Regression models for linkage: issues of traits, covariates, heterogeneity, and interaction

An Accidental Genetic Epidemiologist

I briefly describe my early life and how, through a series of serendipitous events, I became a genetic epidemiologist. I discuss how the Elston–Stewart algorithm was discovered and its contribution to segregation, linkage, and association analysis. New linkage findings and paternity testing resulted from having a genotyping lab. The different meanings of interaction—statistical and biological—are clarified. The computer package S.A.G.E. (Statistical Analysis for Genetic Epidemiology), based on extensive method development over two decades, was conceived in 1986, flourished for 20 years, and is now freely available for use and further development. Finally, I describe methods to estimate and test hypotheses about familial correlations, and point out that the liability model often used to estimate disease heritability estimates the heritability of that liability, rather than of the disease itself, and so can be highly dependent on the assumed distribution of that liability.

Linkage and related analyses of Barrett's esophagus and its associated adenocarcinomas

Background

Familial aggregation and segregation analysis studies have provided evidence of a genetic basis for esophageal adenocarcinoma (EAC) and its premalignant precursor, Barrett's esophagus (BE). We aim to demonstrate the utility of linkage analysis to identify the genomic regions that might contain the genetic variants that predispose individuals to this complex trait (BE and EAC).

Methods

We genotyped 144 individuals in 42 multiplex pedigrees chosen from 1000 singly ascertained BE/EAC pedigrees, and performed both model‐based and model‐free linkage analyses, using S.A.G.E. and other software. Segregation models were fitted, from the data on both the 42 pedigrees and the 1000 pedigrees, to determine parameters for performing model‐based linkage analysis. Model‐based and model‐free linkage analyses were conducted in two sets of pedigrees: the 42 pedigrees and a subset of 18 pedigrees with female affected members that are expected to be more genetically homogeneous. Genome‐wide associations were also tested in these families.

Results

Linkage analyses on the 42 pedigrees identified several regions consistently suggestive of linkage by different linkage analysis methods on chromosomes 2q31, 12q23, and 4p14. A linkage on 15q26 is the only consistent linkage region identified in the 18 female‐affected pedigrees, in which the linkage signal is higher than in the 42 pedigrees. Other tentative linkage signals are also reported.

Conclusion

Our linkage study of BE/EAC pedigrees identified linkage regions on chromosomes 2, 4, 12, and 15, with some reported associations located within our linkage peaks. Our linkage results can help prioritize association tests to delineate the genetic determinants underlying susceptibility to BE and EAC.

Appendiceal neuroendocrine neoplasms: diagnosis and management

Gastrointestinal neuroendocrine neoplasms (GI-NENs) are increasingly being recognised, while appendiceal NENs (aNENs) currently constitute the third most common GI-NEN. Appendiceal NENs are generally considered to follow an indolent course with the majority being localised at diagnosis. Thus, the initial surgical approach is not that of a planned oncological resection. Due to the localised nature of the disease in the majority of cases, subsequent biochemical and radiological assessment are not routinely recommended. Histopathological criteria (size, mesoappendiceal invasion, Ki-67 proliferation index, neuro- and angio-invasion) are mainly used to identify those patients who are also candidates for a right hemicolectomy. Goblet cell carcinoids are a distinct entity and should be treated as adenocarcinomas. Despite the absence of any substantial prospective data regarding optimal management and follow-up, recent consensus statements and guidelines have been published. The purpose of this review is to overview the published studies on the diagnosis and management of appendiceal NENs and to suggest a possible management protocol.

Uncoupling protein 2 gene polymorphisms are associated with obesity

Background

Uncoupling protein 2 (UCP2) gene polymorphisms have been reported as genetic risk factors for obesity and type 2 diabetes mellitus (T2DM). We examined the association of commonly observed UCP2 G(−866)A (rs659366) and Ala55Val (C > T) (rs660339) single nucleotide polymorphisms (SNPs) with obesity, high fasting plasma glucose, and serum lipids in a Balinese population.

Methods

A total of 603 participants (278 urban and 325 rural subjects) were recruited from Bali Island, Indonesia. Fasting plasma glucose (FPG), triglyceride (TG), high density lipoprotein cholesterol (HDL-C), low density lipoprotein cholesterol (LDL-C) and total cholesterol (TC) were measured. Obesity was determined based on WHO classifications for adult Asians. Participants were genotyped for G(−866)A and Ala55Val polymorphisms of the UCP2 gene.

Results

Obesity prevalence was higher in urban subjects (51%) as compared to rural subjects (23%). The genotype, minor allele (MAF), and heterozygosity frequencies were similar between urban and rural subjects for both SNPs. All genotype frequencies were in Hardy-Weinberg equilibrium. A combined analysis of genotypes and environment revealed that the urban subjects carrying the A/A genotype of the G(−866)A SNP have higher BMI than the rural subjects with the same genotype. Since the two SNPs showed strong linkage disequilibrium (D’ = 0.946, r² = 0.657), a haplotype analysis was performed. We found that the AT haplotype was associated with high BMI only when the urban environment was taken into account.

Conclusions

We have demonstrated the importance of environmental settings in studying the influence of the common UCP2 gene polymorphisms in the development of obesity in a Balinese population.

Heritability Estimation using Regression Models for Correlation

Heritability estimates a polygenic effect on a trait for a population. Reliable interpretation of heritability is critical in planning further genetic studies to locate a gene responsible for the trait. This study accommodates both single and multiple trait cases by employing regression models for correlation parameter to infer the heritability. Sharing the properties of regression approach, the proposed methods are exible to incorporate non-genetic and/or non-additive genetic information in the analysis. The performances of the proposed model are compared with those using the likelihood approach through simulations and carotid Intima Media Thickness analysis from Northern Manhattan family Study.

Genetic variation in HTR2A influences serotonin transporter binding potential as measured using PET and [11C]DASB

In a previous study we showed that genetic variation in HTR2A, which encodes the serotonin 2A receptor, influenced outcome of citalopram treatment in patients with major depressive disorder. Since chronic administration of citalopram, which selectively and potently inhibits the serotonin transporter (5-HTT), putatively enhances serotonergic transmission, it is conceivable that genetic variation within HTR2A also influences pretreatment 5-HTT function or serotonergic transmission. The present study used positron emission tomography (PET) and the selective 5-HTT ligand, [11C]DASB, to investigate whether the HTR2A marker alleles that predict treatment outcome also predict differences in 5-HTT binding. Brain levels of 5-HTT were assessed in vivo using PET measures of the non-displaceable component of the [11C]DASB binding potential (BPND). DNA from 43 patients and healthy volunteers, all unmedicated, was genotyped with 14 single nucleotide polymorphisms located within or around HTR2A. Allelic association with BPND was assessed in eight brain regions, with covariates to control for race and ethnicity. We detected allelic association between [11C]DASB BPND in thalamus and three markers in a region spanning the 3' untranslated region and second intron of HTR2A (rs7333412, p=0.000045; rs7997012, p=0.000086; rs977003, p=0.000069). The association signal at rs7333412 remained significant (p<0.05) after applying corrections for multiple testing via permutation. Genetic variation in HTR2A that was previously associated with citalopram treatment outcome was also associated with thalamic 5-HTT binding. While further work is needed to identify the actual functional genetic variants involved, these results suggest that a relationship exists between genetic variation in HTR2A and either 5-HTT expression or central serotonergic transmission that influences the therapeutic response to 5-HTT inhibition in major depression.

Gene--environment-wide association studies: emerging approaches

Despite the yield of recent genome-wide association (GWA) studies, the identified variants explain only a small proportion of the heritability of most complex diseases. This unexplained heritability could be partly due to gene--environment (G×E) interactions or more complex pathways involving multiple genes and exposures. This Review provides a tutorial on the available epidemiological designs and statistical analysis approaches for studying specific G×E interactions and choosing the most appropriate methods. I discuss the approaches that are being developed for studying entire pathways and available techniques for mining interactions in GWA data. I also explore methods for marrying hypothesis-driven pathway-based approaches with 'agnostic' GWA studies.

A genomic scan for age at onset of Alzheimer's disease in 437 families from the NIMH Genetic Initiative

We performed linkage analysis for age at onset (AAO) in the total Alzheimer's disease (AD) NIMH sample (N = 437 families). Families were subset as late-onset (320 families, AAO > or = 65) and early/mixed (117 families, at least 1 member with 50 < AAO < 65). Treating AAO as a censored trait, we obtained the gender and APOE adjusted residuals in a parametric survival model and analyzed the residuals as the quantitative trait (QT) in variance-component linkage analysis. For comparison, AAO-age at exam (AAE) was analyzed as the QT adjusting for affection status, gender, and APOE. Heritabilities for residual and AAO-AAE outcomes were 66.3% and 74.0%, respectively for the total sample, 56.0% and 57.0% in the late-onset sample, and 33.0% for both models in the early/mixed sample. The residual model yielded the largest peaks on chromosome 1 with LOD = 2.0 at 190 cM in the total set, LOD = 1.7 at 116 cM on chromosome 3 in the early/mixed subset, and LOD = 1.4 at 71 and 86 cM, respectively, on chromosome 6 in the late-onset subset. For the AAO-AAE outcome model the largest peaks were identified on chromosome 1 at 137 cM (LOD = 2.8) and chromosome 6 at 69 cM (LOD = 2.3) and 86 cM (LOD = 2.2) all in the late-onset subset. Additional peaks with LOD > or = 1 were identified on chromosomes 1, 2, 3, 6, 8, 9, 10, and 12 for the total sample and each subset. Results replicate previous findings, but identify additional suggestive peaks indicating the genetics of AAO in AD is complex with many chromosomal regions potentially containing modifying genes.

Using linkage analysis to identify quantitative trait loci for sleep apnea in relationship to body mass index

To understand the genetics of sleep apnea, we evaluated the relationship between the apnea hypopnea index (AHI) and body mass index (BMI) through linkage analysis to identify genetic loci that may influence AHI and BMI jointly and AHI independent of BMI. Haseman-Elston sibling regression was conducted on AHI, AHI adjusted for BMI and BMI in African-American and European-American pedigrees. A comparison of the magnitude of linkage peaks was used to assess the relationship between AHI and BMI. In EAs, the strongest evidence for linkage to AHI was on 6q23-25 and 10q24-q25, both decreasing after BMI adjustment, suggesting loci with pleiotropic effects. Also, a promising area of linkage to AHI but not BMI was observed on 6p11-q11 near the orexin-2 receptor, suggesting BMI independent pathways. In AAs the strongest evidence of linkage for AHI after adjusting for BMI was on chromosome 8p21.3 with linkage increasing after BMI adjustment and on 8q24.1 with linkage decreasing after BMI adjustment. Novel linkage peaks were also observed in AAs to both BMI and AHI on chromosome 13 near the serotonin-2a receptor. These analyses suggest genetic loci for sleep apnea that operate both independently of BMI and through BMI-related pathways.

Comparison of affected sibling-pair linkage methods to identify gene x gene interaction in GAW15 simulated data

Non-parametric linkage methods have had limited success in detecting gene by gene interactions. Using affected sibling-pair (ASP) data from all replicates of the simulated data from Problem 3, we assessed the statistical power of three approaches to identify the gene x gene interaction between two loci on different chromosomes. The first method conditioned on linkage at the primary disease susceptibility locus (DR), to find linkage to a simulated effect modifier at Locus A with a mean allele sharing test. The second approach used a regression-based mean test to identify either the presence of interaction between the two loci or linkage to the A locus in the presence of linkage to DR. The third method applied a conditional logistic model designed to test for the presence of interacting loci. The first approach had decreased power over an unconditional linkage analysis, supporting the idea that gene x gene interaction cannot be detected with ASP data. The regression-based mean test and the conditional logistic model had the lowest power to detect gene x gene interaction, possibly because of the complex recoding of the tri-allelic DR locus for use as a covariate. We conclude that the ASP approaches tested have low power to successfully identify the interaction between the DR and A loci despite the large sample size, which may be due to the low prevalence of the high-risk DR genotypes. Additionally, the lack of data on discordant sibships may have decreased the power to identify gene x gene interactions.

Linkage analyses of rheumatoid arthritis and related quantitative phenotypes: the GAW15 experience

The group that formed on the theme of linkage analyses of rheumatoid arthritis RA and related phenotypes (Group 10) in the Genetic Analysis Workshop 15 comprised 18 sets of investigators. Two data sets were available: one was a real set provided by the North American Rheumatoid Arthritis Consortium and collaborators in Canada, France (European Consortium Of Rheumatoid Arthritis Families) and the UK; the other was a simulated data set modelled after the real data set. Whereas a majority of the investigators analyzed the RA affection status as a binary phenotype, a few contributions considered data on correlated quantitative traits such as anti-cyclic citrullinated peptide and rheumatoid factor-immunoglobulin M. The different investigators applied a wide spectrum of linkage methods. As expected, most methods could identify the human leukocyfeantigen region on chromosome 6 as a major genetic factor for RA. In addition, some novel chromosomal regions provided significant evidence of linkage in multiple contributions in the group. In this report, we discuss the different strategies explored by the different investigators with the common goal of improving the power to detect linkage.

Interpreting analyses of continuous covariates in affected sibling pair linkage studies

Datasets collected for linkage analyses of complex human diseases often include a number of clinical or environmental covariates. In this study, we evaluated the performance of three linkage analysis methods when the relationship between continuous covariates and disease risk or linkage heterogeneity was modeled in three different ways: (1) The covariate distribution is determined by a quantitative trait locus (QTL), which contributes indirectly to the disease risk; (2) the covariate is not genetically determined, but influences the disease risk through statistical interaction with a disease susceptibility locus; (3) the covariate distribution differs in families linked or unlinked to a particular disease susceptibility locus. We analyzed simulated datasets with a regression-based QTL analysis, a nonparametric analysis of the binary affection status, and the ordered subset analysis (OSA). We found that a significant OSA result may be due to a gene that influences variability in the population distribution of a continuous disease risk factor. Conversely, a regression-based QTL analysis may detect the presence of gene-environment (GxE) interaction in a sample of primarily affected individuals. The contribution of unaffected siblings and the size of baseline lod scores may help distinguish between QTL and GxE models. As illustrated by a linkage study of multiplex families with age-related macular degeneration, our findings assist in the interpretation of analysis results in real datasets. They suggest that the side-by-side evaluation of OSA and QTL results may provide important information about the relationship of measured covariates with either disease risk or linkage heterogeneity.

Clinical prediction of antidepressant response in mood disorders: linear multivariate vs. neural network models

Predicting the outcome of antidepressant treatment by pre-treatment features would be of great usefulness for clinicians as up to 50% of major depressives may not have a satisfactory response in spite of adequate trials of antidepressant drugs. In the present article we compared a linear multivariate model of predictors with a few artificial neural network (ANN) models differing from one another by outcome definition and validation procedure. The sample consisted of a reanalysis of 116 inpatients with a major depressive episode included in a 6-week open-label trial with fluvoxamine. With the original outcome definition (responders/non-responders), ANN performed better than logistic regression (90% of correct classifications in the training sample vs. 77%). However only 62% of new patients were correctly predicted by ANN for their outcome class. Length of the index episode, psychotic features and suicidal behavior emerged as outcome predictors in both models, while demographic characteristics, personality disorders and concomitant somatic morbidity were pointed to only by ANN analysis. Increase of classes in the outcome field resulted in a more elevated error: 46.4% for three classes, 60.4% for four classes and 70.3% for five classes. Overall, our findings suggest that antidepressant outcome prediction based on clinical variables is poor. The ANN approach is as valid as traditional multivariate techniques for the analysis of psychopharmacology studies. The complex interactions modelled through ANN may eventually be applied at the clinical level for individualized therapy. However, the accuracy of prediction is still far from satisfactory from a clinical point of view.

Testing genetic linkage with relative pairs and covariates by quasi-likelihood score statistics

BACKGROUND/AIMS

Genetic linkage analysis of common diseases is complicated by the heterogeneity of genetic and environmental factors that increase disease risk, and possibly interactions among them. Most linkage methods that account for covariates are restricted to sib pairs, with the exception of the conditional logistic regression model [1] implemented in LODPAL in the S.A.G.E. software [2]. Although this model can be applied to arbitrary pedigrees, at times it can be difficult to maximize the likelihood due to model constraints, and it does not account for the dependence among the different types of relative pairs in a pedigree.

METHODS

To overcome these limitations, we developed a new approach based on score statistics for quasi- likelihoods, implemented as weighted least squares. Our methods can be used to test three different hypotheses: (1) a test for linkage without covariates; (2) a test for linkage with covariates, and (3) a test for effects of covariates on identity by descent sharing (i.e., heterogeneity). Furthermore, our methods are robust because they account for the dependence among different relative pairs within a pedigree.

RESULTS AND CONCLUSION

Although application of our methods to a prostate cancer linkage study did not find any critical covariates in our data, the results illustrate the utility and interpretation of our methods, and suggest, nonetheless, that our methods will be useful for a broad range of genetic linkage heterogeneity analyses.

A score test for linkage analysis of ordinal traits based on IBD sharing

Statistical methods for linkage analysis are well established for both binary and quantitative traits. However, numerous diseases including cancer and psychiatric disorders are rated on discrete ordinal scales. To analyze pedigree data with ordinal traits, we recently proposed a latent variable model which has higher power to detect linkage using ordinal traits than methods using the dichotomized traits. The challenge with the latent variable model is that the likelihood is usually very complicated, and as a result, the computation of the likelihood ratio statistic is too intensive for large pedigrees. In this paper, we derive a computationally efficient score statistic based on the identity-by-decent sharing information between relatives. Using simulation studies, we examined the asymptotic distribution of the test statistic and the power of our proposed test under various levels of heritability. We compared the computing time as well as power of the score test with the likelihood ratio test. We then applied our method for the Collaborative Study on the Genetics of Alcoholism and performed a genome scan to map susceptibility genes for alcohol dependence. We found a strong linkage signal on chromosome 4.

The genetic basis of complex traits: rare variants or "common gene, common disease"?

The goal of the Human Genome Project and the subsequent HapMap Project was to accelerate the pace at which genes for complex human traits were discovered. Elated by the early successes from cloning disease genes for monogenic disorders, the architects of the projects reasoned that complex human diseases were tractable to positional cloning methods. However, a schism emerged in the field, with hot debates regarding two competing hypotheses being publicly waged. These opposing hypotheses pertained to the anticipated allelic spectrum and frequency of disease variants associated with common, complex disease. The common disease, common variant hypothesis (CD/CV) stated that a few common allelic variants could account for the genetic variance in disease susceptibility, whereas the rare variant (CD/RV) hypothesis stated that DNA sequence variation at any gene causing disease could encompass a wide range of possibilities, with the most extreme being that each mutation is only found once in the population. The practical consequence of the debate can be broken into two parts. If the CD/CV hypothesis is true, then application of the positional cloning paradigm to map disease genes would be eminently more feasible, as a common allele would be easier to locate. Conversely, if rare variants cause common disease, then identifying these genetic susceptibility variants would be challenging. Whether a disease is caused by rare or common alleles will have an impact on clinical applications, such as designing prognostic assays, or planning therapeutic interventions; fewer susceptibility alleles will simplify assay design, and the associated reduction in costs would amortize if a universally applicable therapy can be deployed. A current review of the literature suggests that both these hypotheses are correct, depending on the gene and disease examined. Although the controversial debate is revived with the identification of each new disease gene, the time has come to integrate both hypotheses in a manner that best explains biological variation in natural populations. The allelic spectrum of variation in a particular gene may be better explained by one of the two hypotheses but, for a multifactorial trait, a composite encompassing all influential genes needs to be constructed.

The genetic bases of speech sound disorders: evidence from spoken and written language

The purpose of this article is to review recent findings suggesting a genetic susceptibility for speech sound disorders (SSD), the most prevalent communication disorder in early childhood. The importance of genetic studies of SSD and the hypothetical underpinnings of these genetic findings are reviewed, as well as genetic associations of SSD with other language and reading disabilities. The authors propose that many genes contribute to SSD. They further hypothesize that some genes contribute to SSD disorders alone, whereas other genes influence both SSD and other written and spoken language disorders. The authors postulate that underlying common cognitive traits, or endophenotypes, are responsible for shared genetic influences of spoken and written language. They review findings from their genetic linkage study and from the literature to illustrate recent developments in this area. Finally, they discuss challenges for identifying genetic influence on SSD and propose a conceptual framework for study of the genetic basis of SSD.

The affected-/discordant-sib-pair design can guarantee validity of multipoint model-free linkage analysis of incomplete pedigrees when there is marker-marker disequilibrium

Genomewide linkage studies are tending toward the use of single-nucleotide polymorphisms (SNPs) as the markers of choice. However, linkage disequilibrium (LD) between tightly linked SNPs violates the fundamental assumption of linkage equilibrium (LE) between markers that underlies most multipoint calculation algorithms currently available, and this leads to inflated affected-relative-pair allele-sharing statistics when founders' multilocus genotypes are unknown. In this study, we investigate the impact that the degree of LD, marker allele frequency, and association type have on estimating the probabilities of sharing alleles identical by descent in multipoint calculations and hence on type I error rates of different sib-pair linkage approaches that assume LE. We show that marker-marker LD does not inflate type I error rates of affected sib pair (ASP) statistics in the whole parameter space, and that, in any case, discordant sib pairs (DSPs) can be used to control for marker-marker LD in ASPs. We advocate the ASP/DSP design with appropriate sib-pair statistics that test the difference in allele sharing between ASPs and DSPs.

Extension of the Haseman-Elston regression model to longitudinal data

We propose an extension to longitudinal data of the Haseman and Elston regression method for linkage analysis. The proposed model is a mixed model having several random effects. As response variable, we investigate the sibship sample mean corrected cross-product (smHE) and the BLUP-mean corrected cross product (pmHE), comparing them with the original squared difference (oHE), the overall mean corrected cross-product (rHE), and the weighted average of the squared difference and the squared mean-corrected sum (wHE). The proposed model allows for the correlation structure of longitudinal data. Also, the model can test for gene x time interaction to discover genetic variation over time. The model was applied in an analysis of the Genetic Analysis Workshop 13 (GAW13) simulated dataset for a quantitative trait simulating systolic blood pressure. Independence models did not preserve the test sizes, while the mixed models with both family and sibpair random effects tended to preserve size well.

Genome scans with gene-covariate interaction

Genetic models for gene-covariate interactions are described. Methods of linkage analysis that utilize special features of these models and the corresponding score statistics are derived. Their power is compared with that of simple genome scans that ignore these special features, and substantial gains in power are observed when the gene-covariate interaction is strong. Quantitative trait mapping in randomly ascertained sibships and affected sibpair mapping are discussed. For the latter case, a simpler statistic is proposed that has similar performance to the score statistic, but does not require the estimation of nuisance parameters. Since the nuisance parameters are not estimable solely from affected sib-pair data, this statistic would be much easier to apply in practice. Similarities with linkage analysis of models for longitudinal data and multivariate phenotypes are also briefly discussed. Approximations for the P-value and power are derived under the framework of local alternatives.

Advances in statistical human genetics over the last 25 years

The past 25 years has seen an explosion in the number of genetic markers that can be measured on DNA samples at an ever decreasing cost. Although basic statistical methods for analysing such data gathered on samples of either independent individuals or family members, one or two markers at a time, were already well developed before this explosion occurred, there has been a corresponding burst in activity to develop multiple marker models to find disease-causing gene variants, capitalizing on the data that have become available, to increase the power of such methods. This has required the concomitant development of faster algorithms to speed up the computation of various likelihoods. For linkage analysis, to obtain the approximate locations for genes of interest, Mendelian segregation models have been extended to be more realistic and statistical models that do not assume specific modes of inheritance have been extended to allow for the analysis of larger pedigree structures. For association analysis, to obtain more precise locations for genes of interest, the recent completion of the first stage of the HapMap project has spurred the development, still underway, of novel experimental designs and analytical methods to combat the curse of dimensionality and the resulting multiple testing problem. Perhaps the greatest current challenge concerns how best to gather and synthesize the many lines of evidence possible in order to discover the genetic determinants underlying complex diseases.

Linkage analysis of alcohol dependence using both affected and discordant sib pairs

The basic idea of affected-sib-pair (ASP) linkage analysis is to test whether the inheritance pattern of a marker deviates from Mendelian expectation in a sample of ASPs. The test depends on an assumed Mendelian control distribution of the number of marker alleles shared identical by descent (IBD), i.e., 1/4, 1/2, and 1/4 for 2, 1, and 0 allele(s) IBD, respectively. However, Mendelian transmission may not always hold, for example because of inbreeding or meiotic drive at the marker or a nearby locus. A more robust and valid approach is to incorporate discordant-sib-pairs (DSPs) as controls to avoid possible false-positive results. To be robust to deviation from Mendelian transmission, here we analyzed Collaborative Study on the Genetics of Alcoholism data by modifying the ASP LOD score method to contrast the estimated distribution of the number of allele(s) shared IBD by ASPs with that by DSPs, instead of with the expected distribution under the Mendelian assumption. This strategy assesses the difference in IBD sharing between ASPs and the IBD sharing between DSPs. Further, it works better than the conventional LOD score ASP linkage method in these data in the sense of avoiding false-positive linkage evidence.

Two-level Haseman-Elston regression for general pedigree data analysis

The Haseman-Elston (HE) (Haseman and Elston [1972] Behav Genet 2:3-19) method is widely used in genetic linkage studies for quantitative traits. We propose a new version of the HE regression model, a two-level HE regression model (tHE) in which the variance-covariance structure of family data is modeled under the framework of multiple-level regression. An iterative generalized least squares (IGLS) algorithm is adopted to handle the varying variance-covariance structures across families in a simple fashion. In this way, the tHE can compete favorably with any current version of HE in that it can naturally make use of all the trait information available in any general pedigree, simultaneously incorporate individual-level and pedigree-level covariates, marker genotypes for linkage (i.e., the number of allele shared identically by descent [IBD]), and marker alleles for association. Under the assumption of normality, the method is asymptotically equivalent to the usual variance component model for detecting linkage. For the situation where the assumption of normality is critical, a robust globally consistent estimator of the quantitative trait locus (QTL) variance is available. Complex genetic mechanisms, including gene-gene interaction, gene-environmental interaction, and imprinting, can be directly modeled in this version of HE regression.

Issues in Association Analysis: Error Control in Case-Control Association Studies for Disease Gene Discovery

Several sources of errors are discussed. While genotyping errors have little effect on power in case-control association studies, they tend to strongly increase false positive results in TDT type tests unless occurrence of errors is allowed for in the analysis (e.g., TDTae test). Disregarding non-genetic risk factors is shown to lead to a form of hidden heterogeneity, which can strongly reduce power. Stratification of data into more homogeneous subgroups is advocated as a simple solution to allowing for non-genetic risk factors such as socio-economic status and food preferences.

A modified revisited Haseman-Elston method to further improve power

The original and revisited Haseman-Elston methods are simple robust methods to detect linkage, but neither is uniformly optimal in terms of power. In this report, we propose a simple modification of the revisited Haseman-Elston method that retains the simplicity and robustness properties, but increases its power. We demonstrate theoretically that the modification can be more powerful than the optimally weighted Haseman-Elston method when the sibship mean can be correctly specified. We then examine the properties of this modification by simulation when the sibship mean is replaced by its best linear unbiased predictor. The simulation results indicate that this modification maintains good control over type I error, even in the case of larger sibships, and that the empirical power of this modification is similar to that of the optimally weighted Haseman-Elston method in most cases.

Mathematical assumptions versus biological reality: myths in affected sib pair linkage analysis

Affected sib pair (ASP) analysis has become common ever since it was shown that, under very specific assumptions, ASPs afford a powerful design for linkage analysis. In 2003, Vieland and Huang, on the basis of a "fundamental heterogeneity equation," proved that heterogeneity and epistasis are confounded in ASP linkage analysis. A much more serious limitation of ASP linkage analysis is the implicit assumption that randomly sampled sib pairs share half their alleles identical by descent at any locus, whereas a critical assumption underlying Vieland and Huang's proof is that of joint Hardy-Weinberg equilibrium proportions at two trait loci. These are considered as examples of mathematical assumptions that may not always reflect biological reality. More-robust sib-pair designs and appropriate methods for their analysis have long been available.

Comparison of methods incorporating quantitative covariates into affected sib pair linkage analysis

For complex traits, it may be possible to increase the power to detect linkage if one takes advantage of covariate information. Several statistics have been proposed that incorporate quantitative covariate information into affected sib pair (ASP) linkage analysis. However, it is not clear how these statistics perform under different gene-environment (G x E) interactions. We compare representative statistics to each other on simulated data under three biologically-plausible G x E models. We also compared their performance with a model-free method and with quantitative trait locus (QTL) linkage approaches. The statistics considered here are: (1) mixture model; (2) general conditional-logistic model (LODPAL); (3) multinomial logistic regression models (MLRM); (4) extension of the maximum-likelihood-binomial approach (MLB); (5) ordered-subset analysis (OSA); and (6) logistic regression modeling (COVLINK). In all three G x E models, most of these six statistics perform better when using the covariate C1 associated with a G x E interaction effect than when using the environmental risk factor C2 or the random noise covariate C3. Compared with a model-free method without covariates (S(all)), the mixture model performs the best when using C1, with the high-to-low OSA method also performing quite well. Generally, MLB is the least sensitive to covariate choice. However, most of these statistics do not provide better power than S(all). Thus, while inclusion of the "correct" covariate can lead to increased power, careful selection of appropriate covariates is vital for success.

Neural network analysis in pharmacogenetics of mood disorders

Background

The increasing number of available genotypes for genetic studies in humans requires more advanced techniques of analysis. We previously reported significant univariate associations between gene polymorphisms and antidepressant response in mood disorders. However the combined analysis of multiple gene polymorphisms and clinical variables requires the use of non linear methods.

Methods

In the present study we tested a neural network strategy for a combined analysis of two gene polymorphisms. A Multi Layer Perceptron model showed the best performance and was therefore selected over the other networks. One hundred and twenty one depressed inpatients treated with fluvoxamine in the context of previously reported pharmacogenetic studies were included. The polymorphism in the transcriptional control region upstream of the 5HTT coding sequence (SERTPR) and in the Tryptophan Hydroxylase (TPH) gene were analysed simultaneously.

Results

A multi layer perceptron network composed by 1 hidden layer with 7 nodes was chosen. 77.5 % of responders and 51.2% of non responders were correctly classified (ROC area = 0.731 – empirical p value = 0.0082). Finally, we performed a comparison with traditional techniques. A discriminant function analysis correctly classified 34.1 % of responders and 68.1 % of non responders (F = 8.16 p = 0.0005).

Conclusions

Overall, our findings suggest that neural networks may be a valid technique for the analysis of gene polymorphisms in pharmacogenetic studies. The complex interactions modelled through NN may be eventually applied at the clinical level for the individualized therapy.