The theoretical underpinnings under which sensitivity analysis is valid in OLAP databases are dealt with in this paper. Sensitivity analysis is considered to be the reverse of explanation generation in diagnostic reasoning. Our exposition differentiates between sensitivity analysis in systems of purely drill-down equation and mixed systems of equations with also business model equations. It is proven that there is an unique additive drilldown measure defined on all cubes of the aggregation lattice. This proof is the basis for sensitivity analysis in OLAP databases, where a change in some base cell in the lattice is propagated to all descendants in its upset. For sensitivity analysis in mixed systems of equations a matrix notation is presented and the conditions for solvability are discussed. Due to the fact that such systems are typically overdetermined in OLAP databases, the implicit function theorem cannot be applied. Therefore, we proposed a method to reduce the number of equations in the system and apply the implicit function theorem on a subsystem of the original system. We conclude with an alternative method for what-if analysis in mixed systems of equations.