Motivation: Spontaneous adverse event reports have a high potential for detecting adverse drug reactions. However, due to their dimension, exploring such databases requires statistical methods. In this context, disproportionality measures are used. However, by projecting the data onto contingency tables, these methods become sensitive to the problem of co-prescriptions and masking effects. Recently, logistic regressions have been used with a Lasso type penalty to perform the detection of associations between drugs and adverse events. However, the choice of the penalty value is open to criticism while it strongly influences the results. Results: In this paper, we propose to use a logistic regression whose sparsity is viewed as a model selection challenge. Since the model space is huge, a Metropolis-Hastings algorithm carries out the model selection by maximizing the BIC criterion. Thus, we avoid the calibration of penalty or threshold. During our application on the French pharmacovigilance database, the proposed method is compared to well established approaches on a reference data set, and obtains better rates of positive and negative controls. However, many signals are not detected by the proposed method. So, we conclude that this method should be used in parallel to existing measures in pharmacovigilance.