SimIBD, except that it also measures marker similarity between unaffected pairs. We evaluated our statistics on data simulated under different two-locus disease models, comparing our results to those obtained with several other nonparametric statistics. Use of IBD information produces dramatic increases in power over the SimAPM method, which uses only IBS information. The power of our best statistic in most cases meets or exceeds the power of the other nonparametric statistics. Furthermore, our statistics perform comparisons between all affected relative pairs within general pedigrees and are not restricted to sib pairs or nuclear families.     

Iteratively reweighted least squares mapping of quantitative trait loci

Mapping quantitative trait loci (QTL) is a typical problem of regression with uncertain independent variables because the genotype of a putative QTL is not observed. Rather, the genotype is inferred from marker information. The method of maximum likelihood (ML) methods is considered to be the optimal solution for this problem because the distribution of the unobserved QTL genotype is fully taken into account. The simple linear regression method (REG) is a first-order approximation to ML and usually performs very well. In this study, an iteratively reweighted least squares method (IRWLS) is proposed. The new method is a second-order approximation to ML because both the expectation and the variance of the unobserved QTL genotype are taken into consideration. The IRWLS is developed in the context of a single large outbred family. The properties of IRWLS are demonstrated and compared with REG and ML via replicated Monte Carlo simulations. The conclusions are: (1) when marker information content is high, the three methods perform equally well, but ML and IRWLS outperform REG when marker information content is low and the variance explained by the QTL is high; (2) when the residual distribution is not normal, ML can fail or have low power to detect small QTLs, but REG and IRWLS are robust to non-normality; and (3) when the residual distribution is normal, the performance of IRWLS is almost identical to ML, but the computational speed of IRWLS is many times faster than that of ML.     

Genetics of limb development and congenital hand malformations

Differences in breeding values between dominance and additive models were examined theoretically and with field data. Data included 5.2 million records on stature from 3.0 million US Holsteins. The largest full-sib family had 29 animals, and 7% of all animals had at least one full sib. The dominance model, which accounted for dominance covariances, included the following effects: management, age, stage of lactation, permanent environment, animal additive, and parental dominance (one-quarter of dominance variance) as well as a regression coefficient for inbreeding percentage. Two reduced models were also assumed; in the first, the parental dominance effect was removed, and, in the second, the inbreeding regression coefficient was also removed. The correlations between breeding values in the three models were > 0.999, but breeding values of some animals from full-sib families changed > 5 standard deviations of parental dominance. The largest changes were observed for parents with large numbers of full-sib progeny, with limited information from parents, and without individual performance records. On average, the differences were up to four times larger for cows than for bulls and up to five times larger for dams than for sires. The greatest differences in breeding values between the dominance and the additive models were observed for dams with full-sib progeny, female full sibs, and low reliability bulls with full sibs in the extended family. Animals with large amounts of additive information as progeny-tested bulls were influenced little by the inclusion of dominance. Animals with a large proportion of information coming from animals with dominance relationships, such as cows originating via embryo transfer changed the most.     

Phenotypic variation in Meckel syndrome

Four sibs are described with Meckel syndrome, an autosomal recessive disorder with multiple abnormalities. Each sib manifested only two of the three cardinal sings of Meckel syndrome - encephalocoele and polycystic kidneys, lacking polydactyly. The literature is examined to assess the phenotypic variation of the condition: 57% of cases have all the three major abnormalities, 16% have the two found in this family, and the remainder exhibit other variations. In 9 of 17 families where more than one sib is affected, manifestation between sibs is the same, but in the only other two families with as many as four affected sibs, there is variation in expression between sibs.     

Probability Density Estimation Using Entropy Maximization

We propose a method for estimating probability density functions and conditional density functions by training on data produced by such distributions. The algorithm employs new stochastic variables that amount to coding of the input, using a principle of entropy maximization. It is shown to be closely related to the maximum likelihood approach. The encoding step of the algorithm provides an estimate of the probability distribution. The decoding step serves as a generative mode, producing an ensemble of data with the desired distribution. The algorithm is readily implemented by neural networks, using stochastic gradient ascent to achieve entropy maximization.     

Least squares interval mapping of quantitative trait loci under the infinitesimal genetic model in outbred populations

Genetic marker and phenotypic data for a quantitative trait were simulated on 20 paternal half-sib families with 100 progeny to investigate properties of within-family-regression interval mapping of a postulated single quantitative trait locus (QTL) in a marker interval under the infinitesimal genetic model, which has been the basis of the application of quantitative genetics to genetic improvement programs, and to investigate use of the infinitesimal model as null hypothesis in testing for presence of a major QTL. Genetic effects on the marked chromosome were generated based on a major gene model, which simulated a central biallelic QTL, or based on 101 biallelic QTL of equal effect, which approximated the infinitesimal model. The marked chromosome contained 0, 3.3%, 13.3%, or 33.3% of genetic variance and heritability was 0.25 or 0.70. Under the polygenic model with 3.3% of genetic variance on the marked chromosome, which corresponds to the infinitesimal model for the bovine, significant QTL effects were found for individual families. Correlations between estimates of QTL effects and true chromosome substitution effects were 0.29 and 0.47 for heritabilities of 0.25 and 0.70 but up to 0.85 with 33.3% of polygenic variance on the marked chromosome. These results illustrate the potential of marker-assisted selection even under the infinitesimal genetic model. Power of tests for presence of QTL was substantially reduced when the polygenic model with 3.3% of genetic variance on the chromosome was used as a null hypothesis. The ability to determine whether genetic variance on a chromosome was contributed by a single QTL of major effect or a large number of QTL with minor effects, corresponding to the infinitesimal model, was limited.     

Bayesian variable selection method for censored survival data

A Bayesian variable selection method for censored data is proposed in this paper. Based on the sufficiency and asymptotic normality of the maximum partial likelihood estimator, we approximate the posterior distribution of the parameters in a proportional hazards model. We consider a parsimonious model as the full model with some covariates unobserved and replaced by their conditional expected values. A loss function based on the posterior expected estimation error of the log-risk for the proportional hazards model is used to select a parsimonious model. We derive computational expressions for this loss function for both continuous and binary covariates. This approach provides an extension of Lindley's (1968, Journal of the Royal Statistical Society, Series B 30, 31-66) variable selection criterion for the linear case. Data from a randomized clinical trial of patients with primary biliary cirrhosis of the liver (PBC) (Fleming and Harrington, 1991, Counting Processes and Survival Analysis) is used to illustrate the proposed method and a simulation study compares it with the backward elimination procedure.     

Genetic and behavioral risk factors for self-reported joint pain among a population-based sample of Swedish twins.

Self-reported joint pain, a typical manifestation of osteoarthritis, was examined using 335 twin pairs from the Swedish Adoption/Twin Study of Aging to estimate relative genetic and environmental influences on self-reported joint pain and to examine the relationship between joint pain, health behavior, and psychological variables. Findings suggest that family resemblance for self-reported joint pain represents similar environments more than genetic similarity. Data from the early 1970s, including exercise, physical activity at work, obesity, and neuroticism, were used to predict joint pain in 1993. For men, moderate amounts of exercise decreased the likelihood of joint pain, but strenuous amounts of physical activity in the workplace had the opposite effect. For women, exercise and physical activity were not significant predictors, but past obesity and higher levels of neuroticism increased the likelihood of reporting joint pain in 1993. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Molecular dissection of developmental behavior of plant height in rice (Oryza sativa L.)

A doubled haploid population of 123 lines from IR64/Azucena was used to dissect the developmental behavior and genotype by environment interaction for plant height by conditional and unconditional quantitative trait loci (QTL) mapping methods in rice. It was shown that the number of QTL detected was different at various measuring stages. Some QTL could be detected at all stages and some only at one or several stages. More QTL could be found on the basis of time-dependent measures of different stages. By conditional QTL mapping of time-dependent measures, it is possible to reveal dynamic gene expression for quantitative traits. Mapping QTL for genetic main effects and GE interaction effects could help us in understanding the nature of QTL x environment interaction for the development of quantitative traits.     

Streptococcus pyogenes strains containing emm12 and emm55 possess a novel gene coding for distantly related SIC protein

OBJECTIVE: To identify subtypes of attention-deficit/hyperactivity disorder (ADHD) and characterize them as either categorical or continuous; to investigate familial resemblance for ADHD among sibling pairs; and to test the robustness of all results by using contrasting data sets. METHOD: Latent class analysis was applied to the ADHD symptom profiles obtained from parents or best informant about their offspring in 3 samples: a population-based set of female adolescent twins (724 monozygotic pairs, 594 dizygotic pairs) and male (N = 425) and female (N = 430) child and adolescent offspring ascertained from high-risk alcoholic families. RESULTS: Latent class analysis revealed 2 categories of clinically significant ADHD which were replicated in all 3 study groups: a subtype with high endorsements of ADHD inattention symptoms and a second combined type with high endorsements of both inattention and hyperactivity-impulsivity items. Both appeared to be continuous across all 3 data groups. The high-risk families contained a class in which members heavily endorsed the ADHD "fidget" item but not other ADHD items. A large proportion of the monozygotic sibs (80%) versus a smaller proportion of dizygotic sibs (52%) were assigned to the same latent class. Among the high-risk children and adolescents, 51% of the female and 41% of the male siblings were concordant for class membership. CONCLUSIONS: The pattern of latent classes suggested that ADHD consists of an inattentive and a combined subtype, within each of which lies a dimensional domain. These analyses further support that genetic factors are significant determinants of latent class membership.     

Improved confidence intervals for the difference between binomial proportions based on paired data

Existing methods for setting confidence intervals for the difference theta between binomial proportions based on paired data perform inadequately. The asymptotic method can produce limits outside the range of validity. The 'exact' conditional method can yield an interval which is effectively only one-sided. Both these methods also have poor coverage properties. Better methods are described, based on the profile likelihood obtained by conditionally maximizing the proportion of discordant pairs. A refinement (methods 5 and 6) which aligns 1-alpha with an aggregate of tail areas produces appropriate coverage properties. A computationally simpler method based on the score interval for the single proportion also performs well (method 10).     

Cell and organ culture techniques applied to the study of carcinoma of colon and rectum

The hospital records of 197 infants with the respiratory distress syndrome (RDS) were reviewed and the families of 111 of them subsequently contacted to obtain a family history. After correcting for biasis of ascertainment, the incidence of RDS among the full sibs was found to be between 12 and 19% depending on whether the individuals diagnosed as "possible RDS" were counted as affected. Among the low birth weight (LBW, less than or equal to 2.5 kg) and/or preterm (less than or equal to 37 weeks gestation) infants in the sibships, the incidence of RDS was 32-50%. Considering only sibs born after the probands yielded the empiric recurrence risk of 17--27% for all younger sibs and 39--67% for LBW/preterm younger sibs. The risk for maternal half-sibs was of about the same magnitude as that for full sibs, while the risk for paternal half-sibs was minimal. Among the LBW/preterm first cousins of probands, only the infants of maternal aunts showed an RDS incidence clearly higher than that in the general population. We think these data suggest a genetically determined maternal factor predisposing the infants of certain mothers to RDS. Other significant findings include: 1) an excess of males among the probands but a normal sex ratio among the sibs of the probands; 2) a decrease in mean birth weight and mean length of gestation for not only the probands but also their sibs; 3) a decrease in the mean parental ages at the birth of the probands; 4) a relative dearth of first-born and an excess of second-born infants among the probands; 5) an increased incidence of stillbirths in the sibships; 6) an increased number of probands born by cesarean section; and 7) a twin concordance of 75%.     

An amino acid polymorphism in histidine-rich glycoprotein (HRG) explains 59% of the variance in plasma HRG levels

A pedigree-based maximum likelihood method developed by Lange et al. (12) was used to study the contribution of a newly defined di-allelic polymorphism in histidine-rich glycoprotein (HRG) to the plasma levels of HRG. In four families (n = 99) and 20 volunteers we found a heritability of 70%, an age effect of 3% and an effect of individual environmental factors of 27%. These results are remarkably similar to the results found in a previous parent-twin study in which a heritability of 69% and an effect of random environment of 31% was found. The overall genetic influence in the present study can be subdivided into an effect of 59% by the HRG phenotype and 11% by residual genetic factors. The influence of the HRG phenotype of 59% can entirely be explained by adding up the effect of the two alleles that make up the phenotype. These results indicate a codominant inheritance pattern of HRG levels in which the genetic influences can almost completely be ascribed to the additive effect of the di-allelic HRG locus whereas only a small part is due to other loci.     

Maximum likelihood estimation of aggregated Markov processes

We present a maximum likelihood method for the modelling of aggregated Markov processes. The method utilizes the joint probability density of the observed dwell time sequence as likelihood. A forward-backward recursive procedure is developed for efficient computation of the likelihood function and its derivatives with respect to the model parameters. Based on the calculated forward and backward vectors, analytical formulae for the derivatives of the likelihood function are derived. The method exploits the variable metric optimizer for search of the likelihood space. It converges rapidly and is numerically stable. Numerical examples are given to show the effectiveness of the method.     

Bronchoscopic methods of establishing the etiology of enlarged hilar and mediastinal lymph nodes

A matrix method to calculate conditional likelihoods in a pedigree and use them to determine recurrence risks for unilocal disorders in genetic risks is presented in this paper. Different matrices are assigned to individual members of the pedigree and combined into matrix expressions. The method is explained for X-linked recessive conditions and autosomal dominant conditions with incomplete penetrance.     

Ascertainment corrections based on smaller family units

Ascertainment concerns the manner by which families are selected for genetic analysis and how to correct for it in likelihood models. Because such families are often neither drawn at random nor selected according to well-defined rules, the problem of ascertainment correction in the genetic analysis of family data has proved durable. This paper undertakes a systematic study of ascertainment corrections in terms of smaller distinct units, which will usually be sibships, nuclear families, or small pedigrees. Three principal results are presented. The first is that ascertainment corrections in likelihood models for family data can be made in terms of smaller units, without breaking up the pedigree. The second is that the appropriate correction for single ascertainment in a unit is the reciprocal of the sum of the marginal probabilities of all the persons relevant to its ascertainment, as if affected. The third result is a generalization of the single ascertainment-correction formula to k-plex ascertainment, in which each unit has k or more affecteds. The correction is the reciprocal of the sum of the joint probabilities of all distinct sets of k persons in the unit, as if they were all affected. In extended families, two additional ascertainment schemes will be considered and explicit formulas will be presented. One of these schemes is "uniform-proband-status ascertainment," in which nonmembers of a given unit have the same chance as members to become probands if they are affected; the other scheme is the "inverse law of ascertainment," in which the chance that nonmembers of a unit will become probands for that unit decreases with degree of relationship. Several specific recommendations are made for further study.