next up previous index
Next: 4 Model for Age-Correction Up: 3 Fitting Genetic Models Previous: 3 Fitting Genetic Models   Index

1 Major Depressive Disorder in Twins

Data for this example come from a study of genetic and environmental risk factors for common psychiatric disorders in Caucasian female same-sex twin pairs sampled from the Virginia Twin Registry. The Virginia Twin Registry is a population-based register formed from a systematic review of all birth certificates in the Commonwealth of Virginia. Twins were eligible to participate in the study if they were born between 1934 and 1971 and if both members of the pair had previously responded to a mailed questionnaire, to which the individual response rate was approximately 64%. The cooperation rate was almost certainly higher than this, as an unknown number of twins did not receive their questionnaire due to faulty addresses, improper forwarding of mail, and so on. Of the total 1176 eligible pairs, neither twin was interviewed in 46, one twin was interviewed and the other refused in 97, and both twins were interviewed in 1033 pairs. Of the completed interviews, 89.3% were completed face to face, nearly all in the twins' home, and 10.7% (mostly twins living outside Virginia) were interviewed by telephone. The mean age ($\pm$SD) of the sample at interview was 30.1 (7.6) and ranged from 17 to 55. Zygosity determination was based on a combination of review of responses to questions about physical similarity and frequency of confusion as children -- which alone have proved capable of determining zygosity with over 95% accuracy (Eaves et al., 1989b) -- and, in over 80% of cases, photographs of both twins. From this information, twins were classified as either: definitely MZ, definitely DZ, probably MZ, probably DZ, or uncertain. For 118 of the 186 pairs in the final three categories, blood was taken and eight highly informative DNA polymorphisms were used to resolve zygosity. If all probes are identical then there is a .9997 probability that the pair is MZ (Spence et al., 1988). Final zygosity determination, using blood samples where available, yielded 590 MZ pairs, 440 DZ pairs and 3 pairs classified as uncertain. The DNA methods validated the questionnaire- and photograph-based `probable' diagnoses in 84 out of 104 pairs; all 26 of 26 pairs in the definite categories were confirmed as having an accurate diagnosis. The error rate in zygosity assignment is probably well under 2%. Lifetime psychiatric illness was diagnosed using an adapted version of the Structured Clinical Interview for DSM-III-R Diagnosis (Spitzer et al., 1987) an instrument with demonstrable reliability in the diagnosis of depression (Riskind et al., 1987). Interviewers were initially trained for 80 hours and received bimonthly review sessions during the course of the study. Each member of a twin pair was invariably interviewed by a different interviewer. DSM-III-R criteria were applied by a blind review of the interview by K.S. Kendler, an experienced psychiatric diagnostician. Diagnosis of depression was not given when the symptoms were judged to be the result of uncomplicated bereavement, medical illness, or medication. Inter-rater reliability was assessed in 53 jointly conducted interviews. Chance corrected agreement (kappa) was .96, though this is likely to be a substantial overestimate of the value that would be obtained from independent assessments[*]. Contingency tables of MZ and DZ twin pair diagnoses are shown in Table 6.9.

Table 6.9: Contingency tables of twin pair diagnosis of lifetime Major Depressive Disorder in Virginia adult female twins.
    MZ DZ
  Twin 1 Normal Depressed Normal Depressed
Twin 2 Normal 329 83 201 94
  Depressed 95 83 82 63

PRELIS estimates of the correlation in liability to depression are .435 for MZ and .186 for DZ pairs. Details of using PRELIS to derive these statistics and associated estimates of their asymptotic variances are given in Section 2.3. The PMatrix command is used to read in the tetrachoric correlation matrix, and the ACov command reads the asymptotic weight matrices. In both cases we use the File= keyword in order to read these data from files. Therefore our univariate Mx input script is unchanged from that shown in Appendix [*] on page [*], except for the title and the dat file used.
Major depressive disorder in adult female MZ twins
Data NInput_vars=2 NObservations=590
#Include mzdepsum.dat
where the dat file reads
PMatrix File=MZdep.cov
ACov File=MZdep.asy
in the MZ group, with the same commands for the DZ group except for the number of observations (NObs=440) and a global replacement of DZ for MZ. For clarity, the comments at the beginning also should be changed. Results of fitting the ACE and ADE models and submodels are summarized in Table 6.10.

Table 6.10: Major depressive disorder in Virginia adult female twins. Parameter estimates and goodness-of-fit statistics for models and submodels including additive genetic (A), common environment (C), random environment (E), and dominance genetic (D) effects.
  Parameter Estimates Fit statistics
Model $a$ $c$ $e$ $d$ $\chi^2$ df $p$
$E$ -- -- 1.00 -- 56.40 2 .00
$CE$ -- 0.58 0.81 -- 6.40 1 .01
$AE$ 0.65 -- 0.76 -- .15 1 .70
$ACE$ 0.65 -- 0.76 -- .15 0 --
$ADE$ 0.56 -- 0.75 0.36 .00 0 --

First, note that the degrees of freedom for fitting to correlation matrices are fewer than when fitting to covariance matrices. Although we provide Mx with two correlation matrices, each consisting of 1's on the diagonal and a correlation on the off-diagonal, the 1's on the diagonal cannot be considered unique. In fact, only one of them conveys information which effectively `scales' the covariance. There is no information in the remaining three 1's on the diagonals of the MZ and DZ correlation matrices, but Mx does not make this distinction. Therefore, we must adjust the degrees of freedom by adding the option Option DFreedom=-3. Another way of looking at this is that the diagonal 1's convey no information whatsoever, but that we use one parameter to estimate the diagonal elements ($e$; it appears only in the expected variances, not the expected covariances). Thus, there are 4 imaginary variances and 1 parameter to estimate them -- giving 3 statistics too many. Second, the substantive interpretation of the results is that the model with just random environment fails, indicating significant familial aggregation for diagnoses of major depressive disorder. The environmental explanation of familial covariance also fails ($\chi^2_1=6.40$) but a model of additive genetic and random environment effects fits well ($\chi^2_1=.15$). There is no possible room for significant improvement with the addition of any other parameter, since there are only .15 $\chi^2$ units left. Nevertheless, we fitted both ACE and ADE models and found that dominance genetic effects could account for the remaining variability whereas shared environmental effects could not. This finding is in agreement with the observation that the MZ correlation is slightly greater than twice the DZ correlation. The heritability of liability to Major Depressive Disorder is moderate but significant at 42%, with the remaining variability associated with random environmental sources including error of measurement. These results are not compatible with the view that shared family experiences such as parental rearing, social class, or parental loss are key factors in the etiology of major depression. More modest effects of these factors may be detected by including them in multivariate model fitting (Kendler et al., 1992a; Neale et al., 1992). Of course, every study has its limitations, and here the primary limitations are that: (i) the results only apply to females; (ii) the twin population is not likely to be perfectly representative of the general population, as it lacks twins who moved out of or into the state, or failed to respond to initial questionnaire surveys; (iii) a small number of the twins diagnosed as having major depression may have had bipolar disorder (manic depression), which may be etiologically distinct; (iv) the reliance on retrospective reporting of lifetime mental illness may be subject to bias by either currently well or currently ill subjects or both; (v) MZ twins may be treated more similarly as children than DZ twins; and (vi) not all twins were past the age at risk of first onset of major depression. Consideration of the first five of these factors is given in Kendler et al. (1992c). Of particular note is that a test of limitation (v), the `equal environments' assumption, was performed by logistic regression of absolute pair difference of diagnosis (scored 0 for normal and 1 for affected) on a quasi-continuous measure of similarity of childhood treatment. Although MZ twins were on average treated more similarly than DZ twins, this regression was found to be non-significant. General methods to handle the effects of zygosity differences in environmental treatment form part of the class of data-specific models to be discussed in Section [*]. Overall there was no marked regression of age on liability to disease in these data, indicating that correction for the contribution of age to the common environment is not necessary (see the next section). Variable age at onset has been considered by Neale et al. (1989) but a full treatment of this problem is beyond the scope of this volume. Such methods incorporate not only censoring of the risk period, but also the genetic architecture of factors involved in age at onset and their relationship to factors relevant in the etiology of liability to disease. Note, however, that this problem, like the problem of measured shared environmental effects, may also be considered as part of the class of data-specific models.
next up previous index
Next: 4 Model for Age-Correction Up: 3 Fitting Genetic Models Previous: 3 Fitting Genetic Models   Index
Jeff Lessem 2002-03-21