Higher Order Mutation (HOM) has been proposed to avoid equivalent mutants and improve the scalability of mutation testing, but generating useful HOMs remain an expensive search problem on its own. We propose a new approach to generate Strongly Subsuming Higher Order Mutants (SSHOM) using a recently introduced Causal Program Dependence Analysis (CPDA). CPDA itself is based on program mutation, and provides quantitative estimation of how often a change of the value of a program element will cause a value change of another program element. Our SSHOM generation approach chooses pairs of program elements using heuristics based on CPDA analysis, performs First Order Mutation to the chosen pairs, and generates an HOM by combining two FOMs.