Teste da herdabilidade multivariada aplicado a dados de famílias

Abstract

Complex diseases, such as the metabolic syndrome, heart diseases and Alzheimer, are an important public health problem. In general, the occurrences of these diseases are linked to disorders in the mechanisms of control of multiple variables that, through a joint action leads to their manifestation. As these variables are generally influenced by genetic and environmental factors, the study of their inheritance is fundamental. From polygenic mixed model, Blangero et al. (2013) achieved the first known analytical expression to the test of heritability of a single variable. The spectral decomposition of the kinship matrix was used by the authors. In multivariate studies, as in the case of complex diseases, this methodology can only be applied to each variable separately, since similar tests have not yet been developed for the multivariate case. From what has been stated, the present work aimed at developing a new statistical test for multivariate heritability. Due to the correlations among variables, the principal components of heritability (PCH) were used to generate new independent variables. In addition, MANOVA moments estimators were used to estimate genetic and environmental covariance matrices. The new test statistic has a relatively simple analytical form and was evaluated by Monte Carlo simulations with 5000 runs for each scenario chosen according to its parametric heritabilities, correlations and family structure. The performance was measured using type I error rate and power. This methodology also was applied using the Brazilian family data from the Baependi Heart Study. The results showed that the proposed test for multivariate heritability was able to efficiently control type I error rate in all scenarios evaluated under the null hypothesis (absence of multivariate heritability). The power levels were high in general and close to or equal to 1.00 when parametric heritabilities are equal to or greater than 0.20. The proposed test showed power levels substantially higher than the test obtained by Blangero et al. (2013) in the higher heritability univariate case. In summary, the proposed test has excellent performance in all evaluated circumstances, representing an efficient tool for use in studies that involve multivariate heritability, such as those related to complex diseases.