Closed Testing in Pharmaceutical Research: Historical and Recent Developments.

In pharmaceutical research, making multiple statistical inferences is standard practice. Unless adjustments are made for multiple testing, the probability of making erroneous determinations of significance increases with the number of inferences. Closed testing is a flexible and easily explained approach to controlling the overall error rate that has seen wide use in pharmaceutical research, particularly in clinical trials settings. In this article, we first give a general review of the uses of multiple testing in pharmaceutical research, with particular emphasis on the benefits and pitfalls of closed testing procedures. We then provide a more technical examination of a class of closed tests that use additive-combination-based and minimum-based p-value statistics, both of which are commonly used in pharmaceutical research. We show that, while the additive combination tests are generally far superior to minimum p-value tests for composite hypotheses, the reverse is true for multiple comparisons using closure-based testing. The loss of power of additive combination tests is explained in terms worst-case "hurdles" that must be cleared before significance can be determined via closed testing. We prove mathematically that this problem can result in the power of a closure-based minimum p-value test approaching 1, while the power of an closure-based additive combination test approaches 0. Finally, implications of these results to pharmaceutical researchers are given.

Conifer ovulate cones accumulate pollen principally by simple impaction.

In many pine species (Family Pinaceae), ovulate cones structurally resemble a turbine, which has been widely interpreted as an adaptation for improving pollination by producing complex aerodynamic effects. We tested the turbine interpretation by quantifying patterns of pollen accumulation on ovulate cones in a wind tunnel and by using simulation models based on computational fluid dynamics. We used computer-aided design and computed tomography to create computational fluid dynamics model cones. We studied three species: Pinus radiata, Pinus sylvestris, and Cedrus libani. Irrespective of the approach or species studied, we found no evidence that turbine-like aerodynamics made a significant contribution to pollen accumulation, which instead occurred primarily by simple impaction. Consequently, we suggest alternative adaptive interpretations for the structure of ovulate cones.