A latent class model for bivariate binary responses from twins

A LATENT CLASS MODEL FOR BIVARIATE BINARY RESPONSES FROM

TWINS

ANDERS EKHOLM, JUKKA JOKINEN, JOHN W. MCDONALD,

PETER W. F. SMITH

ABSTRACT

We analyse a 2

4

table reporting the presence or absence of alcohol dependence and

depression in both members of 597 pairs of female monozygotic twins. The statistical

analysis is based on a latent class model, formulated as a 2x2 table and parametrized by

two marginal univariate genetic dispositions and the dependence ratio between these

dispositions. The final model, selected after some empirically motivated simplifying

assumptions are adopted, has six parameters and fits the data very well. The

identifiability and stability of the final model is studied by contour plots of profile

log-likelihood functions with two arguments. Numerical results are compared to those

obtained when the measure of association between binary responses is the odds ratio

rather than the dependence ratio. The conditional probability of alcohol dependence

given the disposition for it is approximately 1/3, while the corresponding probability of

depression is approximately 2/3. The association between these two latent dispositions is

strong, the dependence ratio being approximately 3. An extended model, defining

measures of heritability and similarity, for analysing, simultaneously, data on

monzygotic and dizygotic twins is proposed.

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