Cell culture assays are a critical experimental method used to determine how a set of experimental conditions affect the growth and dynamics of a cell population in vitro. Methods used to perturb the conditions include varying the amount of perturbagen or any other culture condition to measure response. In order to quantify the relationship between the culture conditions tested and the change in population growth dynamics, a statistical model is employed to estimate and predict these effects. Current methods treat cell count as the response variable in statistical models and summarize the result in metrics like the IC50. These methods are not invariant to changes in time, seeding count, or other conditions, and can lead to reproducibility issues. Different conditions lead to different results in terms of relative cell count even if the growth dynamics are the same, so results are not easily generalizable to other scenarios. Here we propose a rigorous mechanism-based method for estimation of response that uses a mathematical model for population growth incorporating cell division, death, and transitions between states. The rate of events are the response in hierarchical statistical models that allows variability in conditions and even cell lines. The result is an analysis platform that treats cell-intrinsic properties rather than cell count as outcomes so that they are invariant to experimental duration, seeding density, and other factors. We propose this novel methodology as a standalone framework for analysis of any cell culture experimental data. We model cell growth as a branching process that describes how an individual cell or type of cells divide, die, or undergo cell state transitions by defining each of these events as random variables parameterized by the rates. We attach a statistical model for the rates as a function of covariates of interest. Data in the form of cell counts connects to rates through the branching process, and we use Bayesian methods to approximate the likelihood and estimate the parameter values of the model. This approach creates a rigorous framework for performing estimation of cellular response as a function of the growth rates obtained from counts as input data, and more generally for estimation of branching process parameters. We will establish the statistical methods in the following aims: (1.) We will develop Bayesian methods and a statistical framework for estimation of cell birth and death rates. (2.) We will create a hierarchical model framework to account for cell line and experimental effects to help create reproducible results. (3.) We will develop modeling for more complicated branching processes that can account for dynamics of a population undergoing a variety of state transitions including cycling, differentiation, and size.