Re: "(Mis)use of Factor Analysis in the Study of Insulin Resistance Syndrome"

Suzanne Novak1, Laura M. Stapleton2, John R. Litaker3 and Kenneth A. Lawson1

1 Pharmacy Administration Division, College of Pharmacy, University of Texas at Austin, Austin, TX 78712
2 The Litaker Group, Austin, TX 78712
3 Department of Educational Psychology, The University of Texas at Austin, Austin, TX 78712

A recent Journal paper by Lawlor et al. (1Go) suggests that researchers begin to explore the hypothesis-testing purposes of using confirmatory factor analysis to increase understanding of the insulin resistance syndrome. In contrast to what was reported by these authors, two studies were published prior to their article in which a hypothesis-testing approach was used to examine the factor structure of the syndrome. The models tested include a hierarchical four-factor model, with a higher order, metabolic syndrome factor (2Go); and a four-factor intercorrelated model (without the overlying higher-order factor) (2Go, 3Go).

Shen et al. describe even further the type of a priori hypothesis testing that confirmatory factor analysis may allow by suggesting that "the stability of the hypothesized factor structure can be tested across subgroups with different characteristics" (2Go, p. 702), such as age or diagnosis. It may also be that confirmatory factor analysis can be used to test the construct validity and reliability of the hypothesized latent constructs used in models of insulin resistance syndrome (3Go). This may be of special importance when deciding on the most appropriate proxy variables to use in measuring insulin resistance, which is currently a matter of great controversy (4Go).

As an example, when fasting insulin and fasting glucose were used as variables to measure the insulin resistance factor in a four-factor intercorrelated model of insulin resistance syndrome that included middle-aged, European males (that exhibited good fit using Hu and Bentler criteria (5Go)), poor construct validity was obtained (3Go). Variance extracted was estimated as 0.26 (with a suggested lower limit of 0.50) by using the formula ({sum}{lambda}2)/p, in which {lambda} represents standardized loadings and p represents the number of indicator variables of the underlying latent construct (6Go). This formula, used in factor analysis in general, is equivalent to the proportion of variance extracted as defined as the sum of the eigenvalues over the total variance. Construct reliability was calculated as 0.37 (with a suggested lower limit of 0.70 (7Go)) by using the formula (6Go). In this formula, construct reliability is a function of the squared sum of standardized loadings (or the amount of standardized variance and covariance explained by the factors) over the total amount of standardized variance and covariance (6Go, 8Go).

These values improved in the Shen et al. (2Go) intercorrelated model of North American males with similar demographic characteristics when the additional variables of postchallenge insulin and glucose (variance extracted = 0.39, construct reliability = 0.7) were used. If the postchallenge values for insulin or glucose are removed from this model, the variance extracted drops to 0.36, and construct reliability to 0.49, reducing the construct validity. It may be that, as Shen et al. suggest, inclusion of other physiologic variables (such as uric acid, inflammation, procoagulation, or vitamin K-dependent protein) may be required to improve the construct validity of the insulin resistance factor. Future research may also show that insulin resistance is measured differently in different ethnic groups, in different age groups, and in subjects with more advanced disease such as overt type 2 diabetes mellitus.

Further use of confirmatory factor analysis models for both hypothesis testing of the factor structure of the metabolic syndrome and measurement of construct validity and reliability of variables used to define these factors may give researchers one more statistical tool to help to elucidate better ways of evaluating the best clinical way to approximate insulin resistance in epidemiologic studies.

NOTES

Editor's note: In accordance with Journal policy, Lawlor et al. were asked whether they wanted to respond to these letters. Because of current scheduling demands, Dr. Lawlor has been given the option of responding at a later date.

References

  1. Lawlor DA, Ebrahim S, May M, et al. (Mis)use of factor analysis in the study of insulin resistance syndrome. Am J Epidemiol 2004;159:1013–18.[Abstract/Free Full Text]
  2. Shen BJ, Todaro JF, Niaura R, et al. Are metabolic risk factors one unified syndrome? Modeling the structure of the metabolic syndrome X. Am J Epidemiol 2003;157:701–11.[Abstract/Free Full Text]
  3. Novak S, Stapleton LM, Litaker JR, et al. A confirmatory factor analysis evaluation of the coronary risk factors of metabolic syndrome with emphasis on the insulin resistance factor. Diabetes Obes Metab 2003;5:388–96.[CrossRef][ISI][Medline]
  4. Hanley AJG, Williams K, Gonzalez C, et al. Prediction of type 2 diabetes using simple measures of insulin resistance. Diabetes 2003;52:463–9.[Abstract/Free Full Text]
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