Expected Power for the False Discovery Rate with Independence

Self-reported physical health status of donor sperm-conceived adults

Donor-conceived neonates have poorer birth outcomes, including low birth weight and preterm delivery that are associated with poorer long-term health in adulthood through the developmental origins of health and disease (DOHaD) theory. The aim of this study was to conduct the first investigation of the adult health outcomes of donor-conceived people. An online health survey was completed by 272 donor sperm-conceived adults and 877 spontaneously conceived adults from around the world. Donor and spontaneously conceived groups were matched for age, sex, height, smoking, alcohol consumption, exercise, own fertility and maternal smoking. Donor sperm-conceived adults had significantly higher reports of being diagnosed with type 1 diabetes (P = 0.031), thyroid disease (P = 0.031), acute bronchitis (P = 0.008), environmental allergies (P = 0.046), sleep apnoea (P = 0.037) and having ear tubes/grommets surgically implanted (P = 0.046). This is the first study to investigate the health outcomes of adult donor sperm-conceived people. Donor sperm-conceived adults self-reported elevated frequencies of various health conditions. The outcomes are consistent with birth defect data from donor sperm treatment and are consistent with the DOHaD linking perturbed early growth and chronic disease in adulthood.

Exact calculations of average power for the Benjamini-Hochberg procedure

Exact analytic expressions are developed for the average power of the Benjamini and Hochberg false discovery control procedure. The result is based on explicit computation of the joint probability distribution of the total number of rejections and the number of false rejections, and expressed in terms of the cumulative distribution functions of the p-values of the hypotheses. An example of analytic evaluation of the average power is given. The result is confirmed by numerical experiments and applied to a meta-analysis of three clinical studies in mammography.

Probabilities for separating sets of order statistics

Consider a set of order statistics that arise from sorting samples from two different populations, each with their own, possibly different distribution functions. The probability that these order statistics fall in disjoint, ordered intervals and that of the smallest statistics, a certain number come from the first populations is given in terms of the two distribution functions. The result is applied to computing the joint probability of the number of rejections and the number of false rejections for the Benjamini-Hochberg false discovery rate procedure.

Fast Computation by Block Permanents of Cumulative Distribution Functions of Order Statistics from Several Populations

The joint cumulative distribution function for order statistics arising from several different populations is given in terms of the distribution functions of the populations. The computational cost of our formula in the case of two populations is still exponential in the worst case, but it is a dramatic improvement compared to the general formula by Bapat and Beg. In the case when only the joint distribution function of a subset of the order statistics of fixed size is needed, the complexity is polynomial, for the case of two populations.