Calculating Within-Pair Difference Scores in the Co-twin Control Design. Effects of Alternative Strategies.

Co-twin studies are an elegant and powerful design that allows controlling for the effect of confounding variables, including genetic and a range of environmental factors. There are several approaches to carry out this design. One of the methods commonly used, when contrasting continuous variables, is to calculate difference scores between members of a twin pair on two associated variables, in order to analyse the covariation of such differences. However, information regarding whether and how the different ways of estimating within-pair difference scores may impact the results is scant. This study aimed to compare the results obtained by different methods of data transformation when performing a co-twin study and test how the magnitude of the association changes using each of those approaches. Data was simulated using a direction of causation model and by fixing the effect size of causal path to low, medium, and high values. Within-pair difference scores were calculated as relative scores for diverse within-pair ordering conditions or absolute scores. Pearson's correlations using relative difference scores vary across the established scenarios (how twins were ordered within pairs) and these discrepancies become larger as the within-twin correlation increases. Absolute difference scores tended to produce the lowest correlation in every condition. Our results show that both using absolute difference scores or ordering twins within pairs, may produce an artificial decrease in the magnitude of the studied association, obscuring the ability to detect patterns compatible with causation, which could lead to discrepancies across studies and erroneous conclusions.

Type I Error Rates and Parameter Bias in Multivariate Behavioral Genetic Models.

For many multivariate twin models, the numerical Type I error rates are lower than theoretically expected rates using a likelihood ratio test (LRT), which implies that the significance threshold for statistical hypothesis tests is more conservative than most twin researchers realize. This makes the numerical Type II error rates higher than theoretically expected. Furthermore, the discrepancy between the observed and expected error rates increases as more variables are included in the analysis and can have profound implications for hypothesis testing and statistical inference. In two simulation studies, we examine the Type I error rates for the Cholesky decomposition and Correlated Factors models. Both show markedly lower than nominal Type I error rates under the null hypothesis, a discrepancy that increases with the number of variables in the model. In addition, we observe slightly biased parameter estimates for the Cholesky decomposition and Correlated Factors models. By contrast, if the variance-covariance matrices for variance components are estimated directly (without constraints), the numerical Type I error rates are consistent with theoretical expectations and there is no bias in the parameter estimates regardless of the number of variables analyzed. We call this the direct symmetric approach. It appears that each model-implied boundary, whether explicit or implicit, increases the discrepancy between the numerical and theoretical Type I error rates by truncating the sampling distributions of the variance components and inducing bias in the parameters. The direct symmetric approach has several advantages over other multivariate twin models as it corrects the Type I error rate and parameter bias issues, is easy to implement in current software, and has fewer optimization problems. Implications for past and future research, and potential limitations associated with direct estimation of genetic and environmental covariance matrices are discussed.

FinnTwin16: A Longitudinal Study from Age 16 of a Population-Based Finnish Twin Cohort.

The purpose of this review is to provide a detailed and updated description of the FinnTwin16 (FT16) study and its future directions. The Finnish Twin Cohort comprises three different cohorts: the Older Twin Cohort established in the 1970s and the FinnTwin12 and FT16 initiated in the 1990s. FT16 was initiated in 1991 to identify the genetic and environmental precursors of alcoholism, but later the scope of the project expanded to studying the determinants of various health-related behaviors and diseases in different stages of life. The main areas addressed are alcohol use and its consequences, smoking, physical activity, overall physical health, eating behaviors and eating disorders, weight development, obesity, life satisfaction and personality. To date, five waves of data collection have been completed and the sixth is now planned. Data from the FT16 cohort have contributed to several hundred studies and many substudies, with more detailed phenotyping and collection of omics data completed or underway. FT16 has also contributed to many national and international collaborations.

Extending Causality Tests with Genetic Instruments: An Integration of Mendelian Randomization with the Classical Twin Design.

Although experimental studies are regarded as the method of choice for determining causal influences, these are not always practical or ethical to answer vital questions in health and social research (e.g., one cannot assign individuals to a "childhood trauma condition" in studying the causal effects of childhood trauma on depression). Key to solving such questions are observational studies. Mendelian Randomization (MR) is an influential method to establish causality in observational studies. MR uses genetic variants to test causal relationships between exposures/risk factors and outcomes such as physical or mental health. Yet, individual genetic variants have small effects, and so, when used as instrumental variables, render MR liable to weak instrument bias. Polygenic scores have the advantage of larger effects, but may be characterized by horizontal pleiotropy, which violates a central assumption of MR. We developed the MR-DoC twin model by integrating MR with the Direction of Causation twin model. This model allows us to test pleiotropy directly. We considered the issue of parameter identification, and given identification, we conducted extensive power calculations. MR-DoC allows one to test causal hypotheses and to obtain unbiased estimates of the causal effect given pleiotropic instruments, while controlling for genetic and environmental influences common to the outcome and exposure. Furthermore, the approach allows one to employ strong instrumental variables in the form of polygenic scores, guarding against weak instrument bias, and increasing the power to detect causal effects of exposures on potential outcomes. Beside allowing to test pleiotropy directly, incorporating in MR data collected from relatives provide additional within-family data that resolve additional assumptions like random mating, the absence of the gene-environment interaction/covariance, no dyadic effects. Our approach will enhance and extend MR's range of applications, and increase the value of the large cohorts collected at twin/family registries as they correctly detect causation and estimate effect sizes even in the presence of pleiotropy.

Higher Rates of DZ Twinning in a Twenty-First Century Birth Cohort.

The Colorado Twin Registry is a population based registry initiated in 1984 with the involvement of the Colorado Department of Health, Division of Vital Statistics. Recruitment includes birth cohorts several years prior to 1984 and all subsequent years. As part of a recent evaluation of Colorado birth records for the years 2006 through 2008 we became aware of a shifting trend in the proportion of MZ and DZ twins in the Colorado population. Historically (Bulmer 1970 The biology of twinning in man, Clarendon, Oxford) we have expected a 1/3, 1/3, 1/3 ratio of MZ, same-sex DZ and opposite sex DZ twins in Caucasian populations. An excess of MZ pairs in most studies was assumed to be due to selection bias. Somewhat more recently, Hur et al.(1995 Behav Genet 25, 337-340) provided evidence that the DZ twinning rate was falling and that therefore selection bias was not the reason for higher MZ enrollment in most twin studies. They suggested that twin researchers might consider strategies to over-enroll DZ pairs to maximize statistical power. In contrast, we now find that of the 3217 twin births in Colorado from 2006 to 2008 with identified sex information the MZ rate is estimated at only 22%, and we have corroborating reports from other states of similar estimates. These were calculated applying Weinberg's rule which assumes an equal birth rate for same sex and opposite sex DZ pairs so that the proportion of MZ in a sample is the proportion of same sex (MM + FF) minus the proportion of opposite-sex (MF, FM). We explore factors, such as an increase in the proportion of non-Caucasian parents and an increase in average maternal age, which may contribute to this shift.

Sum Scores in Twin Growth Curve Models: Practicality Versus Bias.

To study behavioral or psychiatric phenotypes, multiple indices of the behavior or disorder are often collected that are thought to best reflect the phenotype. Combining these items into a single score (e.g. a sum score) is a simple and practical approach for modeling such data, but this simplicity can come at a cost in longitudinal studies, where the relevance of individual items often changes as a function of age. Such changes violate the assumptions of longitudinal measurement invariance (MI), and this violation has the potential to obfuscate the interpretation of the results of latent growth models fit to sum scores. The objectives of this study are (1) to investigate the extent to which violations of longitudinal MI lead to bias in parameter estimates of the average growth curve trajectory, and (2) whether absence of MI affects estimates of the heritability of these growth curve parameters. To this end, we analytically derive the bias in the estimated means and variances of the latent growth factors fit to sum scores when the assumption of longitudinal MI is violated. This bias is further quantified via Monte Carlo simulation, and is illustrated in an empirical analysis of aggression in children aged 3-12 years. These analyses show that measurement non-invariance across age can indeed bias growth curve mean and variance estimates, and our quantification of this bias permits researchers to weigh the costs of using a simple sum score in longitudinal studies. Simulation results indicate that the genetic variance decomposition of growth factors is, however, not biased due to measurement non-invariance across age, provided the phenotype is measurement invariant across birth-order and zygosity in twins.

Measuring early or late dependence for bivariate lifetimes of twins.

We consider data from the Danish twin registry and aim to study in detail how lifetimes for twin-pairs are correlated. We consider models where we specify the marginals using a regression structure, here Cox's regression model or the additive hazards model. The best known such model is the Clayton-Oakes model. This model can be extended in several directions. One extension is to allow the dependence parameter to depend on covariates. Another extension is to model dependence via piecewise constant cross-hazard ratio models. We show how both these models can be implemented for large sample data, and suggest a computational solution for obtaining standard errors for such models for large registry data. In addition we consider alternative models that have some computational advantages and with different dependence parameters based on odds ratios of the survival function using the Plackett distribution. We also suggest a way of assessing how and if the dependence is changing over time, by considering either truncated or right-censored versions of the data to measure late or early dependence. This can be used for formally testing if the dependence is constant, or decreasing/increasing. The proposed procedures are applied to Danish twin data to describe dependence in the lifetimes of the twins. Here we show that the early deaths are more correlated than the later deaths, and by comparing MZ and DZ associations we suggest that early deaths might be more driven by genetic factors. This conclusion requires models that are able to look at more local dependence measures. We further show that the dependence differs for MZ and DZ twins and appears to be the same for males and females, and that there are indications that the dependence increases over calendar time.

Testing systematic genotype by environment interactions using item level data.

Investigating genotype by environment interactions (GxE) is generally considered challenging due to the scale dependency of the interaction effect. The present paper illustrates the problems associated with testing for GxEs on summed item scores within the well-known ACE model. That is, it is shown how genuine GxEs may be masked and how spurious interactions can arise from scaling issues in the data. A solution is proposed which explicitly distinguishes between a measurement model for the ordinal item responses and a biometric model in which the GxE effects are investigated. The new approach is studied in a simulation study using both a scenario in which the measurement instrument suffers from mild scaling problems and a scenario in which the measurement instrument suffers from severe scaling problems. Results indicate that the severity of the scale problems affects the power to detect GxE, but it rarely results in false positives. We illustrate the new approach on a real dataset concerning affect.

Multivariate genetic analyses in heterogeneous populations.

Martin and Eaves (Heredity 38(1):79-95, 1977) proposed a multivariate model for twin and family data in order to investigate potential differences in the genetic and environmental architecture of multivariate phenotypes. The general form of the model is the independent pathway model, which differentiates between genetic and environmental influences at the item level, and therefore permits the decomposition to differ across items. A restricted version is the common pathway model, where the decomposition takes place at the factor level. The paper has spurred numerous studies, and evidence for differences in genetic and environmental architecture has been established for personality and several other psychiatric phenotypes by showing a better fit of the independent pathway model compared to the common pathway model. We show that genome-wide association studies (GWAS) that use an aggregate score computed from multiple questionnaire items as a univariate phenotype implicitly assume a similar structure as the common pathway model. It has been shown that in case of a differential genetic and environmental architecture, multivariate GWAS methods can outperform the univariate GWAS approach. However, current multivariate methods rely on the assumptions of phenotypic and genetic homogeneity, that is, item responses are assumed to have the same means and covariances, and genetic effects are assumed to be the same for all subjects. We describe a distance-based regression technique that is designed to account for subgroups in the population, and that therefore can account for differential genetic effects. A first evaluation with simulated data shows a substantial increase of power compared to univariate GWAS.

Research review: the shared environment as a key source of variability in child and adolescent psychopathology.

BACKGROUND: Behavioral genetic research has historically concluded that the more important environmental influences were nonshared or result in differences between siblings, whereas environmental influences that create similarities between siblings (referred to as shared environmental influences) were indistinguishable from zero. Recent theoretical and meta-analytic work {Burt. Psychological Bulletin [135 (2009) 608]} has challenged this conclusion as it relates to child and adolescent psychopathology, however, arguing that the shared environment is a moderate, persistent, and identifiable source of individual differences in such outcomes prior to adulthood. METHODS: The current review seeks to bolster research on the shared environment by highlighting both the logistic advantages inherent in studies of the shared environment, as well as the use of nontraditional but still genetically informed research designs to study shared environmental influences. RESULTS: Although often moderate in magnitude prior to adulthood and free of unsystematic measurement error, shared environmental influences are nevertheless likely to have been underestimated in prior research. Moreover, the shared environment is likely to include proximal effects of the family, as well as the effects of more distal environmental contexts such as neighborhood and school. These risk and protective factors could influence the child either as main effects or as moderators of genetic influence (i.e. gene-environment interactions). Finally, because the absence of genetic relatedness in an otherwise nonindependent dataset also qualifies as 'genetically informed', studies of the shared environment are amenable to the use of novel and non-traditional designs (with appropriate controls for selection). CONCLUSIONS: The shared environment makes important contributions to most forms of child and adolescent psychopathology. Empirical examinations of the shared environment would thus be of real and critical value for understanding the development and persistence of common mental health issues prior to adulthood.

Twins reunited: scientific and personal perspectives/twin research studies: multiple birth effects on IQ and body size; life style, muscles, and metabolism; monochorionic dizygotic twin with blood chimerism; amniocentesis for twins/twins in the media: identical doctors; freedom fighter for twins; twin scholarships; Auguste and Jean-Felix Piccard; twins born apart.

A reunion of 38-year-old female monozygotic twins took place in Daegu, South Korea, on January 14, 2014. Scientific and personal perspectives on this extraordinary event are provided. A review of timely twin research follows, covering the effects of multiple births on IQ and body size, lifestyle and physical fitness associations, a rare case of a dizygotic twin with blood chimerism and definitional issues surrounding amniocentesis-related loss in multiple birth pregnancies. Interesting and informative mention of twins in the media includes twin doctors, a twin freedom fighter, the availability of college scholarships for twins, a new book about the Piccard family (two of whose members were twins), and co-twins born before and after the new year. A follow-up to a previous mention of identical twin biatheletes is also provided.

Matched survival data in a co-twin control design.

When using the co-twin control design for analysis of event times, one needs a model to address the possible within-pair association. One such model is the shared frailty model in which the random frailty variable creates the desired within-pair association. Standard inference for this model requires independence between the random effect and the covariates. We study how violations of this assumption affect inference for the regression coefficients and conclude that substantial bias may occur. We propose an alternative way of making inference for the regression parameters by using a fixed-effects models for survival in matched pairs. Fitting this model to data generated from the frailty model provides consistent and asymptotically normal estimates of regression coefficients, no matter whether the independence assumption is met.

Cross-ratio estimation for bivariate failure times with left truncation.

The cross-ratio is an important local measure that characterizes the dependence between bivariate failure times. To estimate the cross-ratio in follow-up studies where delayed entry is present, estimation procedures need to account for left truncation. Ignoring left truncation yields biased estimates of the cross-ratio. We extend the method of Hu et al., Biometrika 98:341-354 (2011) by modifying the risk sets and relevant indicators to handle left-truncated bivariate failure times, which yields the cross-ratio estimate with desirable asymptotic properties that can be shown by the same techniques used in Hu et al., Biometrika 98:341-354 (2011). Numerical studies are conducted.

Modelling genetic susceptibility to multiple sclerosis with family data.

A genetic contribution to susceptibility is well established in multiple sclerosis (MS) and 57 associated genetic loci have been identified. We have undertaken a meta-analysis of familial risk studies with the aims of providing definitive figures for risks to relatives, performing a segregation analysis and estimating the proportion of the overall genetic risk that currently identified genes represent. We have used standard methods of meta-analysis combined with novel approaches to age adjustment to provide directly comparable estimates of lifetime risk. The overall recurrence risk for monozygotic twins was 18.2% and for siblings 2.7%. The recurrence risk for dizygotic twins was significantly higher than for siblings. The overall estimate of sibling relative risk (λ(S)) was 16.8. Risks for older relatives (parents, siblings, aunts, uncles and cousins) show a latitudinal gradient, in line with population risk. No latitudinal gradient for λ(S) was seen. Segregation analysis supports a multiplicative model of one locus of moderate effect with many loci of small effect. The estimated contribution of the 57 known MS loci is 18-24% of λ(S). This meta-analysis supports the notion of MS being in part the result of multiple genetic susceptibility factors and environmental factors.

Risk prediction measures for case-cohort and nested case-control designs: an application to cardiovascular disease.

Case-cohort and nested case-control designs are often used to select an appropriate subsample of individuals from prospective cohort studies. Despite the great attention that has been given to the calculation of association estimators, no formal methods have been described for estimating risk prediction measures from these 2 sampling designs. Using real data from the Swedish Twin Registry (2004-2009), the authors sampled unstratified and stratified (matched) case-cohort and nested case-control subsamples and compared them with the full cohort (as "gold standard"). The real biomarker (high density lipoprotein cholesterol) and simulated biomarkers (BIO1 and BIO2) were studied in terms of association with cardiovascular disease, individual risk of cardiovascular disease at 3 years, and main prediction metrics. Overall, stratification improved efficiency, with stratified case-cohort designs being comparable to matched nested case-control designs. Individual risks and prediction measures calculated by using case-cohort and nested case-control designs after appropriate reweighting could be assessed with good efficiency, except for the finely matched nested case-control design, where matching variables could not be included in the individual risk estimation. In conclusion, the authors have shown that case-cohort and nested case-control designs can be used in settings where the research aim is to evaluate the prediction ability of new markers and that matching strategies for nested case-control designs may lead to biased prediction measures.

Sibling comparison designs: bias from non-shared confounders and measurement error.

Twins, full siblings, and half-siblings are increasingly used as comparison groups in matched cohort and matched case-control studies. The "within-pair" estimates acquired through these comparisons are free from confounding from all factors that are shared by the siblings. This has made sibling comparisons popular in studying associations thought likely to suffer confounding from socioeconomic or genetic factors. Despite the wide application of these designs in epidemiology, they have received little scrutiny from a statistical or methodological standpoint. In this paper we show, analytically and through a series of simulations, that the standard interpretation of the models is subject to several limitations that are rarely acknowledged.Although within-pair estimates will not be confounded by factors shared by the siblings, such estimates are more severely biased by non-shared confounders than the unpaired estimate. If siblings are less similar with regard to confounders than to the exposure under study, the within-pair estimate will always be more biased than the ordinary unpaired estimate. Attenuation of associations due to random measurement error in exposure will also be higher in the within-pair estimate, leading within-pair associations to be weaker than corresponding unpaired associations, even in the absence of confounding. Implications for the interpretation of sibling comparison results are discussed.

A note on false positives and power in G × E modelling of twin data.

The variance components models for gene-environment interaction proposed by Purcell in 2002 are widely used. In both the bivariate and the univariate parameterization of these models, the variance decomposition of trait T is a function of moderator M. We show that if M and T are correlated, and moderator M is correlated between twins as well, the univariate parameterization produces a considerable increase in false positive moderation effects. A simple extension of this univariate moderation model prevents this elevation of the false positive rate provided the covariance between M and T is itself not also subject to moderation. If the covariance between M and T varies as a function of M, then moderation effects observed in the univariate setting should be interpreted with care as these can have their origin in either moderation of the covariance between M and T or in moderation of the unique paths of T. We conclude that researchers should use the full bivariate moderation model to study the presence of moderation on the covariance between M and T. If such moderation can be ruled out, subsequent use of the extended univariate moderation model, as proposed in this paper, is recommended as this model is more powerful than the full bivariate moderation model.

Gamma frailty model for linkage analysis with application to interval-censored migraine data.

For many diseases, it seems that the age at onset is genetically influenced. Therefore, the age-at-onset data are often collected in order to map the disease gene(s). The ages are often (right) censored or truncated, and therefore, many standard techniques for linkage analysis cannot be used. In this paper, we present a correlated frailty model for censored survival data of siblings. The model is used for testing heritability for the age at onset and linkage between the loci and the gene(s) that influence(s) the survival time. The model is applied to interval-censored migraine twin data. Heritability (obtained from the frailties rather than actual onset times) was estimated as 0.42; this value was highly significant. The highest lod score, a score of 1.9, was found at the end of chromosome 19.

Genetics of menstrual migraine: the epidemiological evidence.

Approximately one of every three to five women with migraine without aura experience migraine attacks in relation to menstruation. The International Classification of Headache Disorders, 2nd Edition provides appendix diagnoses for pure and menstrually related migraine without aura that need further validation. Probands with menstrual migraine might have more affected relatives than probands with nonmenstrual migraine. However, precise epidemiological, family, and twin data still are lacking.