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February 2, 2000

Quality of Health Care and the HMO Marketplace

Author Affiliations

Phil B.FontanarosaMD, Deputy EditorIndividualAuthorStephen J.LurieMD, PhD, Fishbein FellowIndividualAuthor


Copyright 2000 American Medical Association. All Rights Reserved. Applicable FARS/DFARS Restrictions Apply to Government Use.2000

JAMA. 2000;283(5):602-605. doi:10.1001/jama.283.5.601

To the Editor: Although we do not necessarily disagree with the conclusion of Dr Himmelstein and colleagues1 that investor-owned HMOs deliver lower quality of care than not-for-profit plans, we think that their use of linear regression may not be appropriate for analyzing their data. One of the assumptions of linear regression is homoscedasticity, ie, the variance of the dependent variable is the same for any fixed combination of explanatory variables.2 For data used in this study, the dependent variable is a percentage or, equivalently, a proportion (p). The variance of a proportion is p(1 − p)/n, where n is the sample size. Because variance is a function of p, the use of linear regression to model a percentage or p response variable violates the homoscedasticity assumption. The appropriate technique for modeling a percentage or proportion is logistic regression.

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