The aim of this thesis is to provide the applied researcher with a practical approach for quantitative evidence synthesis using the conditional power prior that allows for subjective input and thereby provides an alternative tgbgo deal with the difficulties as- sociated with the joint power prior distribution. In Chapter 2 the use of the power prior distribution is assessed in case a treatment effect is to be estimated in a randomized trial and the historical data come from randomized studies that used slightly different patient populations and slightly different study designs. Sensitivity analyses were performed to evaluate whether simply ranking the historical studies would provide a solid basis for study weight assignment. Chapter 3 elaborates on the assignment of fixed study weights. In this chapter a Delphi procedure to elicit study weights from a panel of experts is designed and evaluated. Experts were asked to rank and weigh four historical studies with respect to quality and relevance. They were asked to report their motivation for their choices in each round of the Delphi study, and the other experts were able to adjust their ranking and weights if needed, and to respond on the other experts in an anonymous way. This process was monitored to evaluate whether this approach is suitable for the elicitation of study weights in applied research. As mentioned before, Ibrahim and Chen (2000) do not only propose a power prior approach in which the weight parameter is fixed and user specified, but also describe a procedure in which the size of the weight parameter is estimated from the commensurability of the historical and new studies results. In Chapter 4 the question is asked whether this procedure might lead to biased results, since differences or similarities in study results might be the product of sampling variability. In this case the value of the weight parameter would depend on the sample results, meaning that natural variation in sampling results might lead to varying values for the size of the weight parameter. Through a numerical example and a simulation study the size of this problem is assessed and discussed. The fifth chapter is dedicated to an application of a power prior procedure for the cross-design synthesis of evidence for drug safety evaluations. A structured approach is proposed for the inclusion of relevant studies per specific research question raised in a meta-analysis and the assessment of study quality is discussed. In this example the prior distribution for the evaluation of drug safety in a meta-analysis of more or less relevant randomized trials is obtained from a set of relatively large observational studies of varying quality. A procedure is evaluated to assess and, where possible, limit the influence of the informative prior distribution on the posterior results. In Chapter 6 the results are presented from an extensive systematic review on the use of Bayesian statistics in medical and epidemiological literature in general, and the use of and reporting on different types of prior distributions in specific. The thesis is concluded with a summary discussion on the results obtained in the different chapters, and with some remarks about the consequences of the main results.