Inverse Probability of Censoring Weighted Estimates of Kendall's τ for Gap Time Analyses

Summary In life history studies, interest often lies in the analysis of the interevent, or gap times and the association between event times. Gap time analyses are challenging however, even when the length of follow‐up is determined independently of the event process, because associations between gap times induce dependent censoring for second and subsequent gap times. This article discusses nonparametric estimation of the association between consecutive gap times based on Kendall's τ in the presence of this type of dependent censoring. A nonparametric estimator that uses inverse probability of censoring weights is provided. Estimates of conditional gap time distributions can be obtained following specification of a particular copula function. Simulation studies show the estimator performs well and compares favorably with an alternative estimator. Generalizations to a piecewise constant Clayton copula are given. Several simulation studies and illustrations with real data sets are also provided.     

Monogamy and polygamy in two species of mirid bugs: a functional-based approach

Multiple mating in females is widespread among insects in spite of the risk of predation, disease acquisition and/or physical injury that may occur. One common consequence of female polyandry is competition among sperm from two or more males within the female to fertilize the ova. This competition is an evolutionary driving force that determines a series of adaptations in both males and females. In this work, we examine some behavioral, morphological and physiological characteristics of males and females of two Heteropteran species that are related to their monoandrous/polyandrous mating behavior. Females of Macrolophus pygmaeus (Het. Miridae), the monoandrous species, were coy about accepting a male partner, spent a short time in copula, and received only a small volume of ejaculate. Even so, with only one mating event, they received enough sperm to fertilize most of their ova (21 days after mating all females were still fertile). In contrast, females of Nesidiocoris tenuis (Het. Miridae), the polyandrous species, readily accepted any mating partner, spent a long time in copula and received a large volume of ejaculate. However, these latter females soon ran out of sperm and needed to mate periodically in order to maintain a sufficient sperm supply to fertilize their eggs. As predicted, based on current theory (Simmons, 2001b), an increased investment in spermatogenesis was detected in N. tenuis with relation to M. pygmaeus. The males of the polyandrous species had larger accessory reproductive glands, seminal vesicles, testes and sperm cells than those of the monoandrous species.     

Seminal fluids mediate sexual inhibition and short copula duration in mated female Queensland fruit flies

Molecules in male seminal fluid transferred to female insects during mating can have potent effects on their subsequent sexual and reproductive behaviour. Like many other tephritids, female Queensland fruit flies (Bactrocera tryoni) typically have diminished sexual receptivity after their first mating. Also, copulations of females that do remate tend to be shorter than those of virgins. We here find that virgin females injected with small doses (0.1, 0.2 or 0.5 male equivalents) of extracts from the male reproductive tract accessory tissues, which consist of male accessory glands, ejaculatory apodeme and ejaculatory duct (AG/EA/ED), have diminished receptivity and short copula duration very similar to naturally mated females. In contrast, virgin females injected with saline or with high doses of AG/EA/ED (1 or 2 male equivalents) that likely exceed the range of natural variation retain the higher levels of sexual receptivity and longer copulations of un-injected virgins. We conclude that reduced sexual receptivity and shorter copulations of mated female Q-flies are mediated by products in the male seminal fluid derived from the male reproductive tract accessory tissues.     

Semiparametric inference for surrogate endpoints with bivariate censored data

Summary .   Considerable attention has been recently paid to the use of surrogate endpoints in clinical research. We deal with the situation where the two endpoints are both right censored. While proportional hazards analyses are typically used for this setting, their use leads to several complications. In this article, we propose the use of the accelerated failure time model for analysis of surrogate endpoints. Based on the model, we then describe estimation and inference procedures for several measures of surrogacy. A complication is that potentially both the independent and dependent variable are subject to censoring. We adapt the Theil–Sen estimator to this problem, develop the associated asymptotic results, and propose a novel resampling-based technique for calculating the variances of the proposed estimators. The finite-sample properties of the estimation methodology are assessed using simulation studies, and the proposed procedures are applied to data from an acute myelogenous leukemia clinical trial.     

Evolution of ejaculates: patterns of phenotypic and genotypic variation and condition dependence in sperm competition traits

Sperm competition is widely recognized as a potent force in evolution, influencing male behavior, morphology, and physiology. Recent game theory analyses have examined how sperm competition can influence the evolution of ejaculate expenditure by males and the morphology of sperm contained within ejaculates. Theoretical analyses rest on the assumption that there is sufficient genetic variance in traits important in sperm competition to allow evolving populations to move to the evolutionarily stable equilibrium. Moreover, patterns of genotypic variation can provide valuable insight into the nature of selection currently acting on traits. However, our knowledge of genetic variance underlying traits important in sperm competition is limited. Here we examine patterns of phenotypic and genotypic variation in four sperm competition traits in the dung beetle Onthophagus taurus. Testis weight, ejaculate volume, and copula duration were found to have high coefficients of additive genetic variation (CV(A)S), which is characteristic of fitness traits and traits subject to sexual selection. Heritabilities were high, and there was some evidence for Y-linked inheritance in testis weight. In contrast, sperm length had a low CV(A), which is characteristic of traits subject to stabilizing selection. Nevertheless, there was little residual variance so that the heritability of sperm length exceeded 1.0. Such a pattern is consistent with Y-linked inheritance in sperm length. Interestingly, we found that testis weight and sperm length were genetically correlated with heritable male condition. This finding holds important implications for potential indirect benefits associated with the evolution of polyandry.     

Composite likelihood and two-stage estimation in family studies

In this paper register based family studies provide the motivation for linking a two-stage estimation procedure in copula models for multivariate failure time data with a composite likelihood approach. The asymptotic properties of the estimators in both parametric and semi-parametric models are derived, combining the approaches of Parner (2001) and Andersen (2003). The method is mainly studied when the families consist of groups of exchangeable members (e.g. siblings) or members at different levels (e.g. parents and children). The advantages of the proposed method are especially clear in this last case where very flexible modelling is possible. The suggested method is also studied in simulations and found to be efficient compared to maximum likelihood. Finally, the suggested method is applied to a family study of deep venous thromboembolism where it is seen that the association between ages at onset is larger for siblings than for parents or for parents and siblings.     

A copula-based approach for creating an index of micronutrient intakes at household level in Pakistan

Deficiency of micronutrients is considered as the basic cause of health issues. There are a large number of micronutrients to be considered for good health, which are analyzed separately. However, such analyses involve practical as well as methodological complications and it requires construction of an index representing malnutrition of micronutrients. This study proposes copula methodology to categorize malnutrition of micronutrients at household level by combining the dependence structure of various correlated variables. Data of eleven micronutrients are extracted from HIICS- 2015–16 published by Pakistan -Bureau of Statistics. Seven out of the eleven variables are highly correlated, which are considered to construct the index. These include calcium, iron, iodine, zinc, riboflavin, thiamine and phosphorus intakes per capita at household level. Normal probability distribution is found as the best fit to the sample data of all variables. Gaussian copula function is used to derive multivariate probability distribution by combining univariate marginal probability distribution of each micronutrient. The Multivariate distribution of Gaussian copula model is used to calculate cumulative probabilities, which provide a base to categorize households’ malnutrition w.r.t. micronutrients. The results show that 60% households lie in very low or low category of micronutrient intakes, 20% of households fall into medium category while 20% fall into high or very high category of micronutrient consumption. The proposed methodology might be helpful to combine other micronutrients as well as a variety of correlated variables in many other fields having a survey data     

Disparity in sexual behaviour between wild and mass‐reared Mexican fruit flies

The sterile insect technique (SIT) is currently used to control Mexican fruit fly Anastrepha ludens Loew (Diptera: Tephritidae). However, mass‐rearing can alter the quality of released males. If males that are mass‐reared have behaviours different from those of their wild counterparts, then this may diminish the effectiveness of SIT. Questions remain as to whether wild females may be able to detect the male condition before, during and/or after copulation with a mass‐reared male. In the present study, copula duration, female remating, female fecundity and fertility of both mass‐reared and wild A. ludens are evaluated. Marked differences are found between mass‐reared and wild females. Specifically, mating latency is longer and copula duration is shorter for wild females compared with mass‐reared females. Importantly, there are no significant differences in mating latency, copula duration or remating probability between wild females paired with either mass‐reared or wild males. All mass‐reared females remate, whereas only approximately half of the wild females remate after first mating with either a wild or mass‐reared male. Fecundity of wild females mated to either wild or mass‐reared males is approximately one‐third lower than that of mass‐reared females, confirming that mass‐reared females may have been selected for high fecundity and are adapted to laboratory conditions. Fertility of females that mate with a wild male for only 10 min is not significantly different from that achieved via a full‐length copulation. By contrast, females mating with mass‐reared males need copulation durations of at least 40 min to achieve fertility comparable with that achieved via a full‐length copulation. The findings of the present study have important implications for A. ludens controlled through SIT and broaden our understanding on the copulatory and post‐copulatory behaviours between wild females and mass‐reared males.