2 Application to Marital Status and Depression

In this section, we determine whether the heritability of self-report depression scores varies according to the marital status of female twins. Our hypothesis is that marriage, or a marriage-type relationship, serves as a buffer to decrease an individual's inherited liability to depression, consequently decreasing the heritability of the trait. The data were collected from twins enrolled in the Australian National Health and Medical Research Council Twin register. In this sample, mailed questionnaires were sent to the 5,967 pairs of twins on the register between November 1980 and March 1982 (see also Chapter 10). Among the items on the questionnaire were those from the state depression scale of the Delusions-Symptoms States Inventory (DSSI; Bedford et al., 1976) and a single item regarding marital status. The analyses performed here focus on the like-sex MZ and DZ female pairs who returned completed questionnaires. The ages of the respondents ranged from 18 to 88 years; however, due to possible differences in variance components across age cohorts, we have limited our analysis to those twins who were age 30 or less at the time of their response. There were 570 female MZ pairs in this young cohort, with mean age 23.77 years (SD=3.65); and 349 DZ pairs, with mean age 23.66 years (SD=3.93). Using responses to the marital status item, pairs were subdivided into those who were concordant for being married (or living in a marriage type relationship); those who were concordant for being unmarried; and those who were discordant for marital status. In the discordant pairs, the data were reordered so that the first twin was always unmarried. Depression scores were derived by summing the 7 DSSI item scores, and then taking a log-transformation of the data [ $x' = log_{10}(x+1)$] to reduce heteroscedasticity. Covariance matrices of depression scores were computed for the six zygosity groups after linear and quadratic effects of age were removed. The matrices are provided in the Mx scripts in Appendices  and , while the correlations and sample sizes are shown in Table 9.3. We note (i) that in all cases, MZ correlations are greater than the corresponding DZ correlations; and (ii) that for concordant married and discordant pairs, the MZ:DZ ratio is greater than 2:1, suggesting the presence of genetic dominance.

Table 9.3: Sample sizes and correlations for depression data in Australian female twins.

Zygosity Group	N	r
MZ - Concordant single	254	0.409
DZ - Concordant single	155	0.221
MZ - Concordant married	177	0.382
DZ - Concordant married	107	0.098
MZ - Discordant	139	0.324
DZ - Discordant	87	0.059

Before proceeding with the G $\times$ E interaction analyses, we tested whether there was a G - E correlation involving marital status and depression. To do so, cross-correlations between twins' marital status and cotwins' depression score were computed. In all but one case (DZ twin 1's depression with cotwin's marital status; $r=-0.156$, $p < 0.01$), the correlations were not significant. This near absence of significant correlations implies that a genetic predisposition to depression does not lead to an increased probability of remaining single, and indicates that a G - E correlation need not be modeled. Table 9.4 shows the results of fitting several models: general G$\times$E (I); full common-effects G $\times$ E (II); three common-effects sub-models (III-V); scalar G x E (VI); and no G $\times$ E interaction (VII). Parameter estimates subscripted $s$ and $m$ refer respectively to single (unexposed) and married twins. Models including genetic dominance parameters, rather than common environmental effects, were fitted to the data. The reader may wish to show that the overall conclusions concerning G $\times$ E interaction do not differ if shared environment parameters are substituted for genetic dominance.

Table 9.4: Parameter estimates from fitting genotype $\times$ marriage interaction models to depression scores.

	MODEL
Parameter	I	II	III	IV	V	VI	VII
$a_{s}$	0.187	0.187	0.207	0.209	0.186	0.206	0.188
$d_{s}$	0.106	0.105	-	-	-	-	-
$e_{s}$	0.240	0.240	0.246	0.245	0.257	0.247	0.246
$a_{m}$	0.048	0.048	0.163	0.162	0.186	0.206	0.188
$d_{m}$	0.171	0.173	-	-	-	-	-
$e_{m}$	0.232	0.232	0.243	0.245	0.232	0.247	0.246
$a'_{m}$	0.008	-	-	-	-	-	-
$k$	-	-	-	-	-	0.916	-
$\chi^{2}$	15.44	15.48	18.88	18.91	22.32	20.08	27.19
$d.f.$	11	12	14	15	15	15	16
$p$	0.16	0.22	0.17	0.22	0.10	0.17	0.04
$AIC$	-6.56	-9.52	-9.12	-11.09	-7.68	-9.92	-4.81

Model I is a general G $\times$ E model with environment-specific additive genetic effects. It provides a reasonable fit to the data ($p$ = 0.16), with all parameters of moderate size, except $a'_{m}$. Under model II, the parameter $a'_{m}$ is set to zero, and the fit is not significantly worse than model I ($\chi^{2}_{1}$ = 0.04, $p$ = 0.84). Thus, there is no evidence for environment-specific additive genetic effects. As an exercise, the reader may verify that the same conclusion can be made for environment-specific dominant genetic effects. Under model III, we test whether the dominance effects on single and married individuals are significant. A $\chi^{2}$ difference of 3.40 ($p$ = 0.183, 2 df.) between models III and II indicates that they are not. Consequently, model III, which excludes common dominance effects while retaining common additive genetic and specific environmental effects, is favored. Models IV - VII are all sub-models of III: the first specifies no differences in environmental variance components across exposure groups; the second specifies no differences in genetic variance components across groups; the third constrains the genetic and environmental variance components of single twins to be scalar multiples of those of married twins; and the fourth specifies no genetic or environmental differences between the groups. When each of these is compared to model III using a $\chi^{2}$ difference test, only model VII (specifying complete homogeneity across groups) is significantly worse than the fuller model ($\chi^{2}_{2}$ = 8.28, p = 0.004). In order to select the best sub-models from IV, V and VI, Akaike's Information Criteria were used. These criteria indicate that model IV -- which allows for group differences in genetic, but not environmental, effects -- gives the most parsimonious explanation for the data. Under model IV, the heritability of depression is 42% for single, and 30% for married twins. This finding supports our hypothesis that marriage or marriage type relationships act as a buffer against the expression of inherited liability to depression.