Modern medical research requires access to patient-level data of significant detail and volume. In this context, privacy concerns and legal requirements demand careful consideration. Data anonymization, which means that data is transformed to reduce privacy risks, is an important building block of data protection concepts. However, common methods of data anonymization often fail to protect data against inference of sensitive attribute values (also called attribute disclosure). Measures against such attacks have been developed, but it has been argued that they are of little practical relevance, as they involve significant data transformations which reduce output data utility to an unacceptable degree. In this article, we present an experimental study of the degree of protection and impact on data utility provided by different approaches for protecting biomedical data from attribute disclosure. We quantified the utility and privacy risks of datasets that have been protected using different anonymization methods and parameterizations. We put the results into relation with trivial baseline approaches, visualized them in the form of risk-utility curves and analyzed basic statistical properties of the sensitive attributes (e.g. the skewness of their distribution). Our results confirm that it is difficult to protect data from attribute disclosure, but they also indicate that it can be possible to achieve reasonable degrees of protection when appropriate methods are chosen based on data characteristics. While it is hard to give general recommendations, the approach presented in this article and the tools that we have used can be helpful for deciding how a given dataset can best be protected in a specific usage scenario.