Estimation of the Interclass Correlation Coefficient

Srivastava, Mukul; Keen, K. J.

doi:10.2307/2336314

Cited by 4 publications

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“…In heredity studies, it is often of interest to study the resemblance between members in the same family with respect to a certain characteristic X. However, computational problems encountered in maximum likelihood estimation of familial correlations have been reported (Rosner, 1979;Srivastava and Keen, 1988). We consider here only the case of a single type of family members, such as brother-brother.…”

Section: Example 4: Analyses Of Familial Datamentioning

confidence: 99%

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Solving Non-Linear Estimation Equations

Mak

1993

Journal of the Royal Statistical Society Series B: Statistical Methodology

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SUMMARY In this paper we consider the numerical computation of a vector parameter estimate trueθ̂ which is a root of a system of unbiased non‐linear estimation equations. A sequence {θ(r)} is constructed which converges with a probability approaching 1 to trueθ̂ from any starting value θ(0). Unlike Newton‐type algorithms, the θ(r) do not involve matrices of partial derivatives. Furthermore it can be shown that θ(r)−θ̂ is of the order Op(n– r/2) so that great accuracy is achieved in very few iterations. When the θ(r) do not have closed forms, an approximation is suggested. An alternative and usually simpler way is also found for deriving analytically the expected value of the matrix of partial derivatives in the asymptotic covariance matrix of trueθ̂. The efficiency of the proposed algorithm is demonstrated numerically and compared with that of the EM and the Newton–Raphson algorithms. Applications to some well‐known statistical problems, including missing data analysis, variance component models, familial correlations and errors‐in‐variables models are also briefly discussed.

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Section: Example 4: Analyses Of Familial Datamentioning

confidence: 99%

“…an analytical expression for the matrix of derivatives a/lao of /may not be easy to obtain in some applications. The deficiency of the quasi-Newton algorithm in obtaining 0has also been noted in some applications; see, for example, Srivastava and Keen (1988). Another major problem with the quasi-Newton method in statistical…”

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confidence: 97%

Solving Non-Linear Estimation Equations

Mak

1993

Journal of the Royal Statistical Society Series B: Statistical Methodology

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“…Note we here establish a theoretical result that the asymptotic distribution of our pedigree estimators are multivariate normal with the asymptotic covariance structure that we have derived; this is a theoretical result that does not depend on extensive simulation. Nevertheless, extensive simulations by Srivastava and Keen [7] and Keen [21] for the univariate case show that sample sizes as small as 30 independent families are su ciently large for asymptotic theory to hold.…”

Section: Estimating Covariances Among Pedigree Correlationsmentioning

confidence: 99%

“…Karlin et al [6] consider the use of two di erent weighting schemes for estimators of correlations in nuclear families but without consideration of the distribution or standard errors of these estimators. Srivastava and Keen [7] develop the asymptotic theory for the estimation of interclass correlations in nuclear families with generalized weights. Srivastava et al [8] consider the situation of estimation of correlation matrices for multiple traits in a random sample of nuclear families.…”

Section: Introductionmentioning

confidence: 99%

“…However, as closed-form expressions do not exist for the maximum likelihood estimators of intraclass and interclass correlations for a simple random sample of nuclear families with variable structures, the theory for a random sample of extended families (pedigrees) is that much less tractable in this regard. Despite the availability of closed-form equations for the asymptotic variances of the ML estimators of the intraclass (Donner and Koval [11]) and interclass (Keen and Srivastava [10]) correlations in nuclear families, calculation of the corresponding ML estimates themselves requires intensive numerical procedures as discussed by Smith [4,5], Rao et al [12], Srivastava and Keen [7,8] and Wette et al [13]. A comparison of the EM, Newton-Raphson, scoring, and quasi-likelihood algorithms is discussed by de Andrade et al [14] with respect to nuclear families but the extension to pedigrees is not trivial.…”

Section: Introductionmentioning

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Robust asymptotic sampling theory for correlations in pedigrees

Keen

Elston

2003

Statistics in Medicine

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Methods to unravel the genetic determinants of non-Mendelian diseases lie at the next frontier of statistical approaches for human genetics. It is generally agreed that, before proceeding with segregation or linkage analysis, the trait under study ought to be shown to exhibit familial correlation. By coding dichotomous traits as binary variables, a single robust approach in the estimation of pedigree correlations, rather than two distinct approaches, can be used to assess the potential heritability of a trait, and, latterly, to examine the mode of inheritance. The asymptotic theory to conduct hypothesis tests and confidence intervals for correlations among different members of nuclear families is well established but is applicable only if the nuclear families are independent. As a further contribution to the literature, we derive the asymptotic sampling distribution of correlations between random variables among arbitrary pairs of members in extended families for the Pearson product-moment estimator with generalized weights. This derivation is done without assuming normality of the traits. The sampling distribution is shown to be asymptotically normal to first order, and hence large-sample hypothesis tests and confidence intervals with estimates of the variances and correlation coefficients are proposed. Discussion concludes with an example and a suggestion for future research.

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Introduction and overview

2000

Stat Methods Med Res

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Common terms used in genetics with multiple meanings are explained and a brief overview given of the four major areas of genetic epidemiology--the study of familial aggregation, segregation, cosegregation and association. Familial aggregation measures the potential for a trait to have a genetic aetiology. Segregation analysis uncovers single gene segregation. Cosegregation with genetic markers gives rise to linkage, which is used to locate trait genes on the genome. Association analysis is used for fine mapping, but rests on the assumption that linkage disequilibrium exists.

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Estimation of the Interclass Correlation Coefficient

Cited by 4 publications

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Solving Non-Linear Estimation Equations

Solving Non-Linear Estimation Equations

Robust asymptotic sampling theory for correlations in pedigrees

Introduction and overview

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