In an on-demand testing program, some items are repeatedly used across test administrations. This poses a risk to test security. In this study, we considered a scenario wherein a test was divided into two subsets: one consisting of secure items and the other consisting of possibly compromised items. In a simulation study of multistage adaptive testing, we used three methods to detect item preknowledge: a predictive checking method (PCM), a likelihood ratio test (LRT), and an adapted Kullback--Leibler divergence (KLD-A) test. We manipulated four factors: the proportion of compromised items, the stage of adaptive testing at which preknowledge was present, item-parameter estimation error, and the information contained in secure items. The type I error results indicated that the LRT and PCM methods are favored over the KLD-A method because the KLD-A can experience large inflated type I error in many conditions. In regard to power, the LRT and PCM methods displayed a wide range of results, generally from 0.2 to 0.8, depending on the amount of preknowledge and the stage of adaptive testing at which the preknowledge was present.