A subgroup of adolescents may carry a physiological risk for major depression which may be either of genetic and/or earlier psychosocial origin.

SynopsisThe association between basal cortisol, dehydroepiandrosterone (DHEA), its sulphate (DHEAS) and major depression was investigated in 8- to 16-year-olds. Eighty-two subjects with major depression, 25 non-depressed psychiatric cases and 40 community controls were systematically assessed for current mental state and hormone levels at 08.00, 12.00 and 20.00 h, assayed from salivary samples collected over a 48 h period. The average mean of the two time points was compared between the three groups. Evening cortisol hypersecretion and morning DHEA hyposecretion were significantly, and independently, associated with major depression. High evening cortisol (> 0·594 ng/ml) and low morning DHEA (< 0·200 ng/ml) identified subgroups of depressives with different types of adrenal hormone dysregulation. The association between high evening cortisol or low morning DHEA and MDD was not affected by either age or gender.

The finding that it is depressed subjects with high cortisol/DHEA ratios at presentation who are specifically at risk for subsequent disappointing life events suggests a putative role for these adrenal steroids in abnormal cognitive or emotional processes associated with disturbed interpersonal behaviour.

Summary The sum of k independent and identically distributed (0, 1) variables has a binomial distribution. If the variables are identically distributed but not independent, this may be generalized to a two‐parameter distribution where the k variables are assumed to have a symmetric joint distribution with no second‐ or higher‐order “interactions”. Two distinct generalizations are obtained, depending on whether the “multiplicative” or “additive” definition of “interaction” for discrete variables is used. The multiplicative generalization gives rise to a two‐parameter exponential family, which naturally includes the binomial as a special case. Whereas with a beta‐binomially distributed variable the variance always exceeds the corresponding binomial variance, the “additive” or “multiplicative” generalizations allow the variance to be greater or less than the corresponding binomial quantity. The properties of these two distributions are discussed, and both distributions are fitted, successfully, to data given by Skellam (1948) on the secondary association of chromosomes in Brassica.

The number of moderate to severe undesirable life events and the quality of friendships were compared between a consecutive series of 100 children aged 7-16 years with emotional disorders and a series of community controls matched for age, sex, and social class. Undesirable events and friendship difficulties exerted independent direct effects of similar magnitude on the probability of developing emotional disorders; 33% of disturbed children experienced both adversities compared with 6% of controls. An additive interaction was found for the two factors. The results were uninfluenced by the sex or pubertal status of the subjects. There appears to be no greater probability of being anxious rather than depressed in the presence of life events, alone or in combinations with friendship difficulties. Recent undesirable life events and friendship difficulties arise through independent social pathways and may exert their effects through different psychological mechanisms.

Summary A relationship is derived between the posterior probability of negative association of rows and columns of a 2 times 2 contingency table and Fisher's “exact” probability, as given in existing tables for testing the hypothesis of no association of rows and columns. The result for the 2 times 2 table is generalized to provide the posterior probability that one discrete‐valued random variable is stochastically larger than another.

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The generalization of Edwards's argument for the measure of association of the rows and columns of 2 x 2 table, to that of an r x s table whose rows and columns are assumed unordered, shows, not surprisingly, that association ought to be measured by some function of the (r-l) (s-1) cross-ratios. Such a function is suggested by the introduction of a metric on certain equivalence classes. The properties of such metrics are examined, and in particular comparisons are made with Good's suggestion of the use of the algebraic rank of the contingency table, and with Lindley's significance test for association in the r x stable. GENERALIZATION OF EDWARD'S ARGUMENTFOR THE 2 x 2 TABLE EDWARDS (1963) has shown that any measure of association of rows and columns for a 2 x 2 contingency table should be a function of the cross-ratio (Pll P22)/(P12 P21)' where the table is represented by (Pij; I~i,j~2). This argument is generalized below to the r x s contingency table, and some suggestions for measures of association are given.Let Pr,s be the class of r x s contingency tables, that is, Pr,s={(Pij):Pij>O,I~i~r,l~j~s and~~Pij= I} It is presumed that no orderings of the rows and columns of tables of P, s are available.Let~be an equivalence relation such that for p,qEPr,s,p~q means that the "association" of rows and columns of P is the same as the "association" of rows and columns of q. A precise definition of "association" is deliberately omitted at this point, but following Edwards, two propositions about it are made.Proposition I If P, q E Pr,s are such thatPij qij -= -, l~i~r, l~j~s-l, Pi. qi.then p~q (employing the usual dot notation for summation over a suffix). 64ALTHAM -Column and Row Measurements for a Contingency Table [No.1, Proposition II If P, q E Pr,s are such that Pij _ qij ---, 1~i~r-l, 1~j~s, P.j q,j A then p--q. Let O,.!! be a relation such that for p,qEPr,s' po"!!q iff PijPrs qijqrs--= --, 1~i~r-l, 1~j~s-l. PisPrj qisqrjThis is easily seen to be an equivalence relation. The generalization of Edwards's result is the following. OR ATheorem. If p,q EP r.s and p--q, then p-q. Proof. Define . PijPrs qijqrs ()(.ij=--=--, l~i~r, l~j~s.PisPrj qisqrj Define 7Tij = 7To ()(.ijPisqrj, where 7To is the normalizing constant, i.e. such that 7TEP r,s' Then 7Tij/7Ti. = qij/qi., 1~i~r, 1~j~s-l, so that 7T1.,q and 7Tij/7T.j = Pij/P.j, 1~i~r-l, 1~j~s, so that 7T1.,p.Hence, by the transitivity of 1." p1.,q as required.Similar versions of this result for r x s x t tables are easily obtained, given suitable modification of Propositions I and II. There are essentially four different types of dependence of rows, columns and layers to be considered, and accordingly four different types of cross-ratio arise as being relevant for the description of these four types of association. An example follows. LetPr,s,!={(Pijk):Pijk>O, l~i~r, l~j~s, l~k~t, and :S:S:SPijk= I}.Let !!., be an equivalence relation such that for P, q E P; s t>P!!., q means that the second order interaction of the rows, columns and layers of P' is the same as that of q. The...