Unbiased estimating equations are used to estimate and compare the odds ratios representing the odds of heightened anxiety following acute exposures relative to baseline in a cross-over study examining indoor air contaminants. Although estimating equations are used in the creation of the estimates and standard errors, inference is conditional on subject. The proposed method produces estimates that are less biased and computationally simpler than pseudo-likelihood. In addition, specification of the form of the random-effects distributions is not required.