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In type 2 diabetes (T2D) treatment, finding a safe and effective basal insulin dose is a challenge. The dose-response is highly individual and to ensure safety, people with T2D titrate by slowly increasing the daily insulin dose to meet treatment targets. This titration can take months. To ease and accelerate the process, we use short-term artificial pancreas (AP) treatment tailored for initial titration and apply it as a diagnostic tool. Specifically, we present a method to automatically estimate a personalized daily dose of basal insulin from closed-loop data collected with an AP. Based on AP-data from a stochastic simulation model, we employ the continuous-discrete extended Kalman filter and a maximum likelihood approach to estimate parameters in a simple dose-response model for 100 virtual people. With the identified model, we compute a daily dose of basal insulin to meet treatment targets for each individual. We test the personalized dose and evaluate the treatment outcomes against clinical reference values. In the tested simulation setup, the proposed method is feasible. However, more extensive tests will reveal whether it can be deemed safe for clinical implementation.