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This paper introduces a general framework to analyze and optimize age-of-information (AoI) in CSMA protocols for distributed uplink transmissions. The proposed framework combines two theoretical approaches. First, it employs second-order analysis that characterizes all random processes by their respective means and temporal variances and approximates AoI as a function of the mean and temporal variance of the packet delivery process. Second, it employs mean-field approximation to derive the mean and temporal variance of the packet delivery process for one node in the presence of interference from others. To demonstrate the utility of this framework, this paper applies it to the age-threshold ALOHA policy and identifies parameter settings that outperform those previously suggested as optimal in the original work that introduced this policy. Simulation results demonstrate that our framework provides precise AoI approximations and achieves significantly better performance, even in networks with a small number of users.