In this letter, I offer some grounds for suggesting why it will be difficult to establish that there is a birth order effect in ankylosing spondylitis (AS), supposing that one actually does exist. Baudoin et al (1) reported an increased risk of AS among first-born siblings versus others in sibships. If these authors are correct, this is an important result and will almost certainly have implications for the etiology of the disease. However, I previously noted a flaw in their demonstration (2). AS is a condition that usually develops in adulthood. So, at a given time in any sibship, the first-born has a greater chance than other siblings to have been diagnosed with AS simply because the first-born has lived through more of the risk interval. Some of the authors responded (3) with the observation that the median age of their patients and siblings was 52 years, and that 90% of patients with AS have been diagnosed by that age.
This argument is not decisive. Therefore, I suggest a method by which the authors might strengthen their argument. For each of their siblings who is (so far) unaffected, a probability (p) that ultimately he or she will develop AS may be estimated. For sibling i, this probability is given by the product of 2 individual probabilities, pi = p1p2, where p1 is the sex-specific sibling recurrence risk for AS, and p2 the probability that a case is not diagnosed until after the age of sibling i. All these pi values may be treated as expected frequencies and pooled with the appropriate observed frequencies of cases, and the result may be retested for a birth order effect. However, even when such adjustment has been made, the result may be subject to reservations, as will be later explained.
Moreover, there is another point that should be considered by the authors. They used a 1-tailed test. As I understand it, their justification for doing so is that some other diseases that they liken to AS (i.e., multiple sclerosis and rheumatoid arthritis) have been associated with birth order effects. The argument is questionable. However, because the grounds themselves are false, this need not detain us. There are no conclusive grounds for supposing that these 2 latter diseases are subject to birth order effects. The claim with regard to rheumatoid arthritis is based on a letter by Sayeeduddin et al (4). This letter reports a study in which the data were uncorrected (as indicated above) for future diagnoses of (mainly younger-born) siblings. Moreover, the claim was based on the test of Haldane and Smith (5), which has the same flaw as that in the test of Greenwood and Yule (6) (described below). Last, in other studies, higher rates of rheumatoid arthritis have been described in later-born men (7) and women (8). With regard to multiple sclerosis, there has been a brisk, but inconclusive, discussion of the possibility of a birth order effect. The last 2 studies (known to me) reported no such effect (9, 10).
The test for a birth order effect used by Baudoin et al (1) is derived from that of Greenwood and Yule (6). On the occasion of the presentation of their test to a meeting of the Royal Statistical Society, Yule (who later became coauthor of the standard volumes on advanced statistics) expressed doubt about the validity of the test, which was later to be widely (and indiscriminately) used. Eighty-seven years later, his words are worth noting. “Mr Yule … thought they both (viz himself and Greenwood) felt, after the conclusion of their work, very doubtful as to the possibility of definitely proving the existence of a real differential incidence of any character in order of birth. The whole question seemed so open to fallacious possibilities in different directions.” One of the grounds for Yule's doubt was that central to the test is the notion that if one ascertains a subject from a sibship of size n, then he or she has equal probabilities (1/n) of being first-, second-, … nth born. This is intuitively appealing but is subject to logical qualification, and empiric testing has shown it to be false under very general circumstances (11, 12). Part of the explanation lies in the fact that population birth rates change across time.
None of the foregoing discussion should be taken to imply that there is no birth order effect in AS, simply that it will be difficult to demonstrate if there actually is one. At first, it might be thought that it would be useful, instead, to concentrate on maternal age rather than birth order. Baudoin et al (1) report a significant maternal age effect. However, one is again faced with the problem of the currently unaffected siblings who will later be diagnosed with the disease. In general, they are younger and thus later-born than the present cases. So, when diagnosis is finally complete in the ascertained sibships, mean maternal age will be higher than estimated at present.
As I see it, there are 2 solutions to the present problem. 1) Because of the established flaw in the Greenwood-Yule test (6), investigators could take the (admittedly more expensive) provision of ascertaining, in addition to their sample of cases, a control group of healthy, unaffected individuals who would be matched for age. The mean birth orders and maternal ages could then be tested for significant contrasts. If such a control group is ascertained, there seems no logical requirement to wait until all of the unaffected siblings have passed the maximum age of onset. 2) Alternatively, it would be possible to wait until the maximum age of onset and then estimate, for each affected case, his or her “expected” birth order, based on population mean birth order for the case's year of birth.