A growing number of safety-critical industries agree that building confidence in complex systems can be achieved through evidence and structured argumentation framed in assurance cases. Nevertheless, according to practical industry experience, assurance cases can easily become too rigorous and difficult to develop and maintain when applied to complex systems. Therefore, we propose to use contract-based development (CBD), a method to manage complexity originally developed in computer science, to simplify assurance cases by modularizing them. This paper will not only summarize relevant previous work such as constructing consistent modular assurance cases using CBD, but more importantly also propose a novel approach to integrate CBD with the argumentation in assurance case modules. This approach will allow subject-matter and domain experts to build assurance case modules together without having to know CBD. This can help a broader application of these methods in industry because subject matter experts outside of computer science can contribute to cross disciplinary co-development of assurance cases without having to learn CBD. Industry experience has proven four rules of thumb helpful for developing high-quality assurance cases. This article illustrates their usefulness and explains how modular assurance enables assurance that accounts for the interdependency of different concerns such as safety, security and performance.