Taking into account various variables such as "sociodemographics and comorbid allergic disease" authors determined that among the 19 cohorts, the majority (12) showed some kind of connection between eczema and elevated odds of speech disorder. Further, when pooled together, the prevalence of speech disorder among those children with eczema was 4.7% compared with a figure of 2.2% for those children without eczema.
One other detail to impart from the Strom/Silverberg study was how eczema plus other labels was also linked to risk of speech disorder as per the sentence: "children with both eczema and attention deficit disorder with or without hyperactivity or sleep disturbance had vastly increased risk of speech disorders than either by itself."
Allowing for the fact that correlation is not necessarily the same as causation and that as the authors admit: "Further, prospective studies are needed to characterize the exact nature of this association" these are interesting data strengthened by the large number of participants included for study. A quick trawl of the research literature in this area suggests that childhood speech disorders may very well be associated with additional health problems  although not necessarily just rooted in something like eczema.
The possibility that a physical ailment like eczema might have implications for a developmental condition like childhood speech disorder is a tantalising one. I've covered the preliminary idea of a 'skin-brain axis' before on this blog (see here) on the basis of data like that reported by Yaghmaie and colleagues  talking about atopic dermatitis and various developmental/psychiatric labels. More generally, allergic disease in infancy has been linked to various neurodevelopmental outcomes (see here) with again, the requirement for quite a bit more investigation of this possible association. Indeed, even the 'big data' of Taiwan has something to say on this topic (see here).
As to any mechanism, well, outside of the suggestion of shared genetic risk between something like eczema and speech (and language) issues, the idea that the immune function (a cardinal mechanism of eczema) might play a much greater role in our health and wellbeing than merely the somatic is becoming more mainstream in these days of immune system and psychiatry intersecting (see here). The more general idea that immune features such as inflammation might be able to 'interact' with psychology is a whole new frontier of medicine (see here) and one that should be incorporated into any future research strategy. The other potentially important question outside of any aetiological association is whether or not early treatment of eczema including attending to some of the possible triggers  might also have important implications for the risk of developing speech disorders?
Music: Blur - Trimm Trabb.
 Strom MA. & Silverberg JI. Eczema Is Associated with Childhood Speech Disorder: A Retrospective Analysis from the National Survey of Children's Health and the National Health Interview Survey. J Pediatr. 2015 Oct 28. pii: S0022-3476(15)01140-3.
 Keating D. et al. Childhood speech disorders: reported prevalence, comorbidity and socioeconomic profile. J Paediatr Child Health. 2001 Oct;37(5):431-6.
 Yaghmaie P. et al. Mental health comorbidity in patients with atopic dermatitis. J Allergy Clin Immunol. 2013 Feb;131(2):428-33.
Strom MA, & Silverberg JI (2015). Eczema Is Associated with Childhood Speech Disorder: A Retrospective Analysis from the National Survey of Children's Health and the National Health Interview Survey. The Journal of pediatrics PMID: 26520915