On assessing surrogacy in a single trial setting using a semicompeting risks paradigm

Summary .  There has been a recent emphasis on the identification of biomarkers and other biologic measures that may be potentially used as surrogate endpoints in clinical trials. We focus on the setting of data from a single clinical trial. In this article, we consider a framework in which the surrogate must occur before the true endpoint. This suggests viewing the surrogate and true endpoints as semicompeting risks data; this approach is new to the literature on surrogate endpoints and leads to an asymmetrical treatment of the surrogate and true endpoints. However, such a data structure also conceptually complicates many of the previously considered measures of surrogacy in the literature. We propose novel estimation and inferential procedures for the relative effect and adjusted association quantities proposed by Buyse and Molenberghs (1998, Biometrics 54, 1014–1029). The proposed methodology is illustrated with application to simulated data, as well as to data from a leukemia study.     

Modelling pairwise dependence of maxima in space

We model pairwise dependence of temporal maxima, such as annualmaxima of precipitation, that have been recorded in space, eitheron a regular grid or at irregularly spaced locations. The constructionof our estimators stems from the variogram concept. The asymptoticproperties of our pairwise dependence estimators are establishedthrough properties of empirical processes. The performance ofour approach is illustrated by simulations and by the treatmentof a real dataset. In addition to bringing new results aboutthe asymptotic behaviour of copula estimators, the latter beinglinked to first-order variograms, one main advantage of ourapproach is to propose a simple connection between extreme valuetheory and geostatistics.     

A class of goodness of fit tests for a copula based on bivariate right-censored data

The copula of a bivariate distribution, constructed by making marginal transformations of each component, captures all the information in the bivariate distribution about the dependence between two variables. For frailty models for bivariate data the choice of a family of distributions for the random frailty corresponds to the choice of a parametric family for the copula. A class of tests of the hypothesis that the copula is in a given parametric family, with unspecified association parameter, based on bivariate right censored data is proposed. These tests are based on first making marginal Kaplan-Meier transformations of the data and then comparing a non-parametric estimate of the copula to an estimate based on the assumed family of models. A number of options are available for choosing the scale and the distance measure for this comparison. Significance levels of the test are found by a modified bootstrap procedure. The procedure is used to check the appropriateness of a gamma or a positive stable frailty model in a set of survival data on Danish twins.     

Control of copula duration and sperm storage by female Queensland fruit flies

Copula duration and sperm storage patterns can directly or indirectly affect fitness of male and female insects. Although both sexes have an interest in the outcome, research has tended to focus on males. To investigate female influences, we compared copula duration and sperm storage of Queensland fruit fly females that were intact, or had been incapacitated through decapitation or abdomen isolation. We found that copulations were far longer when females had been incapacitated, indicating that constraints imposed on copula duration by intact females had been relaxed. Repeatability of copula duration for males was very low regardless of female treatment, and this is also consistent with strong female influence. Number of sperm in the spermathecae was not influenced by female treatment, suggesting that female abdominal ganglia control the transport of sperm to these long-term storage organs. However, more sperm were found in the ventral receptacles of incapacitated females compared to intact females. Overall, results implicate cephalic ganglia in regulation of copula duration and short-term sperm storage in the ventral receptacle and abdominal ganglia in regulation of long-term sperm storage in the spermathecae.     

Regression survival analysis with an assumed copula for dependent censoring: a sensitivity analysis approach

SUMMARY: In clinical studies, when censoring is caused by competing risks or patient withdrawal, there is always a concern about the validity of treatment effect estimates that are obtained under the assumption of independent censoring. Because dependent censoring is nonidentifiable without additional information, the best we can do is a sensitivity analysis to assess the changes of parameter estimates under different assumptions about the association between failure and censoring. This analysis is especially useful when knowledge about such association is available through literature review or expert opinions. In a regression analysis setting, the consequences of falsely assuming independent censoring on parameter estimates are not clear. Neither the direction nor the magnitude of the potential bias can be easily predicted. We provide an approach to do sensitivity analysis for the widely used Cox proportional hazards models. The joint distribution of the failure and censoring times is assumed to be a function of their marginal distributions. This function is called a copula. Under this assumption, we propose an iteration algorithm to estimate the regression parameters and marginal survival functions. Simulation studies show that this algorithm works well. We apply the proposed sensitivity analysis approach to the data from an AIDS clinical trial in which 27% of the patients withdrew due to toxicity or at the request of the patient or investigator.     

Semiparametric analysis of survival data with left truncation and dependent right censoring

Studies of chronic life-threatening diseases often involve both mortality and morbidity. In observational studies, the data may also be subject to administrative left truncation and right censoring. Because mortality and morbidity may be correlated and mortality may censor morbidity, the Lynden-Bell estimator for left-truncated and right-censored data may be biased for estimating the marginal survival function of the non-terminal event. We propose a semiparametric estimator for this survival function based on a joint model for the two time-to-event variables, which utilizes the gamma frailty specification in the region of the observable data. First, we develop a novel estimator for the gamma frailty parameter under left truncation. Using this estimator, we then derive a closed-form estimator for the marginal distribution of the non-terminal event. The large sample properties of the estimators are established via asymptotic theory. The methodology performs well with moderate sample sizes, both in simulations and in an analysis of data from a diabetes registry.     

Ability of male Queensland fruit flies to inhibit receptivity in multiple mates, and the associated recovery of accessory glands

Mating success of male insects is commonly determined by their ability to find and copulate with multiple females, but is also determined by their ability to transfer an effective ejaculate. In order to succeed in these tasks, males must first succeed in replenishing the necessary reproductive reserves between mating opportunities. We here investigate the ability of male Queensland fruit flies ('Q-fly') to recover from their first matings in time to both mate again the following day and to induce sexual inhibition in successive mates. We have previously found that accessory gland fluids (AGFs) transferred in the ejaculate of male Q-flies are directly responsible for induction of sexual inhibition in their mates. We here investigate changes in male accessory gland, testis and ejaculatory apodeme dimensions that are likely to reflect depletion and recovery of contents. We found no differences between virgin and previously mated males in their ability to obtain matings or to induce sexual inhibition in their mates, indicating a full recovery of the necessary reproductive reserves between mating opportunities. Whereas no changes were detected in testis or ejaculatory apodeme size following mating, the recovery of male ability to inhibit female remating was closely reflected in the mesodermal accessory gland dimensions; these accessory glands greatly diminished in size (length and area) immediately after mating, with recovery commencing between 5.5 and 11 h after mating. The accessory glands then expanded to reach their original size in time to mate the following day and induce sexual inhibition in the next mate.     

A bivariate cure-mixture approach for modeling familial association in diseases

For modeling correlation in familial diseases with variable ages at onset, we propose a bivariate model that incorporates two types of pairwise association, one between the lifetime risk or the overall susceptibility of two individuals and one between the ages at onset between two susceptible individuals. For estimation, we consider a two-stage estimation procedure similar to that of Shih (1998, Biometrics 54, 1115-1128). We evaluate the properties of the estimators through simulations and compare the performance with that from a bivariate survival model that allows correlation between ages at onset only. We apply the methodology to breast cancer using the kinship data from the Washington Ashkenazi Study. We also discuss potential applications of the proposed method in the area of cure modeling.