In this article, inference for a left-truncated and right-censored competing risk model is discussed when the cause of failures of units is partially observed and dependent. Under the assumption that latent failure times follow the Marshall-Olkin bivariate generalized lifetime distributions, inference for unknown parameters is obtained using frequentist and Bayesian approaches. Maximum likelihood estimators of parameters, along with their existence and uniqueness, are also provided. Subsequently, approximate confidence intervals are constructed based on the observed Fisher information matrix. Further, Bayes estimates and associated highest posterior density credible intervals are developed using a Gamma-Dirichlet prior under squared error and LINEX loss functions. Inference is also discussed with order restrictions on parameters. The performance of various estimators is evaluated based on extensive simulation study, and comments are obtained. Finally, two real-life applications are provided for illustrative purposes.