Animal models are used to predict the effect of an intervention in humans. An example is the prediction of the efficacy of a vaccine when it is considered unethical or infeasible to challenge humans with the target disease to assess the effect of the vaccine on the disease in humans directly. In such cases, data from animal studies are used to develop models relating antibody level to protection probability in the animal, and then data from a study or studies in human subjects vaccinated with the proposed vaccine regimen are used in combination with the relevant animal models to predict protection in humans, and hence estimate vaccine efficacy. We explain the statistical techniques required to provide an estimate of vaccine efficacy and its precision. We present simulated examples showing that precise estimation of the relationship between antibody levels and protection in animals, at levels likely to be induced in humans by the vaccine regimen, is key to precise estimation of the vaccine efficacy. Because the confidence interval for the estimate of vaccine efficacy cannot be expressed in analytical form, but must be estimated from resampling, or bootstrapping, it is not possible to design studies with required power analytically. Therefore we propose that a simulation-based design of experiments approach using preliminary data is used to maximise the power of further studies and thus minimise the human and animal experimentation required.