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Testing causality Charlotte Huppertz VU University Medical Center Amsterdam Netherlands Twin Register Rationale • Correlation does not equal causation! • Alternative explanation: underlying factors • Example: „Exercising relieves depressive symptoms“ Descriptives • Exercisers are on average happier and less anxious and depressed • This holds in women and men of all ages * 27,5 27,0 26,5 26,0 Non-exercisers Exercisers Non-exercisers Life satisfaction (SWLS) * 2.5 2.0 * 23.0 22.8 22.6 22.4 22.2 22.0 Exercisers Happiness (SHS) * 6.5 34.5 34.0 33.5 33.0 32.5 32.0 31.5 6.0 1.5 5.5 1.0 5.0 0.5 0.0 4.5 Non-exercisers Exercisers Depression (BDI) Non-exercisers Exercisers Anxious depression (YASR) * Non-exercisers 51.0 50.0 49.0 48.0 47.0 46.0 45.0 Exercisers Anxiety (STAI) * Non-exercisers Exercisers Neuroticism (EPQ) Possible explanations Genes Genes (50%) (35-50%) Exercise behaviour Depressive symptoms Genes ”Pleitropy”? Ways to falsify causality ≠ proving causality • Gold standard: experimentation – Randomize individuals to different conditions – Expose them to a treatment vs. control – Assess post-treatment differences • Problems – – – – Really random samples? Generalizable samples? (e.g. students; exercisers) Usually requires a lot of effort/ money! Not everything can be manipulated! (e.g. effect of childhood maltreatment on depression) Ways to falsify causality 1) The MZ twin intrapair differences model 2) Bivariate genetic models 3) (Mendelian randomization) 1) The MZ twin intrapair differences model Control for: shared genes, shared environment MZ twin pair differences model The MZ twin intrapair differences model Within-pair differences in Phenotype 1 should be associated with within-pair differences in Phenotype 2. How to do the calculation? 2) Bivariate genetic models Bivariate genetic model Bivariate genetic models All genetic and environmental factors that influence P1 will also, through the causal chain, influence P2 (If A -> B and B -> C, then A -> C). A E Bivariate genetic model Path diagram 0.5 or 1 1 A C E Time Point 1 A C E Time Point 2 Twin1 A C E Time Point 1 A C E Time Point 2 Twin2 Bivariate genetic model Path diagram 0.5 or 1 1 A C E A C Exercise beh. E Depr. symp. Twin1 A C E Exercise beh. A C E Depr. symp. Twin2 Bivariate genetic model Path diagram 0.5 or 1 A E A Exercise beh. E Depr. symp. Twin1 A E Exercise beh. A E Depr. symp. Twin2 Bivariate genetic model Let‘s start at the beginning... UNIVERIATE TWIN MODEL 1 or 0.5 E A e a Exercise Twin1 A= genes, E= unique environment A E a e Exercise Twin2 Bivariate genetic model Univariate twin model 1 or 0.5 A a11 Exercise Twin1 A a11 Exercise Twin2 Bivariate genetic model Bivariate twin model 1 or 0.5 A a11 Exercise Twin1 A a22 Depr. S. Twin1 1 or 0.5 A a11 Exercise Twin2 A a22 Depr. S. Twin2 Bivariate genetic model Bivariate twin model 1 or 0.5 A A a11 Exercise Twin1 a21 a22 Depr. S. Twin1 1 or 0.5 A a11 Exercise Twin2 A a21 a22 Depr. S. Twin2 Bivariate genetic model Bivariate twin model A2 A1 A1 rgenetic A2 ! a11 Exercise behavior ? e11 a22 Depressive symptoms e22 ! E1 E2 a1 a2 Exercise behavior Depressive symptoms e1 E1 e2 renviron E2 Be careful: order can matter! Bivariate genetic model Practical • Open „BivariateCholesky.R“ • Simulated data • Zygos: 1= MZM, 2= DZM • TASKS: 1) Find four errors in the script 2) Run the main model & write out the path diagram including the estimated parameters 3) Drop the cross-trait genetic path (provided) – conclusion? 4) Drop the cross-trait environmental path (not provided) – conclusion? Bivariate genetic model 1) Four errors Bivariate genetic model 2) The path diagram A E A E 0.46 0.21 0.22 0.05 1.11 1.07 Exercise Twin1 Depr. S. Twin1 Bivariate genetic model 3) Output dropping A Conclusion? Bivariate genetic model 3) Output dropping E Conclusion? Bivariate genetic model Conclusion A E A E 0.46 0.21 0.22 0.05 n.s. 1.11 1.07 Exercise Twin1 Depr. S. Twin1 Not compatible with a causal effect! In „real life“: check power! Bivariate genetic model Result bivariate twin model A1 rgenetic a1 a2 Exercise behavior Depressive symptoms e1 E1 A2 e2 renviron E2 MZ twin pair differences model Result MZ twin intrapair differences model • The twin who exercises more, is not less anxious/depressed Conclusion • The association between exercise and depressive symptoms is best explained by the same genetic vulnerability! ”Our results signal psychiatrists and epidemiologists that the small but robust cross-sectional and longitudinal correlations between voluntary exercise behavior and mental health should be interpreted with caution.” Exercise behavior & other phenotypes “The genetic factors influencing exercise participation and self-rated health partially overlap (r = 0.36) and this overlap fully explains their phenotypic correlation.“ (de Moor et al., 2006, EurJEpid) “Exercise participation is associated with higher levels of life satisfaction and happiness. This association is non-causal and appears to be mediated by genetic factors that influence both exercise behavior and well-being.” (Stubbe et al., 2007, PrevMed) “Regular exercise is associated with reduced anxious and depressive symptoms in the population at large, but the association is not because of causal effects of exercise.“ (de Moor et al., 2008, ArchGenPsychiatry) “Exercise behavior is associated with fewer internalizing problems and higher levels of SWB. The association largely reflects the effects of common genetic factors on these traits.” (Bartels et al., 2012, FronGen) Genetic correlation Cross-trait correlations A2 A1 A1 rgenetic A2 ! a11 Exercise behavior ? e11 a22 Depressive symptoms e22 ! E1 E2 a1 a2 Exercise behavior Depressive symptoms e1 E1 e2 renviron How can we calculate a genetic correlation? E2 Genetic correlation Genetic correlation A E A E e22 a22 a21 e21 a11 e11 Exercise Twin1 Depr. S. Twin1 Genetic correlation Genetic correlation Write out the formulae using a11, a21 and a22! A rxy cov xy sdx * sdy sd var A a21 a22 a11 * a 21 rxy a11² * a 21² a 22² rg a11 Exercise Twin1 a21a11 a * (a a ) 2 11 2 21 2 22 Depr. S. Twin1 What does a rg of 1 mean? Genetic correlation There is even more information in such a bivariate model Explained covariance Can the explained covariance be close to zero when the genetic correlation is 1? Genetic correlation Genetic correlation A1 rgenetic a1 a2 Exercise behavior Depressive symptoms e1 E1 A2 e2 renviron E2 Importance is determined by both the genetic correlation and the heritability of each phenotype! 3) Mendelian randomization Mendelian randomization Problems with the twin approach Latent, unmeasured genetic and environmental effects ACDE cannot easily be measured simultaneously E includes error Needs very large twin samples Mendelian randomization Mendelian randomization • Testing causality based on measured DNA • Apart from than, similar to the bivariate model: „A genetic variant that influences an exposure variable (such as exercise behavior) should also, through the causal chain, predict an outcome variable (e.g. depressive symptoms)!“ • “Randomization to genotype” at conception Mendelian randomization Advantages & problems Based on measured variants Can be applied to any large population-based samples Solid associations between genetic markers and exposure variable first need to be established („genetic instrument“) Take home messages • Necessary conditions for causality based on twin data: – In MZ twins, differences in trait A need to be associated with differences in trait B – In a bivariate Cholesky decomposition, the cross-trait paths need to be significant • Mendelian randomization as a means to test causality in the general population • Physical exercise is not the elixir to happiness ;)