In multiple testing, a challenging issue is to provide an accurate estimation of the proportion pi(0) of true null hypotheses among the whole set of tests. Besides a biological interpretation, this parameter is involved in the control of error rates such as the False Discovery Rate. Improving its estimation can result in more powerful/less conservative methods of differential analysis. Various methods for pi(0) estimation have been previously developed. Most of them rely on the assumption of independent p-values distributed according to a two-component mixture model, with a uniform distribution for null p-values. In a general factor analytic framework, the impact of dependence on the properties of the estimation procedures is first investigated and exact expressions of bias and variance are provided in case of dependent data. A more accurate factor-adjusted estimator of pi(0) is finally presented, which shows large improvements with respect to the standard procedures.