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Multivariate Generalized Linear Models for Twin and Family Data

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Multivariate twin and family studies are one of the most important tools to assess diseases inheritance as well as to study their genetic and environment interrelationship. The multivariate analysis of twin and family data is in general based on structural equation modelling or linear mixed models that essentially decomposes sources of covariation as originally suggested by  Fisher. In this paper, we propose a flexible and unified statistical modelling framework for analysing multivariate Gaussian and non-Gaussian twin and family data. The non-normality is taken into account by actually modelling the mean and variance relationship, while the covariance structure is modelled by means of a linear covariance model including the option to model the dispersion components as functions of known covariates in a regression model fashion. The marginal specification of our models allows us to extend classic models and biometric indices such as the bivariate heritability, genetic, environmental and phenotypic correlations to non-Gaussian data. We illustrate the proposed models through simulation studies and six data analyses and provide computational implementation in R through the package mglm4twin.

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  • Bonat WH, Jørgensen B (2016) Multivariate covariance generalized linear models. J Royal Statist Soc: Series C 65:649–675

    Google Scholar 

  • Bonat WH, Kokonendji CC (2017) Flexible tweedie regression models for continuous data. J Statist Comput Simulat 87(11):2138–2152

    Article  Google Scholar 

  • Bonat WH, Jørgensen B, Kokonendji CC, Hinde J, Demétrio CGB (2018) Extended Poisson–Tweedie: properties and regression models for count data. Stat Modell 18(1):24–49

    Article  Google Scholar 

  • Bonat WH, Peterle R, Hinde J, Demétrio CGB (2018) Flexible regression models for continuous bounded data. Stat Modell

  • Bonat WH, Petterle RR, Hinde J, Demétrio CG (2019) Flexible quasi-beta regression models for continuous bounded data. Stat Model 19(6):617–633

    Article  Google Scholar 

  • Boomsma D, Busjahn A, Peltonen L (2002) Classical twin studies and beyond. Nat Rev Genet 3:872–882

    Article  Google Scholar 

  • Feng R, Zhou G, Zhang M, Zhang H (2009) Analysis of twin data using sas. Biometrics 65(2):584–589

    Article  Google Scholar 

  • Folstein MF, Folstein SE, McHugh PR (1975) Mini-mental state: a practical method for grading the cognitive state of patients for the clinician. J Psychiatr Res 12(3):189–198

    Article  Google Scholar 

  • Holst KK, Scheike TH, Hjelmborg JB (2016) The liability threshold model for censored twin data. Comput Stat Data Anal 93:324–335

    Article  Google Scholar 

  • Jørgensen B (1987) Exponential dispersion models. J Royal Statist Soc Series B 49(2):127–162

    Google Scholar 

  • Jørgensen B (1997) The theory of dispersion models. Chapman & Hall

    Google Scholar 

  • Jørgensen B, Knudsen SJ (2004) Parameter orthogonality and bias adjustment for estimating functions. Scand J Stat 31(1):93–114

    Article  Google Scholar 

  • Jørgensen B, Kokonendji CC (2016) Discrete dispersion models and their tweedie asymptotics. AStA Adv Stat Anal 100(1):43–78

    Article  Google Scholar 

  • Khoury MJ, Beaty TH, Cohen BH (1993) Fundamentals of genetic epidemiology. Oxford University Press, Fundamentals of Genetic Epidemiology

    Google Scholar 

  • Liang K-Y, Zeger SL (1986) Longitudinal data analysis using generalized linear models. Biometrika 73(1):13–22

    Article  Google Scholar 

  • McArdle JJ, Prescott CA (2005) Mixed-effects variance components models for biometric family analyses. Behav Genet 35(5):631–652

    Article  Google Scholar 

  • McGue M, Christensen K (1997) Genetic and environmental contributions to depression symptomatology: evidence from danish twins 75 years of age and older. J Abnorm Psychol 106(3):439–448

    Article  Google Scholar 

  • Neale MC, Maes HH (2004) Methodology for genetic studies of twins and families. Technical report, Virginia Common wealth University, Department of Psychiatry.

  • Neale MC, Hunter MD, Pritikin JN, Zahery M, Brick TR, Kirkpatrick RM, Estabrook R, Bates TC, Maes HH, Boker SM (2016) OpenMx 2.0: extended structural equation and statistical modeling. Psychometrika 81(2):535–549

    Article  Google Scholar 

  • Nelder JA, Wedderburn RWM (1972) Generalized linear models. J R Stat Soc Ser A 135(3):370–384

    Article  Google Scholar 

  • Ozaki K, Toyoda H, Iwama N, Kubo S, Ando J (2011) Using non-normal sem to resolve the acde model in the classical twin design. Behav Genet 41(2):329–339

    Article  Google Scholar 

  • Prescott CA (2004) Using the mplus computer program to estimate models for continuous and categorical data from twins. Behav Genet 34(1):17–40

    Article  Google Scholar 

  • Rabe-Hesketh S, Skrondal A, Gjessing HK (2008) Biometrical modeling of twin and family data using standard mixed model software. Biometrics 64(1):280–288

    Article  Google Scholar 

  • Roth M, Tym E, Mountjoy CQ (1986) Camdex: a standardized instrument for the diagnosis of mental disorder in the elderly with special reference to the elderly detection of dementia. Br J Psychiatry 149:698–709

    Article  Google Scholar 

  • van Dongen J, Slagboom PE, Draisma HHM, Martin NG, Boomsma DI (2012) The continuing value of twin studies in the omics era. Nat Rev Genet 13:640–653

    Article  Google Scholar 

  • Wedderburn RWM (1974) Quasi-likelihood functions, generalized linear models, and the gauss-newton method. Biometrika 61(3):439–447

    Google Scholar 

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Correspondence to Wagner Hugo Bonat.

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Wagner Hugo Bonat and Jacob V. B. Hjelmborg declares that they have no conflict of interest.

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Edited by: Stacey S. Cherny.

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Bonat, W.H., Hjelmborg, J.V.B. Multivariate Generalized Linear Models for Twin and Family Data. Behav Genet 52, 123–140 (2022).

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