Bias correction to secondary trait analysis with case–control design

In genetic association studies with densely typed genetic markers, it is often of substantial interest to examine not only the primary phenotype but also the secondary traits for their association with the genetic markers. For more efficient sample ascertainment of the primary phenotype, a case–control design or its variants, such as the extreme‐value sampling design for a quantitative trait, are often adopted. The secondary trait analysis without correcting for the sample ascertainment may yield a biased association estimator. We propose a new method aiming at correcting the potential bias due to the inadequate adjustment of the sample ascertainment. The method yields explicit correction formulas that can be used to both screen the genetic markers and rapidly evaluate the sensitivity of the results to the assumed baseline case‐prevalence rate in the population. Simulation studies demonstrate good performance of the proposed approach in comparison with the more computationally intensive approaches, such as the compensator approaches and the maximum prospective likelihood approach. We illustrate the application of the approach by analysis of the genetic association of prostate specific antigen in a case–control study of prostate cancer in the African American population. Copyright © 2012 John Wiley & Sons, Ltd.     

Research issues in genetic testing of adolescents for obesity

Obesity is often established in adolescence, and advances are being made in identifying its genetic underpinnings. We examine issues related to the eventual likelihood of genetic tests for obesity targeted to adolescents: family involvement; comprehension of the test's meaning; how knowledge of genetic status may affect psychological adaptation; minors' ability to control events; parental/child autonomy; ability to make informed medical decisions; self-esteem; unclear distinctions between early/late onset for this condition; and social stigmatization. The public health arena will be important in educating families about possible future genetic tests for obesity.     

Estimation of genotype relative risks from pedigree data by retrospective likelihoods

Pedigrees collected for linkage studies are a valuable resource that could be used to estimate genetic relative risks (RRs) for genetic variants recently discovered in case‐control genome wide association studies. To estimate RRs from highly ascertained pedigrees, a pedigree “retrospective likelihood” can be used, which adjusts for ascertainment by conditioning on the phenotypes of pedigree members. We explore a variety of approaches to compute the retrospective likelihood, and illustrate a Newton‐Raphson method that is computationally efficient particularly for single nucleotide polymorphisms (SNPs) modeled as log‐additive effect of alleles on the RR. We also illustrate, by simulations, that a naïve “composite likelihood” method that can lead to biased RR estimates, mainly by not conditioning on the ascertainment process—or as we propose—the disease status of all pedigree members. Applications of the retrospective likelihood to pedigrees collected for a prostate cancer linkage study and recently reported risk‐SNPs illustrate the utility of our methods, with results showing that the RRs estimated from the highly ascertained pedigrees are consistent with odds ratios estimated in case‐control studies. We also evaluate the potential impact of residual correlations of disease risk among family members due to shared unmeasured risk factors (genetic or environmental) by allowing for a random baseline risk parameter. When modeling only the affected family members in our data, there was little evidence for heterogeneity in baseline risks across families. Genet. Epidemiol. 34: 287–298, 2010. © 2009 Wiley‐Liss, Inc.     

Using family members to augment genetic case–control studies of a life‐threatening disease

Survival bias is difficult to detect and adjust for in case–control genetic association studies but can invalidate findings when only surviving cases are studied and survival is associated with the genetic variants under study. Here, we propose a design where one genotypes genetically informative family members (such as offspring, parents, and spouses) of deceased cases and incorporates that surrogate genetic information into a retrospective maximum likelihood analysis. We show that inclusion of genotype data from first‐degree relatives permits unbiased estimation of genotype association parameters. We derive closed‐form maximum likelihood estimates for association parameters under the widely used log‐additive and dominant association models. Our proposed design not only permits a valid analysis but also enhances statistical power by augmenting the sample with indirectly studied individuals. Gene variants associated with poor prognosis can also be identified under this design. We provide simulation results to assess performance of the methods. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

A comparison of three different models for estimating relative risk in meta-analysis of clinical trials under unobserved heterogeneity

We focus on the comparison of three statistical models used to estimate the treatment effect in meta-analysis when individually pooled data are available. The models are two conventional models, namely a multi-level and a model based upon an approximate likelihood, and a newly developed model, the profile likelihood model which might be viewed as an extension of the Mantel-Haenszel approach. To exemplify these methods, we use results from a meta-analysis of 22 trials to prevent respiratory tract infections. We show that by using the multi-level approach, in the case of baseline heterogeneity, the number of clusters or components is considerably over-estimated. The approximate and profile likelihood method showed nearly the same pattern for the treatment effect distribution. To provide more evidence two simulation studies are accomplished. The profile likelihood can be considered as a clear alternative to the approximate likelihood model. In the case of strong baseline heterogeneity, the profile likelihood method shows superior behaviour when compared with the multi-level model.     

Testing Hardy‐Weinberg equilibrium using mother‐child case‐control samples

Genetic association studies of obstetric complications may genotype case and control mothers, or their respective newborns, or both case‐control mothers and their children. The relatively high prevalence of many obstetric complications and the availability of both maternal and offspring's genotype data have provided motivation to study new methods for testing for deviations from Hardy‐Weinberg equilibrium (HWE). We propose four novel test statistics, each of which uses a different type of data as follows: (1) a test using maternal case‐control genotype data, (2) a test using offspring genotype data, (3) a combination of the first and second tests, and (4) a test based on the joint classification of case‐control maternal‐child genotype data. The selection of case and control mothers (and thus their children) is accounted for by weighting both maternal and child contributions to the test statistics with sampling probabilities. Our tests thus do not require that the phenotype be rare as is the case for HWE tests using only controls, and are particularly suitable for genetic association studies of relatively common complications such as premature birth. The third and fourth tests described above utilize both maternal and child genotype data and appropriately account for the correlation between maternal and child genotypes. On the basis of extensive simulation studies to compare the type‐I error and power for proposed tests, we recommend the third combined test statistic for routine use in the analysis of case‐control studies of mother‐child pairs. Genet. Epidemiol. 33:539–548, 2009. © 2009 Wiley‐Liss, Inc.     

Determining linkage and mode of inheritance: Mod scores and other methods

The lod score method remains a popular approach for detecting linkage and estimating the recombination fraction θ between a marker locus and a trait locus. However, its implementation requires knowledge of all parameters of the genetic mechanism, including the number of loci involved and the genotype specific penetrance, which could depend on factors such as age. When some of the penetrance parameters ϕ are unknown, several methods are available, and have been reviewed by Hodge and Elston [(1994) Genet Epidemiol 11:329–342]. These include the “wrod score” (lod score maximized over θ under a wrong value of ϕ) and “mod score” (lod score maximized over both θ and ϕ) methods for inference on θ. It has further been proposed that the mod score also be used for estimating ϕ. In this paper, we review and assess the adequacy of these two methods for inferences on both ϕ and θ. In particular, all of the methods can be seen as variations on likelihood inference, using the information in the conditional likelihood for the marker data, given the trait data. The loss of efficiency of the mod is compared to that of the full likelihood, which utilizes all information available in the trait data. We also propose an alternative, based on the pseudo-likelihood, where ϕ is estimated via the trait information and plugged into the conditional likelihood. This method is compared to the mod score method, and the advantages and disadvantages of each are elucidated. In particular, it is seen that the pseudo-likelihood method can be more efficient than the mod score method if the ascertainment scheme can be modeled. As examples, both a random sample and a multiplex ascertainment scheme are considered. In addition, the pseudo-likelihood method leads to likelihood ratio tests for detecting linkage with a simple, known asymptotic reference distribution, a feature not shared by the mod score. Finally, we discuss the advantages of using the pseudo-likelihood method over the full likelihood method, both of which are valid when the ascertainment scheme is known. © 1996 Wiley-Liss, Inc.     

Genetic variance of tolerance and the toxicant threshold model

A statistical genetics method is presented for estimating the genetic variance (heritability) of tolerance to pollutants on the basis of a standard acute toxicity test conducted on several isofemale lines of cladoceran species. To analyze the genetic variance of tolerance in the case when the response is measured as a few discrete states (quantal endpoints), the authors attempted to apply the threshold character model in quantitative genetics to the threshold model separately developed in ecotoxicology. The integrated threshold model (toxicant threshold model) assumes that the response of a particular individual occurs at a threshold toxicant concentration and that the individual tolerance characterized by the individual's threshold value is determined by genetic and environmental factors. As a case study, the heritability of tolerance to p-nonylphenol in the cladoceran species Daphnia galeata was estimated by using the maximum likelihood method and nested analysis of variance (ANOVA). Broad-sense heritability was estimated to be 0.199?±?0.112 by the maximum likelihood method and 0.184?±?0.089 by ANOVA; both results implied that the species examined had the potential to acquire tolerance to this substance by evolutionary change.     

Increased power for case-control studies of single nucleotide polymorphisms through incorporation of family history and genetic constraints

Association studies assessing the relationship between a common polymorphism and disease generally compare allele frequencies in cases and controls. In such studies, a limited amount of information is often available about disease incidence in relatives. We hypothesised that more power could be obtained by incorporating the constraints imposed by the properties of a genetic polymorphism, and that power could be further increased by using family history (FH) information. We have developed a simple method for incorporating basic FH information from cases and controls into a genetic association study, assuming Hardy-Weinberg equilibrium (HWE) in the general population. We model the likelihood of the data in terms of the allele frequency and its relative risk (RR) of disease and perform likelihood ratio tests. Using simulations, we compared the power to detect an association using this approach with that of a 2 x 2 chi-squared test, for a range of disease models. The sample size required to detect an association is consistently lower for tests including the HWE constraint, with the largest reduction for more common alleles. The required sample size is reduced further by stratifying by FH. Stratifying by FH also improves the precision of the RR estimates. In situations where basic FH data are already available, this study shows that efficiency can be improved by the inclusion of even this small amount of extra information.     

On the robustness of tests of genetic associations incorporating gene-environment interaction when the environmental exposure is misspecified

We consider the robustness of tests of genetic associations that incorporate gene-environment interactions when the environmental exposure is misspecified, which is likely the case when the exposure is continuous. We formally prove that, under the null hypothesis of no genetic association, misspecified ordinary logistic regression and profile likelihood (Chatterjee and Carroll, Biometrika. 2005;92:399-418) analyses of case-control data both consistently estimate the null parameters of no genetic main effect and interaction, provided that genetic and environmental factors are unrelated in the underlying population. However, we argue that the associated likelihood ratio test, score test, and Wald test statistics obtained using the estimated information matrix have incorrect type-1 error rates due to model mis-specification. Based on these observations, we propose the use of the sandwich estimator of variance in conjunction with the consistent maximum (profile) likelihood estimates to construct Wald-type test statistics with correct type-1 error rate for the null of no genetic association.     

Combining two-point genetic linkage analyses using mapping functions

A likelihood ratio statistic is proposed for combining two-point genetic linkage analyses when the two-point analyses are between a trait and a well-defined map of markers. It is assumed that the two-point analyses are independent, as in the case of choosing only the most informative marker per family. The asymptotic distribution of the likelihood ratio statistic is derived under the null hypothesis of no linkage of the trait with a map of 2 markers, with intermarker genetic distance δ. This distribution is shown to be a chi-square mixture distribution with mixing probability depending on δ and the assumed mapping function. We use this asymptotic result to approximate the distribution of the likelihood ratio statistic for the more general case of more than 2 markers. Simulation results indicate that this may be reasonable. Power is evaluated by simulations and results indicate that this approach, which constrains the intermarker distances to their known values, tends to be more powerful than other methods proposed in the literature. © 1994 Wiley-Liss, Inc.     

Methods for detecting interactions between genetic polymorphisms and prenatal environment exposure with a mother‐child design

Prenatal exposures such as polycyclic aromatic hydrocarbons and early postnatal environmental exposures are of particular concern because of the heightened susceptibility of the fetus and infant to diverse environmental pollutants. Marked inter‐individual variation in response to the same level of exposure was observed in both mothers and their newborns, indicating that susceptibility might be due to genetic factors. With the mother‐child pair design, existing methods developed for parent‐child trio data or random sample data are either not applicable or not designed to optimally use the information. To take full advantage of this unique design, which provides partial information on genetic transmission and has both maternal and newborn outcome status collected, we developed a likelihood‐based method that uses both the maternal and the newborn information together and jointly models gene‐environment interactions on maternal and newborn outcomes. Through intensive simulation studies, the proposed method has demonstrated much improved power in detecting gene‐environment interactions. The application on a real mother‐child pair data from a study conducted in Krakow, Poland, suggested four significant gene‐environment interactions after multiple comparisons adjustment. Genet. Epidemiol. 34: 125–132, 2010. © 2009 Wiley‐Liss, Inc.     

A Multi‐Locus Likelihood Method for Assessing Parent‐of‐Origin Effects Using Case‐Control Mother‐Child Pairs

Parent‐of‐origin effects have been pointed out to be one plausible source of the heritability that was unexplained by genome‐wide association studies. Here, we consider a case‐control mother‐child pair design for studying parent‐of‐origin effects of offspring genes on neonatal/early‐life disorders or pregnancy‐related conditions. In contrast to the standard case‐control design, the case‐control mother‐child pair design contains valuable parental information and therefore permits powerful assessment of parent‐of‐origin effects. Suppose the region under study is in Hardy‐Weinberg equilibrium, inheritance is Mendelian at the diallelic locus under study, there is random mating in the source population, and the SNP under study is not related to risk for the phenotype under study because of linkage disequilibrium (LD) with other SNPs. Using a maximum likelihood method that simultaneously assesses likely parental sources and estimates effect sizes of the two offspring genotypes, we investigate the extent of power increase for testing parent‐of‐origin effects through the incorporation of genotype data for adjacent markers that are in LD with the test locus. Our method does not need to assume the outcome is rare because it exploits supplementary information on phenotype prevalence. Analysis with simulated SNP data indicates that incorporating genotype data for adjacent markers greatly help recover the parent‐of‐origin information. This recovery can sometimes substantially improve statistical power for detecting parent‐of‐origin effects. We demonstrate our method by examining parent‐of‐origin effects of the gene PPARGC1A on low birth weight using data from 636 mother‐child pairs in the Jerusalem Perinatal Study.     

The resource implications and service outcomes of genetic services in the context of DNA technology

The use of DNA technology has transformed genetic counselling services for single gene disorders. For conditions such as Duchenne muscular dystrophy and cystic fibrosis, both of which cause severe morbidity and premature death, DNA tests mean that individuals can be told with greater certainty whether they are carriers of a genetic trait and of the likelihood of their having a child affected by the disorder. This paper presents the findings of an evaluation of the resource implications and service outcomes of genetic services in the context of DNA technology (DNA services). Results are based on data collected over a 4-year period from three large genetics centres throughout the United Kingdom. Our conclusions are that for the conditions for which they are commonly used, and as a regionally based service, DNA services are effective and relatively inexpensive. For severe conditions, and for neurological disorders, although tests will not alter family size plans the demand for tests during pregnancy will be high and the results will have a significant impact on individuals' decisions regarding the continuation of their pregnancies. For conditions of variable severity, those that start late in life or are amenable to treatment, the demand for tests is likely to be low. In comparison with the general population we found a greater existence of psychological side effects amongst counsellees. These effects were linked to individuals having a close relative, usually a child, already affected by a disorder rather than being a consequence of the genetic counselling process.     

A likelihood ratio test of population Hardy‐Weinberg equilibrium for case‐control studies

Testing Hardy‐Weinberg equilibrium (HWE) in the control group is commonly used to detect genotyping errors in genetic association studies. We propose a likelihood ratio test for testing HWE in the study population using both case and control samples. This test incorporates underlying association models. Another feature is that, when we infer the disease‐genotype association, we explicitly incorporate HWE or a possible departure from Hardy‐Weinberg equilibrium (DHWE) into the model. Our unified framework enables us to infer the disease‐genotype association when a detected DHWE needs to be part of the model after causes for the DHWE are explored. Real data sets are used to illustrate the application of the methodology and its implication in genetic association studies. Our analysis and interpretation touch on issues such as genotyping errors, population selection, population stratification, or the study sampling plan, that all could be the cause of DHWE. Genet. Epidemiol. 2009. Published 2008 Wiley‐Liss, Inc.     

Secondary phenotype analysis in ascertained family designs: application to the Leiden longevity study

The case‐control design is often used to test associations between the case‐control status and genetic variants. In addition to this primary phenotype, a number of additional traits, known as secondary phenotypes, are routinely recorded, and typically, associations between genetic factors and these secondary traits are studied too. Analysing secondary phenotypes in case‐control studies may lead to biased genetic effect estimates, especially when the marker tested is associated with the primary phenotype and when the primary and secondary phenotypes tested are correlated. Several methods have been proposed in the literature to overcome the problem, but they are limited to case‐control studies and not directly applicable to more complex designs, such as the multiple‐cases family studies. A proper secondary phenotype analysis, in this case, is complicated by the within families correlations on top of the biased sampling design. We propose a novel approach to accommodate the ascertainment process while explicitly modelling the familial relationships. Our approach pairs existing methods for mixed‐effects models with the retrospective likelihood framework and uses a multivariate probit model to capture the association between the mixed type primary and secondary phenotypes. To examine the efficiency and bias of the estimates, we performed simulations under several scenarios for the association between the primary phenotype, secondary phenotype and genetic markers. We will illustrate the method by analysing the association between triglyceride levels and glucose (secondary phenotypes) and genetic markers from the Leiden Longevity Study, a multiple‐cases family study that investigates longevity. © 2017 The Authors. Statistics in Medicine Published by JohnWiley & Sons Ltd.     

Mediation analysis of multiple mediators with incomplete omics data

There is an increasing interest in using multiple types of omics features (e.g., DNA sequences, RNA expressions, methylation, protein expressions, and metabolic profiles) to study how the relationships between phenotypes and genotypes may be mediated by other omics markers. Genotypes and phenotypes are typically available for all subjects in genetic studies, but typically, some omics data will be missing for some subjects, due to limitations such as cost and sample quality. In this article, we propose a powerful approach for mediation analysis that accommodates missing data among multiple mediators and allows for various interaction effects. We formulate the relationships among genetic variants, other omics measurements, and phenotypes through linear regression models. We derive the joint likelihood for models with two mediators, accounting for arbitrary patterns of missing values. Utilizing computationally efficient and stable algorithms, we conduct maximum likelihood estimation. Our methods produce unbiased and statistically efficient estimators. We demonstrate the usefulness of our methods through simulation studies and an application to the Metabolic Syndrome in Men study.     

Case-sibling gene-association studies for diseases with variable age at onset

Studies which compare cases to disease-free siblings are useful for assessing association between a genetic locus and a phenotypic trait, as they eliminate the possibility of confounding by population stratification. Many analytic methods for such family-based studies are based on a binary disease model. However, complex diseases have variable age at onset. Consequently, binary-outcome methods can be inefficient or biased. We review methods for analysing censored age-at-onset data from family studies, including stratified Cox regression and genotype-decomposition regression, an unstratified procedure which regresses age-at-onset on between- and within-family genotype components. We also introduce a retrospective likelihood for censored age-at-onset data, which requires an external estimate of the baseline hazard. Stratified Cox regression does not use controls who have not attained the age of their case sibling(s), potentially leading to a loss of efficiency. Both genotype-decomposition regression and the retrospective likelihood use these younger controls. We assess the performance of these methods via simulation studies. Stratified Cox regression and the retrospective likelihood have appropriate type I error rates in almost all situations studied; genotype-decomposition regression is often anti-conservative. Away from the null, confidence intervals for the relative risk derived from stratified Cox regression are anti-conservative when the disease is rare and case-rich families are sampled. The retrospective likelihood is more efficient than stratified Cox regression and its confidence intervals have correct coverage when the disease is rare or the estimate of the baseline hazard is reasonably accurate. These results suggest that when estimating genotype relative risks is the principal analytic goal, stratified Cox regression is appropriate as long as the disease is common; when the disease is rare, the retrospective likelihood may be more appropriate.     

Präimplantationsdiagnostik – PID

Preimplantation diagnosis (PID) comprises all the relevant diagnostic procedures for the investigation of genetic, structural, or numerical changes of the genetic information in spermatozoa and oocytes as well as in embryos after in vitro fertilization (IVF) or intracytoplasmic sperm injection (ICSI). PID of oocytes is well established in Germany for the above-mentioned indications. PID at the embryonic level, i.e., trophectoderm biopsy of blastocysts, is possible in centers with proven expertise in reproductive medicine and human genetics. A high risk for genetic disease in the child or a high likelihood for stillbirth or miscarriage is a prerequisite for PID. A specialized ethics committee is required to look into each case before making a decision. While PID is still under development in Germany, it has been a well-established technology worldwide for 24 years. International experience in PID and the resulting implications are discussed in this article.