Analysis of survival data from case-control family studies

In case-control family studies with survival endpoint, age of onset of diseases can be used to assess the familial aggregation of the disease and the relationship between the disease and genetic or environmental risk factors. Because of the retrospective nature of the case--control study, methods for analyzing prospectively collected correlated failure time data do not apply directly. In this article, we propose a semiparametric quasi-partial-likelihood approach to simultaneously estimate the effect of covariates on the age of onset and the association of ages of onset among family members that does not require specification of the baseline marginal distribution. We conducted a simulation study to evaluate the performance of the proposed approach and compare it with the existing semiparametric ones. Simulation results demonstrate that the proposed approach has better performance in terms of consistency and efficiency. We illustrate the methodology using a subset of data from the Washington Ashkenazi Study.     

Flexible maximum likelihood methods for bivariate proportional hazards models

This article presents methodology for multivariate proportional hazards (PH) regression models. The methods employ flexible piecewise constant or spline specifications for baseline hazard functions in either marginal or conditional PH models, along with assumptions about the association among lifetimes. Because the models are parametric, ordinary maximum likelihood can be applied; it is able to deal easily with such data features as interval censoring or sequentially observed lifetimes, unlike existing semiparametric methods. A bivariate Clayton model (1978, Biometrika 65, 141-151) is used to illustrate the approach taken. Because a parametric assumption about association is made, efficiency and robustness comparisons are made between estimation based on the bivariate Clayton model and "working independence" methods that specify only marginal distributions for each lifetime variable.     

Miscellanea Kernel-Type Density Estimation on the Unit Interval

We consider kernel-type methods for the estimation of a densityon 0,1 which eschew explicit boundary correction. We proposeusing kernels that are symmetric in their two arguments; thesekernels are conditional densities of bivariate copulas. We giveasymptotic theory for the version of the new estimator usingGaussian copula kernels and report on simulation comparisonsof it with the beta-kernel density estimator of Chen ([1]).We also provide automatic bandwidth selection in the form of‘rule-of-thumb’ bandwidths for both estimators.As well as its competitive integrated squared error performance,advantages of the new approach include its greater range ofpossible values at 0 and 1, the fact that it is a bona fidedensity and that the individual kernels and resulting estimatorare comprehensible in terms of a single simple picture.     

A copula approach for detecting prognostic genes associated with survival outcome in microarray studies

A challenging and crucial issue in clinical studies in cancer involving gene microarray experiments is the discovery, among a large number of genes, of a relatively small panel of genes whose elements are associated with a relevant clinical outcome variable such as time-to-death or time-to-recurrence of disease. A semiparametric approach, using dependence functions known as copulas, is considered to quantify and estimate the pairwise association between the outcome and each gene expression. These time-to-event type endpoints are typically subject to censoring as not all events are realized at the time of the analysis. Furthermore, given that the total number of genes is typically large, it is imperative to control a relevant error rate in any gene discovery procedure. The proposed method addresses the two aforementioned issues by direct incorporation of the censoring mechanism and by appropriate statistical adjustment for multiplicity. The performance of the proposed method is studied through simulation and illustrated with an application using a case study in lung cancer.     

Reproductive behavior and morphology of Paraleptophlebia spinosa (Ephemeroptera: Leptophlebiidae): implications of variation in copula duration

The reproductive behavior and genital morphology of a leptophlebiid mayfly Paraleptophlebia spinosa Ueno were studied in a population inhabiting a mountain stream in Kyoto, central Japan. Males formed swarms along gravel shores, caught females in the air, and mated on the ground. The distribution of the oviposition sites coincided with that of the swarming sites along the stream shore. The lobes of the male penis were characterized by a shallow pocket opening on the ventral side. The female vestibule formed a square-shaped chamber into which eggs were released from the oviducts. The number of eggs carried by females caught during copulation in the field showed a greater variation than the number of eggs of virgin females. Copula duration was strongly correlated with the number of eggs carried by the female. Significantly short copula duration with spent females (egg loading less than 20% of the estimated fecundity) may indicate that males could identify spent females. Copula duration with partially loaded females (egg loading between 20% and 80% of fecundity), however, was not shorter than that with fully loaded females. Male mating tactics with respect to copula duration and the possibility of kinematic sperm displacement are discussed with reference to the behavioral and morphological characteristics of the species. Received: September 3, 1999 / Accepted: December 9, 1999