In longitudinal data analyses, the observation times are often assumed to be independent of the outcomes. In applications in which this assumption is violated, the standard inferential approach of using the generalized estimating equations may lead to biased inference. Current methods require the correct specification of either the observation time process or the repeated measure process with a correct covariance structure. In this article, we construct a novel pairwise pseudolikelihood method for longitudinal data that allows for dependence between observation times and outcomes. This method incorporates both time-dependent and time-independent covariates, while leaving theobservation time process unspecified. The novelty of this method is that specification of neither the observation time process nor the covariance structure of the repeated measure process is required. Large sample properties of the regression coefficient estimates and a pseudolikelihood-ratio test statistic are established. Simulation studies demonstrate that the proposed method performs well in finite samples and is robust to the dependence between the observation times and outcomes. An analysis of weight loss data from a web-based program is presented to illustrate the proposed method.