An exact test for comparing two predictive values in small‐size clinical trials

Positive and negative predictive values describe the performance of a diagnostic test. There are several methods to test the equality of predictive values in paired designs. However, these methods were premised on large sample theory, and they may not be suitable for small‐size clinical trials because of inflation of the type 1 error rate. In this study, we propose an exact test to control the type 1 error rate strictly for conducting a small‐size clinical trial that investigates the equality of predictive values in paired designs. In addition, we execute simulation studies to evaluate the performance of the proposed exact test and existing methods in small‐size clinical trials. The proposed test can calculate the exact P value, and as a result of simulations, the empirical type 1 error rate for the proposed test did not exceed the significance level regardless of the setting, and the empirical power for the proposed test is not much different from the other methods based on large‐sample theory. Therefore, it is considered that the proposed exact test is useful when the type 1 error rate needs to be controlled strictly.     

Host plant conspicuousness and the distribution of eggs and larvae in the butterfly,Anthocharis scolymus (Lepidoptera: Pieridae)

Summary We investigated how the distribution pattern of eggs and larval on the host plant,Turritus glabra, was influenced by the oviposition behavior of the pierid butterflyAnthocharis scolymus. Females searched for the host plants visually and they frequently approached taller host plants with sparse surrounding vegetation. After encountering host plants, oviposition behavior of females was independent of host plant characteristics such as height, density, and type of surrounding vegetation. A female laid eggs singly on a host plants. Most females appeared to lay their eggs regardless of the presense of eggs on the host plant. Consequently egg and larva tended to be abundant on conspicuous host plants as measured by height or relative isolation from other plants. However, overcrowding of eggs on an individual host decreased the survival rate of larvae.