The promise of personalized medicine is that each person can be prescribed the treatment that is most effective for them. One way to achieve this goal is to focus on a single new treatment, and search for subgroups for which this new treatment is particularly effective. We consider testing for differential treatment effect in subgroups defined by binary biomarkers. That is, we examine tests to determine if a pre-specified binary biomarker is predictive. In such tests, one must determine a reference distribution of the test statistic in the event that a marker is not predictive (i.e., if the null hypothesis is true). Because researchers are often interested in multiple potential predictive biomarkers, permutation-based methods to construct the reference are tempting, as they can capture the correlation among the multiple test statistics. Despite published results that point out the mismatch between the multiple marginal hypotheses of interest and the joint hypothesis assumed in permutation, permutation procedures have continued to be proposed and used in the personalized-medicine setting. We extend our previous results to show that, even for randomized trials examining only a single biomarker, simple permutation tests for predictive markers are only guaranteed to be valid when that marker is not also prognostic. We also note that we can construct valid permutation procedures for the case of single hypotheses, and these procedures can be incorporated into accepted broad multiple testing approaches.