A bias-corrected covariance estimate for improved inference with quadratic inference functions

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21 Scopus citations


The method of quadratic inference functions (QIF) is an increasingly popular method for the analysis of correlated data because of its multiple advantages over generalized estimating equations (GEE). One advantage is that it is more efficient for parameter estimation when the working covariance structure for the data is misspecified. In the QIF literature, the asymptotic covariance formula is used to obtain standard errors. We show that in small to moderately sized samples, these standard error estimates can be severely biased downward, therefore inflating test size and decreasing coverage probability. We propose adjustments to the asymptotic covariance formula that eliminate finite-sample biases and, as shown via simulation, lead to substantial improvements in standard error estimates, inference, and coverage. The proposed method is illustrated in application to a cluster randomized trial and a longitudinal study. Furthermore, QIF and GEE are contrasted via simulation and these applications.

Original languageEnglish
Pages (from-to)4003-4022
Number of pages20
JournalStatistics in Medicine
Issue number29
StatePublished - Dec 20 2012


  • Correlated data
  • Coverage probability
  • Marginal model
  • Standard error
  • Test size

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability


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