Genetic evidence for a large overlap and potential bidirectional causal effects between resilience and well-being.

Resilience and well-being are strongly related. People with higher levels of well-being are more resilient after stressful life events or trauma and vice versa. Less is known about the underlying sources of overlap and causality between the constructs. In a sample of 11.304 twins and 2.572 siblings from the Netherlands Twin Register, we investigated the overlap and possible direction of causation between resilience (i.e. the absence of psychiatric symptoms despite negative life events) and well-being (i.e. satisfaction with life) using polygenic score (PGS) prediction, twin-sibling modelling, and the Mendelian Randomization Direction of Causality (MR-DoC) model. Longitudinal twin-sibling models showed significant phenotypic correlations between resilience and well-being (.41/.51 at time 1 and 2). Well-being PGS were predictive for both well-being and resilience, indicating that genetic factors influencing well-being also predict resilience. Twin-sibling modeling confirmed this genetic correlation (0.71) and showed a strong environmental correlation (0.93). In line with causality, both genetic (51%) and environmental (49%) factors contributed significantly to the covariance between resilience and well-being. Furthermore, the results of within-subject and MZ twin differences analyses were in line with bidirectional causality. Additionally, we used the MR-DoC model combining both molecular and twin data to test causality, while correcting for pleiotropy. We confirmed the causal effect from well-being to resilience, with the direct effect of well-being explaining 11% (T1) and 20% (T2) of the variance in resilience. Data limitations prevented us to test the directional effect from resilience to well-being with the MR-DoC model. To conclude, we showed a strong relation between well-being and resilience. A first attempt to quantify the direction of this relationship points towards a bidirectional causal effect. If replicated, the potential mutual effects can have implications for interventions to lower psychopathology vulnerability, as resilience and well-being are both negatively related to psychopathology.

Incorporating Polygenic Risk Scores in the ACE Twin Model to Estimate A-C Covariance.

The assumption in the twin model that genotypic and environmental variables are uncorrelated is primarily made to ensure parameter identification, not because researchers necessarily think that these variables are uncorrelated. Although the biasing effects of such correlations are well understood, a method to estimate these parameters in the twin model would be useful. Here we explore the possibility of relaxing this assumption by adding polygenic scores to the (univariate) twin model. We demonstrate that this extension renders the additive genetic (A)-common environmental (C) covariance (σAC) identified. We study the statistical power to reject σAC = 0 in the ACE model and present the results of simulations.

Expanding the genetic architecture of nicotine dependence and its shared genetics with multiple traits.

Cigarette smoking is the leading cause of preventable morbidity and mortality. Genetic variation contributes to initiation, regular smoking, nicotine dependence, and cessation. We present a Fagerström Test for Nicotine Dependence (FTND)-based genome-wide association study in 58,000 European or African ancestry smokers. We observe five genome-wide significant loci, including previously unreported loci MAGI2/GNAI1 (rs2714700) and TENM2 (rs1862416), and extend loci reported for other smoking traits to nicotine dependence. Using the heaviness of smoking index from UK Biobank (N = 33,791), rs2714700 is consistently associated; rs1862416 is not associated, likely reflecting nicotine dependence features not captured by the heaviness of smoking index. Both variants influence nearby gene expression (rs2714700/MAGI2-AS3 in hippocampus; rs1862416/TENM2 in lung), and expression of genes spanning nicotine dependence-associated variants is enriched in cerebellum. Nicotine dependence (SNP-based heritability = 8.6%) is genetically correlated with 18 other smoking traits (rg = 0.40-1.09) and co-morbidities. Our results highlight nicotine dependence-specific loci, emphasizing the FTND as a composite phenotype that expands genetic knowledge of smoking.

Empirical comparisons of multiple Mendelian randomization approaches in the presence of assortative mating.

BACKGROUND: Mendelian randomization (MR) is widely used to unravel causal relationships in epidemiological studies. Whereas multiple MR methods have been developed to control for bias due to horizontal pleiotropy, their performance in the presence of other sources of bias, like non-random mating, has been mostly evaluated using simulated data. Empirical comparisons of MR estimators in such scenarios have yet to be conducted. Pleiotropy and non-random mating have been shown to account equally for the genetic correlation between height and educational attainment. Previous studies probing the causal nature of this association have produced conflicting results. METHODS: We estimated the causal effect of height on educational attainment in various MR models, including the MR-Egger and the MR-Direction of Causation (MR-DoC) models that correct for, or explicitly model, horizontal pleiotropy. RESULTS: We reproduced the weak but positive association between height and education in the Netherlands Twin Register sample (P= 3.9 × 10-6). All MR analyses suggested that height has a robust, albeit small, causal effect on education. We showed via simulations that potential assortment for height and education had no effect on the causal parameter in the MR-DoC model. With the pleiotropic effect freely estimated, MR-DoC yielded a null finding. CONCLUSIONS: Non-random mating may have a bearing on the results of MR studies based on unrelated individuals. Family data enable tests of causal relationships to be conducted more rigorously, and are recommended to triangulate results of MR studies assessing pairs of traits leading to non-random mate selection.

Genome-Wide Meta-Analyses of FTND and TTFC Phenotypes.

INTRODUCTION: FTND (FagerstrÓ§m test for nicotine dependence) and TTFC (time to smoke first cigarette in the morning) are common measures of nicotine dependence (ND). However, genome-wide meta-analysis for these phenotypes has not been reported. METHODS: Genome-wide meta-analyses for FTND (N = 19,431) and TTFC (N = 18,567) phenotypes were conducted for adult smokers of European ancestry from 14 independent cohorts. RESULTS: We found that SORBS2 on 4q35 (p = 4.05 × 10-8), BG182718 on 11q22 (p = 1.02 × 10-8), and AA333164 on 14q21 (p = 4.11 × 10-9) were associated with TTFC phenotype. We attempted replication of leading candidates with independent samples (FTND, N = 7010 and TTFC, N = 10 061), however, due to limited power of the replication samples, the replication of these new loci did not reach significance. In gene-based analyses, COPB2 was found associated with FTND phenotype, and TFCP2L1, RELN, and INO80C were associated with TTFC phenotype. In pathway and network analyses, we found that the interconnected interactions among the endocytosis, regulation of actin cytoskeleton, axon guidance, MAPK signaling, and chemokine signaling pathways were involved in ND. CONCLUSIONS: Our analyses identified several promising candidates for both FTND and TTFC phenotypes, and further verification of these candidates was necessary. Candidates supported by both FTND and TTFC (CHRNA4, THSD7B, RBFOX1, and ZNF804A) were associated with addiction to alcohol, cocaine, and heroin, and were associated with autism and schizophrenia. We also identified novel pathways involved in cigarette smoking. The pathway interactions highlighted the importance of receptor recycling and internalization in ND. IMPLICATIONS: Understanding the genetic architecture of cigarette smoking and ND is critical to develop effective prevention and treatment. Our study identified novel candidates and biological pathways involved in FTND and TTFC phenotypes, and this will facilitate further investigation of these candidates and pathways.

Fetal Origins of Mental Disorders? An Answer Based on Mendelian Randomization.

The Barker hypothesis states that low birth weight (BW) is associated with higher risk of adult onset diseases, including mental disorders like schizophrenia, major depressive disorder (MDD), and attention deficit hyperactivity disorder (ADHD). The main criticism of this hypothesis is that evidence for it comes from observational studies. Specifically, observational evidence does not suffice for inferring causality, because the associations might reflect the effects of confounders. Mendelian randomization (MR) - a novel method that tests causality on the basis of genetic data - creates the unprecedented opportunity to probe the causality in the association between BW and mental disorders in observation studies. We used MR and summary statistics from recent large genome-wide association studies to test whether the association between BW and MDD, schizophrenia and ADHD is causal. We employed the inverse variance weighted (IVW) method in conjunction with several other approaches that are robust to possible assumption violations. MR-Egger was used to rule out horizontal pleiotropy. IVW showed that the association between BW and MDD, schizophrenia and ADHD is not causal (all p > .05). The results of all the other MR methods were similar and highly consistent. MR-Egger provided no evidence for pleiotropic effects biasing the estimates of the effects of BW on MDD (intercept = -0.004, SE = 0.005, p = .372), schizophrenia (intercept = 0.003, SE = 0.01, p = .769), or ADHD (intercept = 0.009, SE = 0.01, p = .357). Based on the current evidence, we refute the Barker hypothesis concerning the fetal origins of adult mental disorders. The discrepancy between our results and the results from observational studies may be explained by the effects of confounders in the observational studies, or by the existence of a small causal effect not detected in our study due to weak instruments. Our power analyses suggested that the upper bound for a potential causal effect of BW on mental disorders would likely not exceed an odds ratio of 1.2.

Genome-wide association meta-analysis of age at first cannabis use.

BACKGROUND AND AIMS: Cannabis is one of the most commonly used substances among adolescents and young adults. Earlier age at cannabis initiation is linked to adverse life outcomes, including multi-substance use and dependence. This study estimated the heritability of age at first cannabis use and identified associations with genetic variants. METHODS: A twin-based heritability analysis using 8055 twins from three cohorts was performed. We then carried out a genome-wide association meta-analysis of age at first cannabis use in a discovery sample of 24 953 individuals from nine European, North American and Australian cohorts, and a replication sample of 3735 individuals. RESULTS: The twin-based heritability for age at first cannabis use was 38% [95% confidence interval (CI) = 19-60%]. Shared and unique environmental factors explained 39% (95% CI = 20-56%) and 22% (95% CI = 16-29%). The genome-wide association meta-analysis identified five single nucleotide polymorphisms (SNPs) on chromosome 16 within the calcium-transporting ATPase gene (ATP2C2) at P < 5E-08. All five SNPs are in high linkage disequilibrium (LD) (r2  > 0.8), with the strongest association at the intronic variant rs1574587 (P = 4.09E-09). Gene-based tests of association identified the ATP2C2 gene on 16q24.1 (P = 1.33e-06). Although the five SNPs and ATP2C2 did not replicate, ATP2C2 has been associated with cocaine dependence in a previous study. ATP2B2, which is a member of the same calcium signalling pathway, has been associated previously with opioid dependence. SNP-based heritability for age at first cannabis use was non-significant. CONCLUSION: Age at cannabis initiation appears to be moderately heritable in western countries, and individual differences in onset can be explained by separate but correlated genetic liabilities. The significant association between age of initiation and ATP2C2 is consistent with the role of calcium signalling mechanisms in substance use disorders.

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.

The Weighting is the Hardest Part: On the Behavior of the Likelihood Ratio Test and the Score Test Under a Data-Driven Weighting Scheme in Sequenced Samples.

Sequence-based association studies are at a critical inflexion point with the increasing availability of exome-sequencing data. A popular test of association is the sequence kernel association test (SKAT). Weights are embedded within SKAT to reflect the hypothesized contribution of the variants to the trait variance. Because the true weights are generally unknown, and so are subject to misspecification, we examined the efficiency of a data-driven weighting scheme. We propose the use of a set of theoretically defensible weighting schemes, of which, we assume, the one that gives the largest test statistic is likely to capture best the allele frequency-functional effect relationship. We show that the use of alternative weights obviates the need to impose arbitrary frequency thresholds. As both the score test and the likelihood ratio test (LRT) may be used in this context, and may differ in power, we characterize the behavior of both tests. The two tests have equal power, if the weights in the set included weights resembling the correct ones. However, if the weights are badly specified, the LRT shows superior power (due to its robustness to misspecification). With this data-driven weighting procedure the LRT detected significant signal in genes located in regions already confirmed as associated with schizophrenia - the PRRC2A (p = 1.020e-06) and the VARS2 (p = 2.383e-06) - in the Swedish schizophrenia case-control cohort of 11,040 individuals with exome-sequencing data. The score test is currently preferred for its computational efficiency and power. Indeed, assuming correct specification, in some circumstances, the score test is the most powerful test. However, LRT has the advantageous properties of being generally more robust and more powerful under weight misspecification. This is an important result given that, arguably, misspecified models are likely to be the rule rather than the exception in weighting-based approaches.

Short communication: Genetic association between schizophrenia and cannabis use.

BACKGROUND AND AIM: Previous studies have shown a relationship between schizophrenia and cannabis use. As both traits are substantially heritable, a shared genetic liability could explain the association. We use two recently developed genomics methods to investigate the genetic overlap between schizophrenia and cannabis use. METHODS: Firstly, polygenic risk scores for schizophrenia were created based on summary statistics from the largest schizophrenia genome-wide association (GWA) meta-analysis to date. We analysed the association between these schizophrenia polygenic scores and multiple cannabis use phenotypes (lifetime use, regular use, age at initiation, and quantity and frequency of use) in a sample of 6,931 individuals. Secondly, we applied LD-score regression to the GWA summary statistics of schizophrenia and lifetime cannabis use to calculate the genome-wide genetic correlation. RESULTS: Polygenic risk scores for schizophrenia were significantly (α<0.05) associated with five of the eight cannabis use phenotypes, including lifetime use, regular use, and quantity of use, with risk scores explaining up to 0.5% of the variance. Associations were not significant for age at initiation of use and two measures of frequency of use analyzed in lifetime users only, potentially because of reduced power due to a smaller sample size. The LD-score regression revealed a significant genetic correlation of rg=0.22 (SE=0.07, p=0.003) between schizophrenia and lifetime cannabis use. CONCLUSIONS: Common genetic variants underlying schizophrenia and lifetime cannabis use are partly overlapping. Individuals with a stronger genetic predisposition to schizophrenia are more likely to initiate cannabis use, use cannabis more regularly, and consume more cannabis over their lifetime.

Genetic variants associated with subjective well-being, depressive symptoms, and neuroticism identified through genome-wide analyses.

Very few genetic variants have been associated with depression and neuroticism, likely because of limitations on sample size in previous studies. Subjective well-being, a phenotype that is genetically correlated with both of these traits, has not yet been studied with genome-wide data. We conducted genome-wide association studies of three phenotypes: subjective well-being (n = 298,420), depressive symptoms (n = 161,460), and neuroticism (n = 170,911). We identify 3 variants associated with subjective well-being, 2 variants associated with depressive symptoms, and 11 variants associated with neuroticism, including 2 inversion polymorphisms. The two loci associated with depressive symptoms replicate in an independent depression sample. Joint analyses that exploit the high genetic correlations between the phenotypes (|ρ^| ≈ 0.8) strengthen the overall credibility of the findings and allow us to identify additional variants. Across our phenotypes, loci regulating expression in central nervous system and adrenal or pancreas tissues are strongly enriched for association.

Heritability, SNP- and Gene-Based Analyses of Cannabis Use Initiation and Age at Onset.

Prior searches for genetic variants (GVs) implicated in initiation of cannabis use have been limited to common single nucleotide polymorphisms (SNPs) typed in HapMap samples. Denser SNPs are now available with the completion of the 1000 Genomes and the Genome of the Netherlands projects. More densely distributed SNPs are expected to track the causal variants better. Therefore we extend the search for variants implicated in early stages of cannabis use to previously untagged common and low-frequency variants. We run heritability, SNP and gene-based analyses of initiation and age at onset. This is the first genome-wide study of age at onset to date. Using GCTA and a sample of distantly related individuals from the Netherlands Twin Register, we estimated that the currently measured (and tagged) SNPs collectively explain 25 % of the variance in initiation (SE = 0.088; P = 0.0016). Chromosomes 4 and 18, previously linked with cannabis use and other addiction phenotypes, account for the largest amount of variance in initiation (6.8 %, SE = 0.025, P = 0.002 and 3.6 %, SE = 0.01, P = 0.012, respectively). No individual SNP- or gene-based test reached genomewide significance in the initiation or age at onset analyses. Our study detected association signal in the currently measured SNPs. A comparison with prior SNP-heritability estimates suggests that at least part of the signal is likely coming from previously untyped common and low frequency variants. Our results do not rule out the contribution of rare variants of larger effect-a plausible source of the difference between the twin-based heritability estimate and that from GCTA. The causal variants are likely of very small effect (i.e., <1 % explained variance) and are uniformly distributed over the genome in proportion to chromosomes' length. Similar to other complex traits and diseases, detecting such small effects is to be expected in sufficiently large samples.

Sandwich corrected standard errors in family-based genome-wide association studies.

Given the availability of genotype and phenotype data collected in family members, the question arises which estimator ensures the most optimal use of such data in genome-wide scans. Using simulations, we compared the Unweighted Least Squares (ULS) and Maximum Likelihood (ML) procedures. The former is implemented in Plink and uses a sandwich correction to correct the standard errors for model misspecification of ignoring the clustering. The latter is implemented by fast linear mixed procedures and models explicitly the familial resemblance. However, as it commits to a background model limited to additive genetic and unshared environmental effects, it employs a misspecified model for traits with a shared environmental component. We considered the performance of the two procedures in terms of type I and type II error rates, with correct and incorrect model specification in ML. For traits characterized by moderate to large familial resemblance, using an ML procedure with a correctly specified model for the conditional familial covariance matrix should be the strategy of choice. The potential loss in power encountered by the sandwich corrected ULS procedure does not outweigh its computational convenience. Furthermore, the ML procedure was quite robust under model misspecification in the simulated settings and appreciably more powerful than the sandwich corrected ULS procedure. However, to correct for the effects of model misspecification in ML in circumstances other than those considered here, we propose to use a sandwich correction. We show that the sandwich correction can be formulated in terms of the fast ML method.

Investigating the possible causal association of smoking with depression and anxiety using Mendelian randomisation meta-analysis: the CARTA consortium.

OBJECTIVES: To investigate whether associations of smoking with depression and anxiety are likely to be causal, using a Mendelian randomisation approach. DESIGN: Mendelian randomisation meta-analyses using a genetic variant (rs16969968/rs1051730) as a proxy for smoking heaviness, and observational meta-analyses of the associations of smoking status and smoking heaviness with depression, anxiety and psychological distress. PARTICIPANTS: Current, former and never smokers of European ancestry aged ≥16 years from 25 studies in the Consortium for Causal Analysis Research in Tobacco and Alcohol (CARTA). PRIMARY OUTCOME MEASURES: Binary definitions of depression, anxiety and psychological distress assessed by clinical interview, symptom scales or self-reported recall of clinician diagnosis. RESULTS: The analytic sample included up to 58 176 never smokers, 37 428 former smokers and 32 028 current smokers (total N=127 632). In observational analyses, current smokers had 1.85 times greater odds of depression (95% CI 1.65 to 2.07), 1.71 times greater odds of anxiety (95% CI 1.54 to 1.90) and 1.69 times greater odds of psychological distress (95% CI 1.56 to 1.83) than never smokers. Former smokers also had greater odds of depression, anxiety and psychological distress than never smokers. There was evidence for positive associations of smoking heaviness with depression, anxiety and psychological distress (ORs per cigarette per day: 1.03 (95% CI 1.02 to 1.04), 1.03 (95% CI 1.02 to 1.04) and 1.02 (95% CI 1.02 to 1.03) respectively). In Mendelian randomisation analyses, there was no strong evidence that the minor allele of rs16969968/rs1051730 was associated with depression (OR=1.00, 95% CI 0.95 to 1.05), anxiety (OR=1.02, 95% CI 0.97 to 1.07) or psychological distress (OR=1.02, 95% CI 0.98 to 1.06) in current smokers. Results were similar for former smokers. CONCLUSIONS: Findings from Mendelian randomisation analyses do not support a causal role of smoking heaviness in the development of depression and anxiety.

The use of imputed sibling genotypes in sibship-based association analysis: on modeling alternatives, power and model misspecification.

When phenotypic, but no genotypic data are available for relatives of participants in genetic association studies, previous research has shown that family-based imputed genotypes can boost the statistical power when included in such studies. Here, using simulations, we compared the performance of two statistical approaches suitable to model imputed genotype data: the mixture approach, which involves the full distribution of the imputed genotypes and the dosage approach, where the mean of the conditional distribution features as the imputed genotype. Simulations were run by varying sibship size, size of the phenotypic correlations among siblings, imputation accuracy and minor allele frequency of the causal SNP. Furthermore, as imputing sibling data and extending the model to include sibships of size two or greater requires modeling the familial covariance matrix, we inquired whether model misspecification affects power. Finally, the results obtained via simulations were empirically verified in two datasets with continuous phenotype data (height) and with a dichotomous phenotype (smoking initiation). Across the settings considered, the mixture and the dosage approach are equally powerful and both produce unbiased parameter estimates. In addition, the likelihood-ratio test in the linear mixed model appears to be robust to the considered misspecification in the background covariance structure, given low to moderate phenotypic correlations among siblings. Empirical results show that the inclusion in association analysis of imputed sibling genotypes does not always result in larger test statistic. The actual test statistic may drop in value due to small effect sizes. That is, if the power benefit is small, that the change in distribution of the test statistic under the alternative is relatively small, the probability is greater of obtaining a smaller test statistic. As the genetic effects are typically hypothesized to be small, in practice, the decision on whether family-based imputation could be used as a means to increase power should be informed by prior power calculations and by the consideration of the background correlation.

Sex differences in genetic architecture of complex phenotypes?

We examined sex differences in familial resemblance for a broad range of behavioral, psychiatric and health related phenotypes (122 complex traits) in children and adults. There is a renewed interest in the importance of genotype by sex interaction in, for example, genome-wide association (GWA) studies of complex phenotypes. If different genes play a role across sex, GWA studies should consider the effect of genetic variants separately in men and women, which affects statistical power. Twin and family studies offer an opportunity to compare resemblance between opposite-sex family members to the resemblance between same-sex relatives, thereby presenting a test of quantitative and qualitative sex differences in the genetic architecture of complex traits. We analyzed data on lifestyle, personality, psychiatric disorder, health, growth, development and metabolic traits in dizygotic (DZ) same-sex and opposite-sex twins, as these siblings are perfectly matched for age and prenatal exposures. Sample size varied from slightly over 300 subjects for measures of brain function such as EEG power to over 30,000 subjects for childhood psychopathology and birth weight. For most phenotypes, sample sizes were large, with an average sample size of 9027 individuals. By testing whether the resemblance in DZ opposite-sex pairs is the same as in DZ same-sex pairs, we obtain evidence for genetic qualitative sex-differences in the genetic architecture of complex traits for 4% of phenotypes. We conclude that for most traits that were examined, the current evidence is that same the genes are operating in men and women.

Genetic association in multivariate phenotypic data: power in five models.

This article concerns the power of various data analytic strategies to detect the effect of a single genetic variant (GV) in multivariate data. We simulated exactly fitting monozygotic and dizygotic phenotypic data according to single and two common factor models, and simplex models. We calculated the power to detect the GV in twin 1 data in an ANOVA of phenotypic sum scores, in a MANOVA, and in exploratory factor analysis (EFA), in which the common factors are regressed on the genetic variant. We also report power in the full twin model, and power of the single phenotype ANOVA. The results indicate that (1) if the GV affects all phenotypes, the sum score ANOVA and the EFA are most powerful, while the MANOVA is less powerful. Increasing phenotypic correlations further decreases the power of the MANOVA; and (2) if the GV affects only a subset of the phenotypes, the EFA or the MANOVA are most powerful, while sum score ANOVA is less powerful. In this case, an increase in phenotypic correlations may enhance the power of MANOVA and EFA. If the effect of the GV is modeled directly on the phenotypes in the EFA, the power of the EFA is approximately equal to the power of the MANOVA.