CRISPR loss of function screens are a powerful tool to interrogate cancer biology but are known to exhibit a number of biases and artifacts that can confound the results, such as DNA cutting toxicity, incomplete phenotype penetrance and screen quality bias. Computational methods that more faithfully model the CRISPR biological experiment could more effectively extract the biology of interest than typical current methods. Here we introduce Chronos, an algorithm for inferring gene knockout fitness effects based on an explicit model of the dynamics of cell proliferation after CRISPR gene knockout. Chronos is able to exploit longitudinal CRISPR data for improved inference. Additionally, it accounts for multiple sources of bias and can effectively share information across screens when jointly analyzing large datasets such as Project Achilles and Score. We show that Chronos outperforms competing methods across a range of performance metrics in multiple types of experiments.