Abstract

Robert Haley contends that our factor analysis does not approximate his factor analysis and that our mathematical methods were incorrect. The main objective of our study was to test whether the factor structure of the symptoms reported in a randomly selected UK Gulf War cohort was different from the factor structure of symptoms in two other randomly selected military cohorts. To do this, we obtained a Gulf War reponse rate of 70%, a sample size of 3225, and two large control groups of Bosnia and Era veterans. We emphasise that our key findings are that subjective reporting of symptoms in the Gulf War cohort was similar to that in two military control groups. Three other large scale epidemiology studies have also used control groups and reported similar findings.1Fukuda K Nisenbaurn R Stewart G et al.Chronic multi-symptom illness affecting air force veterans of the Gulf War.JAMA. 1998; 280: 981-988Crossref PubMed Scopus (550) Google Scholar, 2Doebbeling BN, Woolson RF, Torner JC, et al. Self-reported illness following service in the Persian Gulf: multiple medical conditions. Presented at 125th Annual Meeting of the American Public Health Association, Indianapolis, IN, USA, 1997: 5.Google Scholar, 3Knoke J, Smith TC, Gray G, et al. Factor analysis of self reported symptoms: does it identify a Gulf War Syndrome? Am J Epidemiol (in press).Google Scholar At present, there is no compelling evidence for the existence of a unique Gulf War syndrome.By contrast, Haley reported results from a single unit, with a sample size of 249, a response rate of 41%, and no control group, military or otherwise. As many commentators have noted,4Landrigan PJ Illness in Gulf War veterans. Causes and consequences.JAMA. 1997; 277: 259-261Crossref PubMed Google Scholar Haley's design does not allow him to address the central question of the existence or otherwise of a Gulf War syndrome.It was only a secondary objective for us to examine Haley's reported factors, since Haley's work was published after we embarked on our study. Haley's penultimate paragraph demonstrates both his confusion over the differences between exploratory factor analysis and confirmatory factor analysis, and (like many other nonstatisticians) a naïve faith in the statistical criteria associated with the former. These criteria, the scree test, and the number of eigenvalues greater than one test, are nothing more than rough guides to the number of factors. And Haley's appeal to that old favourite clinical interpretability is also not wholly convincing in view of the well known difficulties with the reification of factors and the dangers of their over interpretation.With these points in mind, and noting that the last three of Haley's factors accounted for only small amounts of variance, we decided to base a model on only the first three of his factors emphasising that this was an approximation.What we then did was to try to match the symptoms that loaded onto the first three factors he identified to symptoms measured in our study. We found 17 symptoms from our 52 symptoms questionnaire that had face validity with the 23 symptoms that loaded onto his first three factors. Out of courtesy, we labelled this approximation the Haley model and then used it as the basis of one of our confirmatory factor analyses. We also draw attention to the many publications showing the general nonspecificity of chronic self-reported somatic symptoms in the general population,5Wessely S Chalder T Hirsch S Wallace P Wright D Psychological symptoms, somatic symptoms and psychiatric disorder in chronic fatigue and chronic fatigue syndrome: a prospective study in primary care.Am J Psychiatry. 1996; 153: 1050-1059Crossref PubMed Scopus (189) Google Scholar as well as the dangers of assuming that each individual symptom can be ascribed to a precise pathological process, as Haley seems to believe.This Haley model was tested with confirmatory factor analysis on the three cohorts in our data. The loadings of some variables in the model were allowed to be free parameters to be estimated, with the remainder having loadings constrained to be zero. The factor loadings from Haley's analysis were used only to suggest which variables should have zero loadings, and which should not; their numerical values were never used. The correlations between factors were also allowed to be free parameters to be estimated during the analysis. Haley objects to this procedure since in his own exploratory factor analysis orthogonal factors were derived. His suggestion that what we did was equivalent to an oblique rotation merely underscores his unfamiliarity with confirmatory factor analysis. And since the estimated correlations were all significantly different from zero, constraining them to be zero could only have made the fit of the model worse. The model loosely based on his results did not fit our data well. Robert Haley contends that our factor analysis does not approximate his factor analysis and that our mathematical methods were incorrect. The main objective of our study was to test whether the factor structure of the symptoms reported in a randomly selected UK Gulf War cohort was different from the factor structure of symptoms in two other randomly selected military cohorts. To do this, we obtained a Gulf War reponse rate of 70%, a sample size of 3225, and two large control groups of Bosnia and Era veterans. We emphasise that our key findings are that subjective reporting of symptoms in the Gulf War cohort was similar to that in two military control groups. Three other large scale epidemiology studies have also used control groups and reported similar findings.1Fukuda K Nisenbaurn R Stewart G et al.Chronic multi-symptom illness affecting air force veterans of the Gulf War.JAMA. 1998; 280: 981-988Crossref PubMed Scopus (550) Google Scholar, 2Doebbeling BN, Woolson RF, Torner JC, et al. Self-reported illness following service in the Persian Gulf: multiple medical conditions. Presented at 125th Annual Meeting of the American Public Health Association, Indianapolis, IN, USA, 1997: 5.Google Scholar, 3Knoke J, Smith TC, Gray G, et al. Factor analysis of self reported symptoms: does it identify a Gulf War Syndrome? Am J Epidemiol (in press).Google Scholar At present, there is no compelling evidence for the existence of a unique Gulf War syndrome. By contrast, Haley reported results from a single unit, with a sample size of 249, a response rate of 41%, and no control group, military or otherwise. As many commentators have noted,4Landrigan PJ Illness in Gulf War veterans. Causes and consequences.JAMA. 1997; 277: 259-261Crossref PubMed Google Scholar Haley's design does not allow him to address the central question of the existence or otherwise of a Gulf War syndrome. It was only a secondary objective for us to examine Haley's reported factors, since Haley's work was published after we embarked on our study. Haley's penultimate paragraph demonstrates both his confusion over the differences between exploratory factor analysis and confirmatory factor analysis, and (like many other nonstatisticians) a naïve faith in the statistical criteria associated with the former. These criteria, the scree test, and the number of eigenvalues greater than one test, are nothing more than rough guides to the number of factors. And Haley's appeal to that old favourite clinical interpretability is also not wholly convincing in view of the well known difficulties with the reification of factors and the dangers of their over interpretation. With these points in mind, and noting that the last three of Haley's factors accounted for only small amounts of variance, we decided to base a model on only the first three of his factors emphasising that this was an approximation. What we then did was to try to match the symptoms that loaded onto the first three factors he identified to symptoms measured in our study. We found 17 symptoms from our 52 symptoms questionnaire that had face validity with the 23 symptoms that loaded onto his first three factors. Out of courtesy, we labelled this approximation the Haley model and then used it as the basis of one of our confirmatory factor analyses. We also draw attention to the many publications showing the general nonspecificity of chronic self-reported somatic symptoms in the general population,5Wessely S Chalder T Hirsch S Wallace P Wright D Psychological symptoms, somatic symptoms and psychiatric disorder in chronic fatigue and chronic fatigue syndrome: a prospective study in primary care.Am J Psychiatry. 1996; 153: 1050-1059Crossref PubMed Scopus (189) Google Scholar as well as the dangers of assuming that each individual symptom can be ascribed to a precise pathological process, as Haley seems to believe. This Haley model was tested with confirmatory factor analysis on the three cohorts in our data. The loadings of some variables in the model were allowed to be free parameters to be estimated, with the remainder having loadings constrained to be zero. The factor loadings from Haley's analysis were used only to suggest which variables should have zero loadings, and which should not; their numerical values were never used. The correlations between factors were also allowed to be free parameters to be estimated during the analysis. Haley objects to this procedure since in his own exploratory factor analysis orthogonal factors were derived. His suggestion that what we did was equivalent to an oblique rotation merely underscores his unfamiliarity with confirmatory factor analysis. And since the estimated correlations were all significantly different from zero, constraining them to be zero could only have made the fit of the model worse. The model loosely based on his results did not fit our data well. Is there a Gulf War syndrome?Khalida Ismail and colleagues (Jan 16, p 179)1 claim to have approximated the factor analysis of symptoms that I did in US Gulf War veterans and found it unable to detect the same syndromes in British Gulf War veterans. They were sufficiently satisfied with their replication of my work that they referred to their analysis as the Haley model. This analysis, however, does not approximate my factor analysis, could not have identified the same syndromes even if tested in the same sample we studied, and does not test the validity of my findings. Full-Text PDF

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