Purpose: Prior-image-based reconstruction (PIBR) is a powerful tool for low-dose CT, however, the nonlinear behavior of such approaches are generally difficult to predict and control. Similarly, traditional image quality metrics do not capture potential biases exhibited in PIBR images. In this work, we identify a new bias metric and construct an analytical framework for prospectively predicting and controlling the relationship between prior image regularization strength and this bias in a reliable and quantitative fashion. Methods: Bias associated with prior image regularization in PIBR can be described as the fraction of actual contrast change (between the prior image and current anatomy) that appears in the reconstruction. Using local approximation of the nonlinear PIBR objective, we develop an analytical relationship between local regularization, fractional contrast reconstructed, and true contrast change. This analytic tool allows prediction bias properties in a reconstructed PIBR image and includes the dependencies on the data acquisition, patient anatomy and change, and reconstruction parameters. Predictions are leveraged to provide reliable and repeatable image properties for varying data fidelity in simulation and physical cadaver experiments. Results: The proposed analytical approach permits accurate prediction of reconstructed contrast relative to a gold standard based on exhaustive search based on numerous iterative reconstructions. The framework is used to control regularization parameters to enforce consistent change reconstructions over varying fluence levels and varying numbers of projection angles - enabling bias properties that are less location- and acquisition-dependent. Conclusions: While PIBR methods have demonstrated a substantial ability for dose reduction, image properties associated with those images have been difficult to express and quantify using traditional metrics. The novel framework presented in this work not only quantifies this bias in an intuitive fashion, but it gives a way to predict and control the bias. Reliable and predictable reconstruction methods are a requirement for clinical imaging systems and the proposed framework is an important step translating PIBR methods to clinical application.