Collaborative biostatistics is the creative application of statistical tools to biomedical problems. The relatively modest literature about the traits of effective collaborative biostatisticians focuses on four core competencies: (a) technical and analytical; (b) substance-matter knowledge; (c) communication; and (d) problem solving and problem framing. Most statistical education concentrates on the technical and analytical competency; here, we focus on the remaining ones. Case studies describing consultations about study design and data analysis are presented, and the task is to deconstruct the knowledge used by an experienced collaborative biostatistician into components which are more explicit (and, ultimately, teachable). These components include specific and concrete information about statistical procedures; substance-matter knowledge about biology and medicine; general knowledge about biomedical studies, especially study design; insights about the process of effective collaboration; and high-level synthesis. Implications for curriculum design are discussed. To follow up on these qualitative and provisional efforts, the next step in scholarly research about to teach communication, problem framing and problem solving within the context of collaborative biostatistics should focus on a finer-grained and evidence-based description of what these competencies actually entail.